HORSTEMEYER INTERNATIONAL SYMPOSIUM (7TH INTL. SYMP. ON MULTISCALE MATERIAL MECHANICS & SUSTAINABLE APPLICATIONS)
Editors: F. Kongoli,E. Aifantis, A, Konstantinidis, D, Bammann, J. Boumgardner, K, Johnson, N, Morgan, R. Prabhu, A. Rajendran

Tribology—the study of the interaction of sliding surfaces—has numerous applications, particularly in the design of biomedical devices. However, an important engineering challenge in contact mechanics and tribology is the evaluation and prediction of the transition from one contact mode to another. The principal difference in the contact interaction during friction is the dynamic loading with a variation in the roughness parameters, stress, strain, and wear particle formation. The complexity in the prediction of friction results from the gradient variation of the mechanical, physical, and chemical properties at the thin surface layers during contact interaction.
The objective of this work is to compare the elastic-plastic analytical models with the actual results of friction and wear researches. Since the friction phenomena are dominated by plastic deformation, the elastic models of contact interaction were not considered in this work. The parameters of the elastic-plastic models are compared with the recently published experimental results on the friction, wear, and structure of several face-centered cubic (fcc) metals in lubricated conditions. The main focus is on the boundary lubrication—friction and wear in more severe lubricant contact conditions. The following aspects of the elastic-plastic models will be considered: the contact area versus external load and yield stress, the deformation hardening, a statistical description of the contact geometry, the sinusoidal surface under contact loading, the plasticity index, and the multiscale modeling of materials. The parameters calculated in the analytical simulation are compared with the results of the experimental friction and wear tests. The non-dimensional parameters such as the normal load, yield stress, and the real area of contact calculated in the simulation were significantly greater than those in the friction tests. A balance between the external and internal parameters during contact interaction and friction is considered as: the balance between the contact pressure (loading external parameter) and the yield stress (internal structural parameter) in simulation, and a balance between the applied stress (loading) and the internal stress (internal deformed structure) in friction. The analysis of the elastic-plastic and wear models of contact interaction and damage development allows us to conclude that our knowledge and understanding of such complex phenomena as the mechano-chemical and defect interaction of the moving contact pairs could not be predicted in a short time.

In this paper, we examine multi-axial stress states using a coupled experimental and computational methodology for analyzing high strain rate phenomena of a 6061-T6 aluminum alloy. A variety of experiments and computations were performed to highlight the value of coupling experiments with simulations to gain insight into complex loading conditions. Tensile, torsion/shear, and compression results of a 6061-T6 aluminum alloy were obtained as a base material by a variety of established high strain rate testing methods. Three different Hopkinson/Kolsky pressure bar setups were used: a compression setup to analyze compression, tension, and shear; a tension setup to analyze tension; and a torsion setup to analyze torsion. The resulting methodology allows for experimental corroboration, and the simulations to probe some phenomena that is otherwise impossible to observe during an experiment, while simultaneously testing the validity of the model via direct comparison with measured strain gage histories. While caution must be exercised when using such methods, significant insight during complex loading or loading of complex structures can be acquired, especially those for which the equilibrium conditions necessary for traditional Hopkinson/Kolsky bar testing are impossible to obtain but the dynamic response is still essential.

We present a corrosion Internal State Variable (ISV) damage model based upon the Integrated Computational Materials Engineering (ICME) hierarchical multiscale paradigm. Structure-property experiments for magnesium alloys were used where the only inputs are the volume fractions of each element of the Periodic Table. This macroscale ISV corrosion model finds its basis in Horstemeyer’s mechanical damage model, which includes three separate ISVs for damage nucleation, growth, and coalescence and Walton’s inclusion of corrosion, which introduces five new ISVs for pit nucleation, growth, and coalescence, along with general corrosion and intergranular corrosion. While Walton’s corrosion ISVs were phenomenological in nature, we develop herein a multiscale physical basis for the corrosion ISVs. Parameters for the macroscale corrosion ISVs were garnered from the mesoscale Butler-Volmer equations. Pure magnesium with differing amounts of aluminum were used in corrosion tests to exemplify the different pitting, general corrosion, and intergranular corrosion rates, and the macroscale ISV model was calibrated with said data, in which the only inputs to the model are the volume percent of elements of magnesium and aluminum. Although magnesium alloys were used to motivate and calibrate the model, the model is abstract enough to possibly capture other material systems as well.

Uncertainty quantification (UQ) in metallic additive manufacturing (AM) has attracted tremendous interests in order to dramatically improve product reliability. Model-based UQ, which relies on the validity of a computational model, has been widely explored as a potential substitute for the time-consuming and expensive UQ solely based on experiments. However, its adoption in practical AM process requires the overcoming of two main challenges: (1) the inaccurate knowledge of uncertainty sources and (2) the intrinsic uncertainty associated with the computational model. Here we propose a novel data-driven framework to tackle these two challenges by combining high throughput physical simulations and limited experimental data. We first construct a machine learning (ML) model trained by high throughput physical simulations, for predicting the three-dimensional (3D) melt pool geometry and its uncertainty with respect to AM parameters and uncertainty sources. We then employ a novel sequential Bayesian calibration method to perform parameter calibration and model correction, by using experimental data from AM-Bench of National Institute of Standards and Technology (NIST). The application of the calibrated melt pool model to UQ of the porosity level, an important quality factor, of AM parts, demonstrates its potential use in AM quality control. The proposed UQ framework can be generally applicable to different AM processes, towards physics-based quality control of AM products.

