TROVALUSCI INTERNATIONAL SYMPOSIUM (17TH INTL. SYMP. ON MULTISCALE AND MULTIPHYSICS MODELLING OF 'COMPLEX' MATERIAL (MMCM17) )

The determination of elastic constants of carbon fiber composites via the non-destructive testing method is an important input both for structural design, performance assessment and structural health monitoring. For the non-destructive ultrasonic wave based method, the determination of the elastic properties highly depends the accurate estimation of the arrival time of quasi-longitudinal and quasi-transverse waves. The conventional available methods estimate the arrival time by using the envelope approach, which is extremely sensitive to noise and prone to inaccuracy in practice. In this study, a new time localization method based on time-reassigned synchrosqueezing transform is proposed. The new method could reassign the time-frequency coefficients in the time direction based on the group delay operator. We demonstrate that this method can provide high estimation accuracy for the arrival time, which is beneficial for the determination of elastic constants. Furthermore, the experiment work is carried out to verify the effectiveness of the proposed method.

Modelling fracture in batteries has attracted the research community as it accounts for more than 80% capacity loss within the first few cycles of charging/discharging. Cracking leads to loss of contact between particles and no longer participates in the insertion/extraction process and becomes inactive, leading to decreased capacity. Further, there are also local changes in the material properties, which has influence on the macroscopic response of the battery. In this work, we present a novel adaptive phase field formulation to simulate fracture in Li-ion batteries. Within this, a multi-physics framework is adopted where in the influence of the stress induced diffusion and diffusion induced stress on the fracture is numerically studied. A promising aspect of this framework is that complex fracture networks can easily be handled thanks to phase field method and the computational overhead is addressed by a novel adaptive technique based on physics based refinement. The influence of various boundary conditions, size of the particles on the fracture process are systematically studied. The results from the present framework are compared with experimental results where available.

Here we apply our general method [1] for providing rigorous asymptotic mathematical models to the case of a structure made of a thin linearly thermo-elastic adhesive layer connecting two linearly thermo-elastic bodies. The principle is to consider the geometrical and physical data as parameters and to rigorously study the asymptotic behavior of the structure when the parameters go to their natural limits. We will provide 5x5 asymptotic models depending on 5 possible relative behaviors for the stiffness and for the thermal conductivity with respect to the thickness of the adhesive layer. From the physical and mathematical points of view, thermo-elasticity is interesting in asymptotic modeling because it involves coupled transient phenomena which, at the limit, may induce a change in the nature of the constitutive equations! More precisely, we are facing a coupling between a hyperbolic equation (the motion equation) and a parabolic one (the heat equation). Our strategy is to formulate the problem in terms of a sequence of evolution equations set in Hilbert spaces of possible states with finite thermomechanical energy governed by m-dissipative operators. According to Trotter theory [1,2] it suffices to study the limit of the associated static problems. In certain cases (low stiffness and conductivity) state variables additional to the traces of the displacement and temperature of the adherents do appear in order to describe the state of the surface the layer shrinks to. By keeping these additional state variables, the structure of the limit equations for the surface remains as those of the layer. The 25 models are very different ranging from thermomechanical constraints to material thermo-elastic surfaces with constitutive equations strongly depending on the relative behaviors of the thermo-mechanical parameters with respect to the thickness of the layer. This study improves [3] and may be considered as a framework to assess the partial and formal study obtained through asymptotic expansion [4] devoted to poro-elasticity...

