TROVALUSCI INTERNATIONAL SYMPOSIUM (17TH INTL. SYMP. ON MULTISCALE & MULTIPHYSICS MODELLING OF 'COMPLEX' MATERIAL (MMCM17) )
Editors: F. Kongoli, E. Aifantis, R. Das, V.Eremeyev, N. Fantuzzi.

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.

Machine learning methods [1], such as the Artificial Neural Networks (ANNs), have been applied to solve various science and engineering problems. TrumpetNets and TubeNets were recently proposed by the author [2][3] for creating two-way deepnets using the standard finite element method (FEM) [4] and S-FEM [5][6]as trainers. The significance of these specially configured ANNs is that the solutions to inverse problems have been, for the first time, analytically derived in explicit formulae. Such advancements have shown that fundamental understanding on physics law-based and data-based methods has found critical for development of novel methods for various types of engineering problems [9][10][12].
This paper discusses general issues related to law-based [4]-[8] and data-based [1][3] methods, including the principle, procedure, predictability, and property of these two types of methods in dealing with different types of problems. We present also a novel neural element method (NEM) [9][10] as a typical example of a possible combination of these two types of methods. The key idea in NEM is to use artificial neurons to form elemental units called neural-pulse-units (NPUs), using which shape functions can then be constructed, and used in the standard weak and weakened-weak (W2) formulations to establish discrete stiffness matrices, similar to the standard FEM. Detailed theory, formulation and codes in Python and numerical examples are presented to demonstrate this NEM. For the first time, we have made a clear connection, (in theory, formulation, and coding), between ANN methods and physical-law-based computational methods. We believe that his novel NEM changes fundamentally the way approaching mechanics problems, and opens a possible new window of opportunity for a range of applications. It offers a new direction of research on un-conventional computational methods. It may also have an impact on how the well-established weak and W2 formulations can be introduced to machining learning processes, for example, creating well-behaved loss functions with preferable convexity.

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...

The mechanical behavior of materials endowed with specific microstructure, characterized by complex non-linear behavior and complex internal sub-structure (micro), strongly depends on their microstructural features. In particular, in the modelling of these materials, such as particle composites, that are polycrystals with interfaces or with thin or thick interfaces, as well as rock or masonry-like materials, the discrete and heterogeneous nature of the matter must be taken into account, because interfaces and/or material internal phases dominate the gross behaviour. And this is definitely ascertained. What is not completely recognized instead, is the possibility of preserving memory of the microstructure, and of the presence of material length scales, without resorting to the discrete modelling that can often be cumbersome, in terms of non-local continuum descriptions.
In particular, for materials made of particles of prominent size and/or strong anisotropic media, by lacking in material internal scale parameters and in the possibility of accounting non-symmetries in strains and stresses, the classical Cauchy continuum (Grade1) does not always seem appropriate for describing the macroscopic behaviour taking into account the size, the orientation and the disposition of the micro-heterogeneities. This calls for the need of non-classical continuum descriptions [1-3], that can be obtained through multiscale approaches, aimed at deducing properties and relations by bridging information at proper underlying sub-levels via energy equivalence criteria. In the framework of such a multiscale modelling, the non-local character of the description is then crucial for avoiding physical inadequacies and theoretical computational problems. In particular, in problems in which a characteristic internal (material) length is comparable to the macroscopic (structural) length [4]. Among non-local theories, it is useful to distinguish between ‘explicit’ or ‘strong’ and ‘implicit’ or ‘weak’ non-locality [1, 3, 5]; where implicit non-locality concerns generalised continua with extra degrees of freedom, such as micromorphic continua [2] or continua with configurational forces [3].
This talk wants firstly to focus on the origins of multiscale modelling, related to the corpuscular(molecular)-continuous models developed in the 19th century to give explanations ‘per causas’ of elasticity (Cauchy, Voigt, Poincare), in order to find conceptual guidelines for deriving discrete-to scale-dependent continua, that are essentially non-local models with internal length and dispersive properties [5, 6]. Then, a discrete-to-scale dependent continuous formulation, developed for particle composite materials basing on a generalized version of Voigt’s molecular/continuum approach, is proposed. Finally, with the aid of some numerical simulations - concerning ceramic matrix composites (CMC), microcracked media and masonry assemblies – focus will be on the advantages of the micropolar modelling with respect to other generalised continuum formulations [9-12].

The deterministic internal length gradient (ILG) mechanics framework for elasticity and plasticity is extended to account for internal stress fluctuations due to stochastic effects associated with deformation-induced microstructures. Various existing approaches are first briefly reviewed and then an integrated discussion is provided. The role of probability density functions (PDFs) is examined in terms of existing experimental data. Emphasis is placed on Tsallis q-statistics and the related modification of classical PDFs (e.g. q-Gaussian, q-exponential). Then some example problems from the composites’ literature are discussed.

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.