We present a magneto-thermo-mechanical literature review of Rare-Earth free magnets, focusing on Mn-based binary alloys in relation to their Chemistry-Process-Structure-Property- Performance (CPSPP) relationships. Recent electric performance systems and technologies use Rare-Earth (RE) magnets due to the high magnetic power they provide; however, the limited resources of RE elements in the earth, has pushed the emerging need to identify and understand Mn-based magnetic alloys. Mn is abundant, fairly inexpensive, easily manufacturable, and eco- friendly. Although previous literature reviews included magnetic properties of different RE based and RE free magnets, none of the previous literature reviews related the magnetic properties to the mechanical properties nor did they relate the complete CPSPP relationship. Magnetic and mechanical properties interdependently affect each other with more complexity added under different temperature materials processing and performance environments. The thermomechanical deformation processes impact the multiscale hierarchical structures and the associated magnetic behavior at different size scales (electrons, subgrains, grains, and polycrystals). The magneto- thermo-mechanical properties of Mn-based alloys with a focus on MnAl, MnBi, and MnZn binary alloys and an associated CPSPP map are presented.

Plastic deformation and failure of structural integrity in materials are frequently accompanied by acoustic emission (AE). AE is a multi-scale phenomenon, defined as stress waves generated within the material due to (micro)structure changes (usually linked with structural defects dynamics), ranging from earthquakes and landslides to collective dislocation motion on micron scales. Recently, AE measurements performed on bulk as well as miniaturized samples (micropillars) revealed that the motion of dislocations resembles a stick-and-slip process, which may even develop in a series of unpredictable local strain bursts with a scale-free size distribution, e.g. in single crystals. Despite of fundamental differences in the mechanism as well as length and timescales, dislocation avalanches and earthquakes can be, from the point of view of AE, described in a similar way.
The talk will cover an introduction to the AE technique, followed by discussion of several applications, from fundamentals of defect dynamics to a couple of topics in geology and materials engineering.

Atomistic-based strain gradient elasticity theory, in the framework of finite deformations, is proposed.
As a fundamental quantity of this approach, an objective relative displacement between atomic-pairs is considered. Besides, a deformation energy of an atomic-pair is defined in terms of such a measure in the form of a Lennard-Jones type potential.
Thus, the objective relative displacement between atomic-pairs has been Taylor's series expanded up to second order in order to obtain the deformation energy of atomic-pairs in terms of (i) non-linear strain (the Green-Saint-Venant tensor), (ii) its gradient, (iii) the orientation of the atomic-pair and (iv) Lennard-Jones coefficients, including the inter-atomic distance.
The strain energy of the continuum is assumed to be the integral over the unit sphere of the previous Lennard-Jones potential and the isotropic case will be obtained by assuming the independence of the Lennard-Jones coefficients with respect to the inter-atomic orientation.

TeraHertz phonons are produced in solids and fluids by mechanical instabilities at the nano-scale (fracture and cavitation). They present a frequency that is close to the resonance frequency of the atomic lattices and an energy that is close to that of thermal neutrons. A series of fracture experiments on natural rocks and the systematic monitoring of seismic events have demonstrated that TeraHertz phonons are able to induce fission reactions on medium-weight elements (in particular, iron and calcium) with neutron and/or alpha particle emissions. The same phenomenon appears to have occurred in several different situations and to explain puzzles related to the history of our planet, like the primordial carbon pollution (and correlated iron depletion) or the ocean formation (and correlated calcium depletion), as well as scientific mysteries, like the so-called cold fusion or the correct radio-carbon dating of organic materials. Very important applications to earthquake precursors, climate change, and energy production are likely to develop in the next future.
Three different forms of energy might be used as earthquake precursors. At the tectonic scale, Acoustic Emission (AE) prevails, as well as Electro-Magnetic Emission (EME) at the meso-scale, and Neutron Emission (NE) at the nano-scale. The three fracto-emissions tend to anticipate the next seismic event with an evident and chronologically ordered shifting: high frequencies and neutron emission about one week before, then lower frequencies and electromagnetic and acoustic waves. The experimental observations reveal a strong correlation between the three fracto-emission peaks and the major earthquakes occurring in the closest areas.
Regarding cold fusion, despite the great amount of experimental results, the comprehension of these phenomena still remains unsatisfactory. On the other hand, as reported by most of the articles devoted to cold fusion, one of the principal features is the appearance of micro-cracks on the electrode surfaces after the experiments. A mechanical explanation is proposed as a consequence of hydrogen embrittlement of the electrodes during electrolysis. The preliminary experimental activity was conducted using a Ni-Fe anode and a Co-Cr cathode immersed in a potassium carbonate solution. Emissions of neutrons and alpha particles were measured during the experiments as well as evident chemical composition changes of the electrodes revealing the effects of fission reactions occurring in the host lattices. The symmetrical fission of Ni appears to be a clear evidence. Such reaction would produce two Si atoms or two Mg atoms with alpha particles and neutrons as additional fragments. In order to confirm the preliminary investigation, further electrolytic tests have been conducted using Pd and Ni electrodes. As for the early experiments, relevant compositional changes and the appearance of ligther elements previously absent have been observed. The most relevant process emerging from the experiments is the primary fission of palladium (decrement of 30%) into iron and calcium. Then, secondary fissions appear in turn producing oxygen atoms, alpha particles, and neutrons. The chemical composition changes were confirmed by four repetitions of the same experiment. An extensive evaluation of the heat generation has been carried out showing a positive energy balance in correspondence to the major neutron emission peaks.