Advanced fibrous composites are being used in many advanced structural applications, especially in aerospace. The problem which involving the use of reinforced plastic composite materials is the susceptibility to accidental low energy impact. In particular, such damage may be invisible causing a significantly lowering of the residual strength of composite component. Therefore this critical design aspect, implies application of conservative safety factors to the ultimate load values of composite components. In particular, in order to take into account low velocity impact damages and notch sensitivity effects the ultimate load value is generally reduced by 30%. Typical sources of low velocity impact are tool falling during manufacturing or maintenance operations, hail, debris on the track, bird collision, etc. The object of the analysis are composite plates made of GFRP laminate. The purpose of this work is to analyze the behavior of a composite plates taking into account barely visible impact damage generated by low velocity impact and the damage onset and evolution. The numerical calculations were conducted with the implementation of the progressive failure algorithm, based on the material property degradation method and implementation of the Hashin criterion as the damage initiation criterion. In all analyzed cases high consistency of numerical and experimental results was achieved. The occurrence of delamination, and their evolution was modeled in accordance with a bilinear traction-separation law. The obtained results were compared with the results of the experiment. Numerical calculations showed that delamination modeling enhances the compliance of experimental and numerical results (more than Progressive Failure algorithm application). Additionally, it was found out that the correct estimation of the areas and the nature of damages caused by the impact requires taking into account the In-Situ effect. Based on the results of experimental and numerical studies, it was stated that the highest compliance of determined material degradation was achieved by using the LaRC criterion.

An elastic-plastic continuum theory is developed based on the incompatibility of the deformation. An approach based on the differential geometry of Riemann-Cartan seems the appropriate tool for this purpose. The work gives some insights to the linking the relative gravitation and the theory of incompatible deformations of continuum. Plastic deformation is defined from the deformation incompatibilities and then by means of affine connection in addition to metric tensor.
Two approaches for elastoplastic models are investigated : the first is based on the Internal State Variables with a dissipation potential, and the second starts with the definition of a Lagrangian combined with the Poincaré’s Invariance to obtain addition conservation laws involving stress, and hyper-stresses (or hyper-momenta), analogous of micro- stress and polar micro-stress. The general approach is in fine applied to Relative Gravitation and Continuum Plasticity to obtain conservation laws.

The mechanical behavior of materials with microstructure, such as particle composites, should consider their discontinuous and heterogeneous nature, because interfaces and/or material phases dominate the mechanical behavior. Non-local description is necessary for problems wherein the structural macroscopic scale is comparable with the local microscopic one (see for instance Trovalusci et al. (2017), Tuna et al. (2020), Tuna and Trovalusci (2020)). Non-classical and non-local continuum descriptions can be carried out by multi-scale approaches via energy equivalence criteria, as presented by Trovalusci and Masiani (1999). In this work, anisotropic materials with irregular hexagonal microstructure are considered. This model is capable of accounting for the particle size and orientation, as well as of the asymmetries in strain and stress occurring as a consequence of anisotropy (Fantuzzi et al. (2019a,b)). The present dynamic model is a suitable enrichment of the study presented by Fantuzzi et al. (2019b) where a composite of hexagonal rigid particles interacting through elastic interfaces was derived in a static context. Some paradigmatic cases are discussed, showing how the orientation of the crystal lattice clearly affects the dynamics at the equivalent continuum scale. The reliability of the proposed multiscale strategy is evaluated comparing the results with those provided by finite element simulations.

ABSTRACT:
In this study, a completely new numerical method, Finite Line Method (FLM), is proposed for solving general thermal and mechanical problems. In this method, the computational domain is discretized into a number of collocation nodes as in the free element method [1], and at each node a set of straight or curved lines crossing the node is formed, which is called the cross-line element [2] and represented by a few nodes distributed over each line. The shape functions for each cross-line element are constructed using the Lagrange interpolation formulation and their first and high order partial derivatives with respect to the global coordinates are derived through an ingenious technique. The derived spatial partial derivatives are directly substituted into the governing differential equations and related boundary conditions of thermal and mechanical problems to form the final system of equations.
FLM is a type of collocation method, not needing any integration to establish the solution scheme. Therefore, it is very convenient to be used to solve multi-physics coupled problems. Besides, since the Lagrange interpolation formulation is used to construct the shape functions, high order lines can be easily formulated. A number of numerical examples for heat conduction, elasticity, and thermal stress analysis of composite structures will be given to demonstrate the efficiency and stability of the proposed method.
KEY WORDS: Cross line method, Finite line method, Free element method, Thermal mechanical problem, Composite structure