Recently, a data-model-coupling method has been proposed based on a unified functional. This approach represents both the governing equations of data-driven computing and model-driven computing by using the same distance-based functional, thus enabling the two algorithms to be freely interconverted. The present study aims to further demonstrate the effectiveness of this coupling method in fracture analysis of composite structures. The data-driven algorithm is used in the area where the material modelling is complex, while the model-driven algorithm is applied in the rest areas to ensure high computational efficiency. The extended finite element method (XFEM) is employed to model the crack discontinuity and track the crack propagation path. We take a sandwich structure with an initial crack as an example to verify the effectiveness of the coupling method. The results demonstrate the capability of this coupling method to correctly predict the crack propagation path in composite structures.

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

Nanotechnology has emerged as one of the most promising tools for development of high performance Nano-Electro-Mechanical Systems (NEMS) with a variety of modern engineering
applications. Ground breaking NEMS have been rapidly developed and extensively adopted as
nano-sensors, nano-actuators, nano-transistors, nano-probes and nano-resonators with a wide
domain of conceivable applications. Nanomaterials are designed for the development of modern
nano-devices and are efficiently exploited as excellent components for reinforcement in
composite nanostructures. Appropriate modelling and exact assessment of size effects in nanomaterials and nanostructures are then themes of current interest in the community of Engineering
Science [1]. It is well established that the mechanical behaviour of NEMS significantly deviates from the macroscopic one, due to size effects. However, size dependent behaviours of continua can be conveniently described by Structural Mechanics by resorting to nonlocal constitutive models [2]. The nonlocal approach is still in the main focus of scientific research. The challenge regards consistency of theoretical formulations, validation by experimental results and predictive capability of characteristic phenomena in the nano-scale range [3]. This thematic lecture is aimed to describe available constitutive theories for size dependent problems and to illustrate new proposals which are contributing to an improvement of the state of the art on nonlocal modelling of nanostructures [4, 5].

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.

Three-dimensional comprehensive model of micro-scale transport in positive electrode/electrolyte/negative electrode(PEN) and macro-scale transport in gas channel of anode-supported solid oxide fuel cells (SOFCs) is developed in object-oriented computational fluid dynamics (CFD) code Open Field Operation and Manipulation (OpenFOAM) [1]. Figure 1 illustrates the schematic of planar-type anode-supported SOFCs. The numerical procedure consists of calculations of complex phenomena which are fully coupled together with electrochemical reaction kinetics, mass balance, and energy balance, interacting between porous PEN structure and fluid gas channel. CFD was performed in flow channels with calculations of mass balance and continuum micro-scale model were used to predict the electrochemical characteristics in PEN. The distributions of current density and mass fraction are employed to suggest a dependency. To validate our numerical model, we compare the simulated results with experimental data at intermediate temperatures. This study provides detailed information of heat and mass transport phenomena with electro-chemical characteristics for intermediate temperature SOFCs.

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 main goal of this work is to provide a thorough scientific understanding of the interplay between stochastics and mechanics, by classifying what can be achieved by representing mechanical system parameters in terms of deterministic values (homogenization) versus random variables or random fields (stochastic upscaling). The latter is of special interest for novel Bayesian applications capable of successfully handling the phenomena of fracture in both the quasi-static and the dynamic evolution of heterogeneous solids where no scale separation is present, which we refer to as stochastic upscaling. We seek to quantify the sensitivity of these phenomena with respect to the size-effect (changes in characteristic system dimension) and to the scale-effect (changes in characteristic time evolution). The challenge is to provide an answer as to why a system that is big does not break under quasi-static loads in the same way as a small system, even when both are built of the same material, and further extend this to inelasticity and fracture under dynamic loads. We plan to illustrate the crucial role of fine-scale heterogeneities and to develop the groundbreaking concept of stochastic upscaling that can capture their influence on instability and dynamic fracture at the system macro-scale. The stochastic upscaling is the key to size and scale laws in the proposed multi-scale approach, which can reach beyond homogenization to properly account for epistemic uncertainties of system parameters and the stochastic nature of dynamical fracture.

The methodology proposed in this work develops novel concepts in irreversible thermodynamics of nonequilibirum processes (yet referred to as nonequilibrium statistical thermodynamics, where neither space nor time scales are separated. This groundbreaking concept is here referred to as stochastic upscaling, providing a fruitful interaction of Mechanics (multi-scale approach) and Mathematics (uncertainty quantification). The stochastic upscaling truly applies across many scientific and engineering domains, where multiscale structure models are used to replace the testing procedure used to validate structure integrity or structure durability.
The main difficulty pertains to characterizing a number of different failure modes that require the most detailed description and interaction across the scales. Here, we seek to significantly improve the currently dominant experimental approach, because the latter is either not applicable for the sheer size of the structure, or unable to exactly reproduce the extreme loads. We propose to use stochastic upscaling, where extensive small-scale (material) testing is supplemented with large-scale (structure) computations, which allows exploring the real fracture behavior of the system under various load scenarios in optimal design studies, and thus accelerate innovations in this domain. More details are given in refs. [1,2,3].

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.

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