The creep of minerals in Earth’s interior controls a wide variety of large-scale, geodynamic processes. A dominant focus of previous studies has been the steady-state flow of Earth’s upper over long time scales. However, there are a variety of geological processes that involve creep but occur on much shorter timescales, including the rebound of Earth’s surface after melting of ice sheets and the reloading of stresses on seismogenic faults after major earthquakes. Early work rooted in the materials sciences emphasized the likelihood that these short-time-scale processes are dominated by transient creep rather than steady-state behavior [1]. However, relatively little work has subsequently been completed to provide the constitutive laws necessary to incorporate transient processes into large-scale geodynamic simulations. Some experiments have been conducted [2, 3], and theoretical frameworks proposed [4], but the available data do not allow complete calibration of existing models or sufficiently reveal the microphysical processes controlling transient creep.
Here we present several data sets that elucidate the mechanisms that control transient creep in olivine, the dominant mineral in Earth’s upper mantle. These data sets consist of uniaxial stress-reduction experiments at temperatures >1200°C, cyclical loading experiments at room temperature, nanoindentation load-reduction experiments at room temperature, and microstructural characterization with high-resolution electron backscatter diffraction. Mechanical experiments reveal evidence for anelasticty at all investigated temperatures and a pronounced Bauschinger effect at low temperatures. Microstructural observations reveal significant stress heterogeneity associated with geometrically necessary dislocations.
Taken together, these data suggest that transient creep in olivine is associated with the buildup and evolution of backstresses associated with the dislocation population. We developed a set of constitutive laws based on dislocation density and the evolution of backstresses that are able to explain the yield stress, the magnitude of anelastic strain recovery in stress reductions, the magnitude of the Bauchinger effect, and the characteristic timescales of transient creep in olivine, providing a level of insight into the microphysics of transient creep not yet available for minerals.

An FEM and a novel hybrid FEM and Peridynamic modelling approach are used to predict the forerunning fracture behavior in dry and saturated porous solids. Both mechanical loading case and fluid-driven fracture case are investigated. Under the action of the applied forces or fluid injection, a forerunning fracture event is observed in the structure. It will be shown that i) in dry bodies, the forerunning increases the overall fracturing speed and is, in fact, a mechanism for a crack to move faster when a steady-state propagation is no longer supported by the body/structure due to a high level of external forces; ii) in presence of the forerunning, interaction with the waves in the fluid phase increases the average speed even further comparing to the movement in the same dry bodies; iii) the forerunning is an undeniable source of stepwise crack tip advancement of the main crack in continuum models; and iv) the forerunning phenomenon deserves further scrutiny because of its importance in geophysics as far as earthquake events are concerned.

Additive manufacturing is generally associated with powder-based beam melting or sintering methods. However, recent innovations in solid-state additive methods such as additive friction stir deposition (AFS-D) provide unique capabilities to additively manufacture or repair alloys with wrought like properties. The AFS-D process is a novel method that exploits high-shear and severe plastic deformation to produce fully-dense, near net-shape structures. In the AFS-D process, feedstock material is deposited through a hollow rotating tool that generates frictional heat which results in solid-state metallurgical bonding. While the feasibility of the AFS-Deposition process has been demonstrated on various materials, the fatigue performance of this new manufacturing process for difficult to weld alloys is unknown. As such, in this talk, we present an investigation of the fatigue mechanisms of 6xxx and 7xxx aluminum alloys fabricated from the AFS-D process. In particular, fatigue crack nucleation and crack propagation mechanisms associated with the longitudinal and build directions of the AFS-D process are discussed. In addition, the effect of heat treatment on fatigue behavior is also presented. Lastly, we discuss the potential of the AFS-D process in repair applications and barriers to further implementation.

Hierarchical materials consist of microstructural elements which have themselves internal structure, forming a self-similar pattern on multiple scales [1]. Such materials are ubiquitous in biological materials [2] such as collagen [3], bone [4], and wood [2]. We analyse the process of damage accumulation and global failure in hierarchically patterned materials, and compare them with non-hierarchical reference patterns.
The nucleation and propagation of crack in uniaxially loaded materials with statistically distributed local failure thresholds is studied using a beam lattice model [1, 5].
We show that hierarchical material failure is characterized by diffuse local damage nucleation that eventually spreads throughout the network. Nonhierarchical materials, on the other hand, fail in a sequence of damage nucleation, crack formation, and stress-driven crack propagation.