The phase field method has emerged as a promising mathematical model for solving interfacial problems. First proposed for modelling microstructural evolution, phase field is now the de facto tool in a wide variety of physical problems, from viscous fingering to vesicle dynamics. One of the areas where the phase field method is enjoying a remarkable success is fracture mechanics, a discipline that has long attracted a great deal of interest from the computational mechanics community.
In this talk, I will describe the theoretical foundations of phase field fracture methods, discuss implementation details and showcase some of the pioneering applications pursued by my group. Emphasis will be placed on the application of phase field models to multi-physics problems, with particular focus on hydrogen embrittlement – a long-standing scientific challenge that has come very much to the fore in recent years due to the need of developing structures for (hydrogen) energy storage. Moreover, I will show how our phase field models for hydrogen embrittlement have been benchmarked against experimental results and are currently being used by industrial partners to conduct Virtual Testing, for the first time in the energy sector (wind energy and Oil&Gas). Finally, I will show how the phase field paradigm can also open new modelling horizons in another scientifically-challenging phenomenon of notable technological importance: corrosion damage.

We propose and elaborate a new concept of nonsingular cracks, the rationale for which is based on processing a large amount of experimental data taken from various scientific sources. It is important that the use of the gradient theory of elasticity is carried out simultaneously with the identification of the scale parameter and an indication of its physical meaning and fundamental role in fracture mechanics. We use the feature of the strain gradient elasticity theory (SGET) related to the regularization of classical singularity problems and show that structural analysis of the pre-cracked materials can be reduced to the failure analysis within SGET by using appropriate failure criteria formulated in terms of the Cauchy stresses. These stresses are workconjugated to strains and they have non-singular values in SGET solutions for the problems with cracks and sharp notches. Using experimental data for the samples made of the same material but containing different type of cracks we identify the additional length scale parameters within two simplified formulations of SGET. To do this we fitted the modeling results to the experimental data assuming that for the prescribed maximum failure load (known from the experiment) the chosen failure criterion should be fulfilled at the crack tip. For the most of the considered experiments with brittle and quasi-brittle materials (glass, ceramics, concrete) we found that the maximum principal stress criterion is valid.
The main peculiarity of the presented results is the proposed approach for the assessment of the material fracture. For the considered brittle and quasi-brittle materials we propose to use the failure criteria formulated with respect to the Cauchy stresses estimated within SGET. These stresses have the finite values in the whole domain and also at the crack tip. Due to this, we call the presented approach the "failure analysis" since the linear fracture mechanics approaches with singular fields do not involved here. Other words, we propose to transfer the standard approaches of the failure analysis to the bodies with cracks accounting for the strain gradient effects within SGET.
We confirm our suggestion based on the full-field numerical simulations and provide the examples of identification of SGET parameters for the known experimental data with pre-cracked brittle and quasi-brittle materials. It was shown that identified parameters allow us to predict the failure loads for the experimental samples with different type of cracks by using maximum principal Cauchy stress criterion.
As the main result, we show that identified values of the length scale parameters allows us to predict the maximum failure loads for the materials samples with different type of cracks (of different length, offset, inclination). Therefore, we show 1) that the length scale parameter of SGET can be treated as the shape independent material constant that controls the material fracture and 2) that the failure analysis of the structures with non-smooth geometry can be performed by using FEM simulations within SGET involving the failure criteria formulated in terms of the Cauchy stresses.
Presented approach can be treated as some type of the alternative to the classical LEFM among other known theories (theory of critical distances, cohesive zone models, Bazant theory of size effect, etc.). The main advantages of this approach is the possibility of the mesh-independent assessments for the material fracture and the caption of size effects
This work was supported by the Ministry of Science and Higher Education of the Russian Federation (Grant agreement 075-11-2020-023).