A proposal is advanced for enhancing classical quantum mechanical and empirical potentials with a Laplacian term incorporating nonlocal effects. It is shown that this results in a “repulsive” branch, in addition to its classical “attractive” branch derived by rigorous quantum mechanical considerations. By properly choosing the gradient coefficient (or internal length) multiplying the Laplacian term, it is shown that the gradient-enhanced London potential recovers the structure of the empirical Lennard-Jones potential, and the same holds for the Stillinger-Weber potential. In the sequel, an attempt is made to address the role of such gradient enhancement for the case of Baskes embedded atom method (EAM) to determine whether or not the Laplacian term can account for non pairwise interactions and angular/orientation effects. Finally, the role of bi-Laplacian and fractional/fractal effects is briefly discussed.

A proposal is advanced for enhancing classical quantum mechanical and empirical potentials with a Laplacian term incorporating nonlocal effects. It is shown that this results to a “repulsive” branch, in addition to its classical “attractive” branch derived by rigorous quantum mechanical considerations. By properly choosing the gradient coefficient (or internal length) multiplying the Laplacian term, it is shown that the gradient-enhanced London potential recovers the structure of the empirical Lennard-Jones potential, and the same holds for the Stillinger-Weber potential. In the sequel, an attempt is made to address the role of such gradient enhancement for the case of Baskes embedded atom method (EAM) to determine whether or not the Laplacian term can account for non pair-wise interactions and angular/orientation effects. Finally, the role of bi-Laplacian and fractional/fractal effects is briefly discussed.

Parametric accelerated life testing (ALT) with the reliability quantitative (RQ) statements is offered as a reliability methodology to identify and rectify design flaws. The methodology includes: (1) BX lifetime with ALT scheme, (2) fatigue design, (3) ALTs with alterations, and (4) discernment whether the design(s) obtains targeted BX life. A quantum/transport-based life-stress prototype and sample size for generating RQ specifications were suggested. The equivalent elevated damage potential in parametric ALT was applied, represented by a field power spectral density (PSD). A case study was used to evaluate refrigerator fatigue failures that occurred during rail transport. In the 1st ALT, for RQ specifications, the refrigerator tubes made of ethylene propylene diene monomer (EPDM) rubber fractured because of the compressor mount design. The failure in the 1st ALT was similar to those found from failed refrigerators in the field. After the compressor mounts and tubes were redesigned, there were no difficulties during the 2nd ALT. The refrigerator was then assured to fulfil a B1 lifetime for required travel distance.

Pyramidal dislocations are important dislocations that are able to accommodate the c-axis strain when a single crystal magnesium is compressed along its c-axis. Generally, pyramidal dislocations require higher stresses to activate than basal and prismatic slip systems. But the nature of these dislocations, which have very large Burgers vectors (0.612 nm), has been controversial in terms of slip plane, dislocation dissociation, and dislocation mobility. In this work, we present in-situ TEM observation of pyramidal dislocations in submicron single crystal magnesium during c-axis compression. High density pyramidal dislocations were observed, which generated a large plastic strain, in stark contrast to bulk samples. Computational tomography was conducted to analyze the slip plane of the pyramidal dislocations. The results show that both pyramidal-I and pyramidal-II dislocations were activated. Atomistic simulations were also performed and the simulation results were consistent with the in-situ TEM observations.

Integrated Computational Materials Engineering (ICME) as reflected by hierarchical multiscale modeling along with modeling the Process-Structure-Property-Performance (PSPP) sequence will be discussed with several applications demonstrating the methodologies. The modeling methodologies will be shown to address a broad range of engineering problems. To predict the performance of a structural component, an analyst needs to consider the microstructure-property relationship to capture material history effects in the constitutive relations when performing the simulations. An effective method to capture the microstructure-property relationship is by use of internal state variable evolution equations, which reflect lower spatial size scale microstructural rearrangements so that history effects can be modeled. This methodology has now been applied to the geophysics of the earth. In engineering practice, once something is made, it is done. However, in the earth, the processing is continuous thus complicating the PSPP sequence. Finally, the past, present, and future will be discussed in the aforementioned context where the future is focused

Predicting location-specific microstructure and properties of industrial castings is a critical part of the Integrated Computational Materials Engineering (ICME) framework for lightweight casting design and manufacturing. This talk will present an overview on several models/methods developed at The Ohio State University (in collaboration with industrial partners) for the ICME framework. The talk will include a) three-dimensional grain structure model coupling process modeling and cellular automaton techniques [1]; b) microporosity model including both gas (hydrogen) and shrinkage effects [2, 3]; c) oxide-related defect prediction based on a new Oxide Entrainment Number (OEN) model [4]; and d) a new design methodology [5] linking location-specific microstructure (including defects) to location-specific mechanical properties of an aluminum casting. The modeling results on a simple wedge casting of a ternary aluminum alloy have been validated by X-ray Micro Computed Tomography experiments and mechanical testing. This new ICME framework proves to be a critical tool for efficient and effective casting design based on location-specific properties.