Recently the interest in flexoelectricity-related phenomena grows with respect to possible applications in MEMS and NEMS for energy harvesting, sensors and actuators. Flexoelectricity is the general property of dielectrics. Although the magnitude of the flexoelectric response is small, in general, its contribution may become dominant at the nanoscale. The static flexoelectric response relates the electric polarization with the strain gradients and vice versa whereas dynamic flexoelectric response includes time derivatives of the polarization in the kinetic energy. In addition, the surface/interfacial flexoelectricity is known [1, 2], which includes surface/interfacial densities of strain and kinetic energy.
We discuss the influence of dynamic flexoelectric properties and surface flexoelectricity on vibrations of nanometer-sized structures as nanobeams and nanoplates considering all mentioned above responses considering oscillations of a nanobeam. For simplicity, we consider isotropic materials and infinitesimal deformations. We apply the Timoshenko-Reissner-Mindlin-type kinematics. In other words, we consider a beam with kinematicallly independent translations and rotations. Various boundary conditions are considered. For the derivation of the governing equations we used the least action principle generalized for dynamic flexoelectricity. Here the least action functional includes both surface and bulk strain and kinetic energies.The eigen-frequencies are calculated and their dependence on the material parameters are analysed.

Shape memory polymers are a class of materials that can be brought to a temporary shape while "remembering" its permanent shape. The material can stay in the temporary shape indefinitely, and can recover its permanent shape under certain thermal/mechanical processes. Compared to other shape memory materials, shape memory polymers possess advantages of large recoverable strains (400% reported, compared to 8% for shape memory alloys), low energy consumption for shape programming, light weight, low cost, excellent manufacturability, and bio-degradability. Due to these properties, shape memory polymers are finding various applications, especially in aerospace engineering and biomedical engineering.
A constitutive theory is developed for the shape memory polymers, for which the basic shape memory effect is due to glass transition. The theory is based on the framework of nonlinear thermoelasticity, and is capable of describing large shape changes of the material in arbitrarily prescribed temperature/loading paths.
It is well-known that polymeric materials typically undergo glass transition gradually in a temperature range. We thus introduce a frozen volume fraction function which gives the volume fraction of the material regions that are in the glassy phase for a given temperature. The thermal/mechanical properties of the material are assumed to be given by two constitutive equations for the rubbery and glassy phases, respectively. It is further assumed that when a material point undergoes the transition from the rubbery phase to the glassy
phase with continuous temperature and stress, the strain must be continuous despite the change of the constitutive equation. This is achieved by taking a new reference configuration for the constitutive description of the material in the glassy phase. This
new reference configuration, termed the frozen reference configuration, depends on the temperature and stress when the glass transition is taking place. The overall constitutive equation is obtained by integrating the constitutive equations for individual material
points. The property of one way shape memory is captured in the constitutive equations through a net cooling history function that erases the dependence of the current rubbery state on past events. A comparison of the model predictions and the experimental
data shows good agreement.