References:
1. C. Gu, Y. Lu, E. Cinkilic, J. Miao, A.D. Klarner, X. Yan, A.A. Luo, “Predicting grain structure in high pressure die casting of aluminum alloys: A coupled cellular automaton and process model”, Computational Materials Science, 2019, 161, 64-75.
2. C. Gu, Y. Lu, C.D. Ridgeway, E. Cinkilic, J. Miao, A.A. Luo, “Three-dimensional cellular automaton simulation of coupled hydrogen porosity and microstructure during solidification of ternary aluminum alloys”, Scientific Reports, 2019, 9, (1), 1-12, https://doi.org/10.1038/s41598-019-49531-0.
3. C. Gu, C.D. Ridgeway, E. Cinkilic, Y. Lu, A.A. Luo, “Predicting Gas and Shrinkage Porosity in Solidification Microstructure: A coupled Three-dimensional Cellular Automaton Model”, Journal of Materials Science and Technology, 2020, 49, 91-105, https://doi.org/10.1016/j.jmst.2020.02.028.
4. C.D. Ridgeway, K. Ripplinger, D. Detwiler, M. A.A Luo, “A New Model for Predicting Oxide-related Defects in Aluminum Castings”, Metallurgical and Materials Transactions B, 2020, in press.
5. C.D. Ridgeway, C. Gu, K. Ripplinger, D. Detwiler, M. Ji, S. Sohgrati, A.A Luo, “Prediction of location specific mechanical properties of aluminum casting using a new CA-FEA (cellular automaton-finite element analysis) approach”, Materials and Design, 2020, 108929, https://doi.org/10.1016/j.matdes.2020.108929.

We add damage, recrystallization, and texture treatments to the Bammann inelasticity internal state variable (BIISV) model framework to significantly improve the representation of the deformation-related processes in the earth’s mantle. We implement these additional features into the existing BIISV model in TERRA2D and show that all three physical mechanisms exert considerable influence on the flow history in simple 2D internally heated convection test cases. Using the enhanced BIISV framework we perform a limited parametric study to explore the model’s effects on stability of the cold upper thermal boundary layer. As expected the damage and recrystallization treatments enhance the cold upper thermal boundary layer’s tendency to weaken and plunge into the hotter region below. The texture treatment increases the intensity of rotational flow within the hotter zone as cold boundary material plunges downward which in turn aids in destabilizing the cold upper thermal boundary layer. Having all these treatments in a single integrated rheological framework that tracks internal history variables in a common manner represents a significant advance in handling deformational physics for mantle phenomena in a comprehensive, unified, and automatic manner.

Computational modeling of the damage response of a heterogeneous and anisotropic glass-reinforced plastics (GRP) under shock and impact is complex. Tsai et al [1] employed a plate impact test configuration to study shock wave propagation in a S-2 glass fiber – polyester matrix composite. They observed “Hugoniot Elastic Limit (HEL)” like points in the VISAR (“free surface velocity profiles”) data. The interpretations of experimentally observed HEL and nonlinearity in the data for two different GRP thicknesses at a range of impact velocities require further investigation remained speculative and inconclusive.
Recently, Scott et al., [2] performed computational modeling of the plate impact tests with continuum damage mechanics based hyperelastic constitutive equations in ALE 3D finite element code [3]. The parameters for strain-based damage initiation and propagation models to describe: matrix shear cracking and volume expansion under compressive loading conditions, delamination, and fiber breaking in tension and shear were calibrated through comparisons between the VISAR data and computed free surface velocity profiles. Based on the simulation results, Scott et al., suggested that the HEL point is due to elastic-elastic cracking (EEC) of the matrix materials under compressive loading. In simulations, the damage (microcracking of the matrix) emanates from the impact plane and progressively damage the GRP target plate in the plate impact experiments.
Fraser [4] implemented the hyperelasticity damage model in a commercial finite element code, Abequs [5] to study the response of GRP to projectile penetration. This work further examines the possibility of extending the CDM / hyperelasticity model to predict depth of penetration of a projectile into thick target plates at high velocities. In addition, the focus of the work is to validate the generality of the calibrated model parameters through comparison between the depth of penetration measured in ballistic tests and abequs simulations.

We introduce a computational framework for performing numerical experiments in weak gravity dynamics under the conditions of non-flat inherent geometry of space. It
is a generalization of the Particle Mesh method for the case of non-Euclidean geometry. As such, it includes a solver for the Poisson Equation and particle accelerations
for the general case of a non-flat three-dimensional space. The framework is useful for performing numerical experiments to investigate the Inherent Structure Hypothesis
explanation of the dark matter effect described in earlier work by Tenev and Horstemeyer (2019). It assumes weak gravity and nearly static gravitational fields,
which are valid assumptions for our common experience of gravity and are consistent with the conditions under which the Dark Matter effect has been observed. The
inputs to the framework are: 1) a displacement function into a transverse fourth dimensions used to specify the inherent curvature of space, 2) a fixed mass density
field, and 3) a collection of point particles that only interact through their contribution to the gravitational field. The framework was implemented in MATLAB R and was validated by using it to compute the Sun’s gravitational field and comparing the result to the theoretical prediction.

Conflicts in different parts of the world and impacts among fast moving objects produce extreme loads of very high intensity but of short duration that severely damage structures. A goal of this work to design lightweight sandwich structures that successfully protect the object to which they are strongly bonded. Realizing that design by experimentally testing several prototypes is very expensive, we use the finite element method to first ensure that the mathematical model of the problem predicts results close to test findings. Subsequently, we couple it with an optimization algorithm to find the lay-up and the thickness of 8 core layers and the fiber-reinforced face sheets to simultaneously minimize the mass and maximize either the back face deflection or the force transmitted to the rigid body perfectly bonded to the rear face-sheet. It is found that in the core the mass density and the mechanical properties do not continuously vary through the thickness.

With the development of the electric-automobiles, magnetic materials are strongly emerging as major parts to improve the efficiency of the electric motor. In this respect, we strongly believe that soft & hard magnets can be bound to be the main field of powder metallurgy (P/M) technology because P/M magnets have unique selling points with three-dimensional flux properties. In this research, we propose a new prediction system in an injection-molded magnet. By developing the magnetic particle orientation model and magneto-rheological model, complicated flow behaviors of powder-polymer binder mixtures can be predicted during field-induced injection molding. The orientation prediction system in the injection-molded magnet can be made up of three factors; i) the magneto-rheological model for the macro phenomenon, ii) the magnetic particle orientation model for the micro phenomenon, iii) Simulation of the mold flow with the external magnetic field. Our approach opens the way to calculate the degree of alignment in the hard magnet and further design the anisotropic flux direction in the complex magnetic components.

The mechanical products such as automobile, airplane, and refrigerator [1] manage power to accomplish a task that involves forces and movement, which eventually produce mechanical advantages by adapting product mechanisms. A refrigerator consists of several different modules and parts – compressor, doors, cabinet, heat exchanger, shelves and drawers, etc. Its lifetime is determined by design faults. To avoid the mechanical system such as a compressor failure in the field [2], it must be designed to handle the operating conditions imposed by the consumers who purchase and use. Any faulty designs therefore should be identified and modified through statistical methodology [3] or reliability testing [4] before a product is launched. However, they requires huge computations but have no results because of not figuring out failure mechanics. That is, if there are faulty designs that cause an inadequacy of strength (or stiffness) when a product is subjected to repetitive loads, the product will collapse before its expected lifetime due to fatigue failure. Based on failure mechanism and design, new reliability methodology – parametric Accelerated Life Testing (ALT) – suggests to assess the design of mechanical systems subjected to repetitive stresses. It includes: (1) a parametric ALT plan based on product BX lifetime, (2) a load analysis for accelerated life time test, (3) a tailored sample of parametric ALTs with the design modifications, and (4) an evaluation of whether the final design(s) of the product achieves the target BX lifetime. So we suggest a generalized life-stress failure model with a new effort concept, accelerated factor, and sample size equation with the acceleration factor. This new parametric ALT should help an engineer uncover the design parameters of the mechanical system affecting reliability during the design process. As the improper design parameters are experimentally identified, the mechanical system should improve in reliability as measured by the increase in lifetime, and the reduction in failure rate. Consequently, companies can avoid recalls due to the product failures in the field.

The present paper deals with the opposite natural trends in composite systems: catastrophe and chaos arising from simple nonlinear rules, as well as order and structure emerging from heterogeneity and randomness.
Part I deals with Nonlinear Fracture Mechanics models (in particular, the Cohesive Crack Model to describe strain localization both in tension and in compression) and their peculiar consequences: fold catastrophes (post-peak strain-softening and snap-through instabilities) or cusp catastrophes (snap-back instabilities) in plain or reinforced structural elements. How can a relatively simple nonlinear constitutive law, which is scale-independent, generate a size-scale dependent ductile-to-brittle transition? Constant reference is made to Dimensional Analysis and to the definition of suitable nondimensional brittleness numbers that govern the transition. These numbers can be defined in different ways, according to the selected theoretical model. The simplest way is that of directly comparing critical LEFM conditions and plastic limit analysis results. This is an equivalent way --although more effective for finite-sized cracked plates-- to describe the ductile-to-brittle size-scale transition, if compared to the traditional evaluation of the crack tip plastic-zone extension in an infinite plate. In extremely brittle cases, the plastic zone or process zone tends to disappear and the cusp catastrophe conditions prevail over the strain-softening ones and tend to coincide with the LEFM critical conditions in the case of initially cracked plates.
Part II deals with the occurrence of self-similar and fractal patterns in the deformation, damage, fracture, and fragmentation of heterogeneous disordered materials, and with the consequent apparent scaling in the nominal mechanical properties of the same materials. Such a scaling is negative (lacunar fractality) for tensile strength and fatigue limit, whereas it is positive (invasive fractality) for fracture energy, fracture toughness, and fatigue threshold. At the same time, corresponding fractal (or renormalized) quantities emerge, which are the true scale-invariant properties of the material. They appear to be the constant factor (the universal property) in the power-law relating the nominal canonical quantity to the size-scale of observation. When the reference sets from self-similar become self-affine, we obtain Multi-fractal Scaling Laws, which are asymptotic and present a decreasing fractality for increasing structural sizes. They reproduce the experimental data very consistently. On the other hand, Critical Phenomena are always associated with the emergence of self-similar or self-affine patterns, to fractal (renormalized) or multi-fractal quantities, and to spontaneous self-organization. Typical examples are represented by: phase transformations, laminar-to-turbulent fluid flow transitions, avalanches in granular media, earthquakes, micro-cracking, and fracture in structural materials. In a fractal framework, it is then possible to define a scale-invariant constitutive law: the so-called Fractal Cohesive Crack Model, in which stress and strain are defined over lacunar fractal sets and the fracture energy in an invasive fractal set, which is the Cartesian product of the two previous sets.