The fatigue life of titanium alloys, such as Ti-7Al and Ti-6242 has been experimentally observed to be strongly affected by the microstructure and loading conditions. These materials are characterized by heterogeneous polycrystalline microstructures, exhibiting nonuniform distributions of crystallographic orientation, misorientation and morphological features. Considerable non-uniformity exists in the crystallographic orientation, crystallographic misorientation, grain size etc. at the microscopic length-scale. Material heterogeneities also exist at higher length scales e.g. in the form of micro-textured regions (MTRs). These clusters of grains with similar crystallographic orientation have been associated with poor fatigue performance in Ti-Al alloys [1, 2, 3]. Microstructural morphology and crystallography have strong effects on the fatigue response of the material at different scales. Nucleation of dwell fatigue cracks has been attributed to the load-shedding phenomenon in experimental and micromechanical studies. Load shedding occurs due to local creep in grains oriented for easy prismatic or basal- a slip (soft grains), causing time-dependent stress amplification in adjacent hard grains ([0001] axis parallel to the principal stress axis) with eventual cracking. Experimental observations in indicate that micro-cracks form on planes inclined at ∼15o to the (0001) plane in the hard grain. Dwell fatigue cracks nucleate in subsurface regions of the specimen, a phenomenon that is not well-understood in the literature. A major challenge in modeling this phenomenon is that it involves several spatial scales, viz. the scale of dislocation slip and crystallography-induced load-shedding (∼ µm), the scale of micro-textured regions and the scale of the specimen to be modeled. Representing events at this combination of scales requires a computationally efficient, microstructure-sensitive modeling framework.
This paper develops a robust multi-scale model for investigating fatigue crack nucleation in Ti alloys. For structural scale modeling of the specimen, it introduces the Parametrically Homogenized Constitutive Models or (PHCMs) that have been recently developed [4-7] for modeling deformation and fatigue crack initiation in Ti alloys. PHCMs are thermodynamically consistent, reduced-order models whose constitutive parameters are explicit functions of Representative Aggregated Microstructural Parameters or (RAMPs), representing statistical distributions of morphological and crystallographic descriptors of the microstructure. The basic forms of the PHCM equations are a-priori selected to reflect the fundamental deformation characteristics of the aggregated response of crystal plasticity finite element model (CPFEM) simulations of microstructural statistically equivalent representative volume elements or (SERVEs). Machine learning tools are employed to obtain these functional forms using micromechanical time-dependent plastic deformation and fatigue crack nucleation data-sets that are generated from image-based CPFEM simulations of the SERVEs. These constitutive parameters also incorporate state variables representing the up-scaled effect of microstructural deformation mechanisms. The PHCMs are readily incorporated in commercial FE software like ABAQUS through user-defined material modeling interfaces such as UMAT, for microstructure-sensitive structural response predictions. Significantly reduced number of solution variables in the PHCM simulations, compared to DNS of micromechanical models, make them several orders of magnitude more efficient with good accuracy. In addition to the PHCM, a parametrically homogenized crack nucleation model (PHCNM) is developed in [7,10] to identify hot-spots of potential fatigue nucleation in test specimens, with underlying explicit fatigue crack nucleation in the microstructure. While the PHCMs provide a novel framework for predicting microstructure-dependent structural response, they are not complete without accounting for uncertainties that persist in their development. Uncertainties arise in the PHCM forms and equations predominantly due to the limited size of datasets used in the calibration process, as well as natural variabilities in the microstructure. Two categories of uncertainty are often associated with the modeling of physical systems. They are: (i) the epistemic uncertainty in the model form resulting from incomplete knowledge and data on the system being modeled, and (ii) the aleatoric uncertainty that arises from inherent variabilities in the phenomenon that cannot be reduced by further investigation. The explicit representation of microstructural variables in the PHCM constitutive equations makes them particularly suitable for incorporating the uncertainty quantification (UQ) capabilities. Uncertainties due to model reduction error and data sparsity error are accounted for by employing a Bayesian framework to calibrate the functional forms of constitutive parameters from CPFEM-generated analysis data, in contrast to the deterministic calibration. Microstructural variability in this formulation is represented by a stochastic extension of the representative aggregated microstructural parameters or RAMPs. For computationally efficient propagation of uncertainty from the three sources to time-dependent material state and model output variables, a Taylor series expansion-based uncertainty propagation (UP) method is developed in this work.