Traveltimes due to compressional (P) and shear (S) waves have been proven essential in many applications of earthquake seismology. Therefore, an accurate and efficient traveltime computation approach for P and S waves is essential for successful applications. However, construction of a solution to the Eikonal equation with a complex velocity field in an anisotropic medium is challenging. The Eikonal equation is a first-order, hyperbolic, nonlinear partial differential equation (PDE) that represents a high-frequency approximation of the wave equation.
The fast marching method (FMM) and the fast sweeping method (FSM) are the most accepted techniques due to their efficiency for the solution of the Eikonal equation. However, these methods tend to suffer from numerical accuracy in the presence of anisotropic media with sharp heterogeneity, irregular surface topography and complex velocity fields. In order to overcome these difficulties, this study presents a solution method to the Eikonal equation by employing the peridynamic differential operator (PDDO) [1-3]. The PDDO provides the nonlocal form of the Eikonal equation by introducing an internal length parameter (horizon) and a weight function with directional nonlocality. It is immune to discontinuities and invokes the direction of information travel in a consistent manner. It enables numerical differentiation through integration; thus, the field equations are valid everywhere regardless of the presence of discontinuities. The weight function controls the degree of association among points within the horizon. Also, it enables directional nonlocality based on the knowledge of characteristic directions along which information travels. Solutions are constructed in a consistent manner without special treatments through simple discretization. The capability of this approach is demonstrated by considering different types of Eikonal equations with a complex velocity field in anisotropic media. Numerical stability is ensured and solutions compare well with the reference solutions.

Silicon electrode is the most promising candidate for the next generation anodes for Li-ion batteries due to its highest theoretical capacity and abundance on earth. However, lithium ion insertion and de-insertion can lead to significant volume changes. As a result, diffusion-induced stress (DIS) can occur. Especially for these active materials with high theoretical capacity, phase transformation is often involved. The high stresses arising from mismatch between the swelling part and non-swelling part can lead to capacity decay, failure and fracture of the active particles and strongly affects the cycle life. In addition, silicon would experience decrease in elastic properties due to lithium insertion and plastic deformation can occur due to large volume expansions and contractions. In this study, phase field models for DISs in spherical phase-transformation electrode materials are developed. For electrodes with relatively small volume variations, elastic models can be employed while for electrodes with large volume changes, plastic models are preferred. The models account for the effects of phase change, chemo-mechanical coupling and concentration-dependent material properties. The sharp phase boundary is naturally captured by the phase field model. Concentration field is obtained by a mixed formulation of the fourth-order Cahn-Hilliard equation. DISs are obtained by solving the variational form of the mechanical equilibrium equations. It is found that the DISs arise from the inhomogeneous volume expansions resulting from Li concentration gradients and the hydrostatic stress facilitates the diffusion of Li-ions under elastic deformation while hinders diffusion in plastic case. Material softening shows decreases in DISs but increases in strains under elastic deformation. It’s the opposite for plastic case. Under elastic deformation, radial stress is always positive and, hoop stress is positive in core region and is negative in the shell. In plastic case, radial stress shows a transition from tension in initial stage to compression at late stage. Hoop stress in the core region also shows similar trend while hoop stress in the shell shows transition from compression to tension. Furthermore, if strain softening due to plastic deformation is assumed, smaller stresses and higher plastic strains are predicted than strain hardening case. To sum up, the models highlight the importance of chemo-mechanical coupling effects, concentration-dependent material properties and plastic deformation on diffusion-induced stresses. To sum up, concentration-dependent material properties due to Li insertion and hardening behavior of the material due to plastic deformation plays a significant role on DISs in spherical phase transformation electrodes. By taking these factors into consideration, more accurate predictions of the DISs can be achieved, thus providing an improved theoretical basis and insight for designing next-generation mechanically stable phase transforming electrode materials.

The subloading surface model proposed by the author possesses the high generality and it is regarded as the governing law of the irreversible deformation behavior of solids. The distinguished features of the subloading surface model will be explained concisely in the presentation. The main items are listed below.
1) The underlying concept of the subloading surface which insists that the plastic strain rate develops as the stress approaches the yield surface, exhibiting the smooth elastic-plastic transition leading to the continuous variation of the tangent stiffness modulus,
2) The subloading surface model by which the cyclic loading behavior is described accurately, while the other models, e.g. the multi surface (Mroz), the bounding (Dafalias) surface and the superposed kinematic hardening (Chaboche) models are incapable of describing the cyclic loading behavior for small stress amplitudes because they are based on the the yield surface enclosing the purely-elastic domain,
3) The subloading-overstress model by which the viscoplastic strain rate is described accurately at the general rate of deformation from the static to the impact loading,
4) The multiplicative-subloading hyperelastic-based (visco)plasticity for the exact descriptions of the finite elastic and (visco)plastic deformations,
5) The multiplicative-subloading hyperelastic-based crystal (visco)plasticity model for the exact description of the finite elastic and (visco)plastic deformations of crystalline solids,
6) The subloading-friction model for the exact description of the dry and the fluid (lubricated) frictions at the general rate of sliding from the static to the impact sliding.

A challenging issue in solid mechanics is to optimally designing lightweight structures. One way to achieve this is to have either one or more components of the stress tensor or the effective stress or strain uniform throughout the structure with the choice depending upon the adopted failure criterion. Having succeeded in doing so for incompressible and heterogeneous Hookean materials we now explore the possibility of tailoring in the radial direction the two moduli for the Mooney-Rivlin material for achieving this.

The importance of theoretical models in Science and Engineering far outweighs that of experimental based models. The result of our lack of transparency towards the use of a more unified approach to analytical integration for solving some of the most difficult problems related to the Physical and Biological Sciences has forced us to become to dependent on the use of experimental based models. In reality this has never been a matter of choice for all of us but rather as a direct consequence in our failure to fully understand exactly why the vast majority of differential equations behave the way they do by not admitting highly predictable patterns of analytical solutions for resolving them.
In this talk I will begin by extending the traditional concept of a “differential” in Calculus by introducing an entirely new algorithm capable of representing all mathematical equations consisting of only algebraic and elementary functions in complete specialized differential form. Such a universal algorithm would involve the use of multivariate polynomials and the differential of multivariate polynomials all defined in a very unique algebraic configuration.
At first glance this may not sound like a major breakthrough in the Physical Sciences but progressively throughout this entire presentation, it will become very apparent that such a specialized differential representation of all mathematical equations would lead to some form of a unified theory of integration. It is only from the general numerical application of such a universal theory in mathematics can we expect to arrive at some form of a unified theory of Physics. This would be constructed from the development of very advanced physical models that would be built exclusively on general rather than on the local analytical solutions of many well known fundamental differential equations of the Physical and Biological Sciences.
We will be presenting a very large amount of empirical results that were gathered from the numerical application of our unified theory of integration on a number of very specific mathematical models. This would include a general first order ODE followed by a second order PDE where a detailed empirical analysis of the data collected on each of these differential equations would lead to their complete integration in terms of generalized analytical solutions involving only the algebraic and elementary functions.
We will also be presenting a series of Physical models which have been chosen very carefully just for demonstrating the applicability of our unified theory of integration into the Physical Sciences. These will include the equations for describing general linear elasticity and a very specific case of the Navier-Stokes equations for an incompressible fluid with heat transfer and variable viscosity. For each of these physical models we will be developing a universal numerical process that would be based entirely on the general application of our specialized differential form representation of all mathematical equations for the exact integration of the corresponding set of PDEs in terms of only generalized exact analytical solutions that can satisfy a wide range of boundary conditions.

The importance of theoretical models in Science and Engineering far outweighs that of experimental based models. The result of our lack of transparency towards the use of a more unified approach to analytical integration for solving some of the most difficult problems related to the Physical and Biological Sciences has forced us to become to dependent on the use of experimental based models. In reality this has never been a matter of choice for all of us but rather as a direct consequence in our failure to fully understand exactly why the vast majority of differential equations behave the way they do by not admitting highly predictable patterns of analytical solutions for resolving them.
In this talk I will begin by extending the traditional concept of a “differential” in Calculus by introducing an entirely new algorithm capable of representing all mathematical equations consisting of only algebraic and elementary functions in complete specialized differential form. Such a universal algorithm would involve the use of multivariate polynomials and the differential of multivariate polynomials all defined in a very unique algebraic configuration.
At first glance this may not sound like a major breakthrough in the Physical Sciences but progressively throughout this entire presentation, it will become very apparent that such a specialized differential representation of all mathematical equations would lead to some form of a unified theory of integration. It is only from the general numerical application of such a universal theory in mathematics can we expect to arrive at some form of a unified theory of Physics. This would be constructed from the development of very advanced physical models that would be built exclusively on general rather than on the local analytical solutions of many well known fundamental differential equations of the Physical and Biological Sciences.
We will be presenting a very large amount of empirical results that were gathered from the numerical application of our unified theory of integration on a number of very specific mathematical models. This would include a general first order ODE followed by a second order PDE where a detailed empirical analysis of the data collected on each of these differential equations would lead to their complete integration in terms of generalized analytical solutions involving only the algebraic and elementary functions.
We will also be presenting a series of Physical models which have been chosen very carefully just for demonstrating the applicability of our unified theory of integration into the Physical Sciences. These will include the equations for describing general linear elasticity and a very specific case of the Navier-Stokes equations for an incompressible fluid with heat transfer and variable viscosity. For each of these physical models we will be developing a universal numerical process that would be based entirely on the general application of our specialized differential form representation of all mathematical equations for the exact integration of the corresponding set of PDEs in terms of only generalized exact analytical solutions that can satisfy a wide range of boundary conditions.

Physics and mathematics have traditionally served as the technical knowledge bank of other quantitative subjects. Rarely, though, a reverse mapping has been successfully attempted. In a recent study, we mapped an established technique from epidemiology to solve a problem in material science. This technique, popularly referred to as 'reproduction number generator', that is used to calculate the speed and number of secondary infections, can estimate transport properties of a generic interactive double diffusion process. We showed that the analytical solution agrees closely with the exact numerical solution to a high order of accuracy with the key advantage of minimalist representation in interpreting the impact of parameters in nanocomposite double diffusion. The technique is generic enough to be implementable in all forms of nonlinear multi-diffusion modelling in material science and biology.

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