A. Fluid Dynamical point of view.
My initial reaction, after reading this report, was that it was a conjecture on a very topical subject with small chance of success. In fact, I thought that writing a report on it would be somehow a straightforward affair. It has proven though, upon closer examination, that this application is anything but trivial, and deserves special attention.
In this talk I will provide my view, as to how combining theoretical approaches from fluid dynamics can be combined with pattern formation in solids to form a universal theory of approaching turbulence, that is applicable to both these rather distinct phases.
In order to understand how this is possible it is necessary to understand and subsequently combine two concepts. The first is the array of computational techniques, such as spectral element and Galerkin spectral collocation-tau methods, Zenolli patching, finite difference and other iterative methods, that I have developed over the past decades, and their application to puzzling experimental results and observations in fluids. These methods have had applications in non-trivial solution with impact on both basic science and modern engineering.
The figure included in his application, in particular, explains how the proposed sequence of bifurcations approach (SBA) can, in a fully deterministic manner, explain the beginning of a/approach to the phenomenon that is aperiodic/chaotic and which we term as ‘turbulence’. It is based on Ref [1].
The second concept is described extensively in Ref [2] of the application, where a detailed account is presented of the author’s internal length gradient (ILG) mechanics framework. It is based on the assignment of internal lengths (ILs) (associated with the local geometry/topology of material substructures) as scalar multipliers of extra Laplacian terms that are introduced to account for heterogeneity effects and weak nonlocality. This pioneering new concept clearly paves the way to understand hydro- and solid- dynamics under one umbrella, by incorporating, relatively simple extensions to the fluid constitutive equations, when describing pattern formation in fluids. If we combine the ILG framework with the computational ability of the proprietary software of the PI, it is not difficult to conclude that the theoretical concepts, such as classical laws for solids (Hooke) and fluids (Navier–Stokes) can be unified under one unified banner. This new view of solids, as a type of fluid, coupled with the aid of the tried SBA based and developed proprietary software, will allow the probing of the structure of the pattern formation.
B. Physics point of view.
1. The work of the team member Elias C. Aifantis on gradient theory has rejuvenated the field of engineering based on Hooke’s law and has provided new avenues for considering size effects and stability of solid materials and structures. The main aspect of this work will be on extending the methodology used for extending Hooke’s equation for elastic motion to the extension of the Navier-Stokes equations for Newtonian fluids and points out the similarities in addressing flow and instabilities of polymer based materials and plastics. This will be a very useful tool for developing protocol and design criteria for recycling, with great benefits to environmental and renewable energy sectors.
2. Of particular importance is the proposed transfer of new ideas and novel techniques recently developed for fluid flow and turbulence to describe plastic flow and spatio-temporal instabilities in plastic processing. The success of the methodology is proven for Newtonian fluids (see recent publication [1]), which have been numerically implemented for stability and turbulence, will open up a new field of rheological materials, such as plastics. In particular, I will explain the direct connection of this work with LAMMPS, The Large-scale Atomic/Molecular Massively Parallel Simulator, that deals with calculations at the molecular level. This proposal has already started work in the direction with the Horizon 2020 Research and Innovation Staff Exchange (RISE) award, ATM2BT – Atomistic to Molecular To Bulk Turbulence - which am leading and in which Professor Aifantis is a critical member. This association will ensure close interaction of the fluid and solids communities. The result will be a unifying framework for treating the higher order terms in fluids and solids within the same footing.

SIPS is the flagship event of FLOGEN STARS OUTREACH, a not-for-profit, non-political and all-inclusive science organization. SIPS as well as FLOGEN STARS OUTREACH takes no sides in political, scientific or technological debates. We equally welcome, without reservations, all spectrum of ideas, theories, technologies and related debates. Statements and opinions expressed are those of individuals and/or groups only and do not necessary reflect the opinions of FLOGEN, its sponsors or supporters.

FLOGEN Stars OUTREACH | Home | Contact Us | Privacy Policy | Cancellations/Refund Policy
© Copyright of FLOGEN Stars Outreach Organization: The content of this page including all texts and photos are copyright of FLOGEN Stars Outreach and none can be used in their original or in any modified or combined form in any publication, web site or in any other medium whatsoever without prior written permission from FLOGEN Stars Outreach.