Effects of initial anisotropy on the finite strain deformation behavior of glassy polymers

Solid phase deformation processing of glassy polymers produces highly anisotropic polymer components as a result of the massive reorientation of molecular chains during the large strain forming operation. Indeed, the polymer preform used as the starting materials is usually anisotropic owing to its prior deformation history. The process end product has often been fashioned for a particular application, i.e. to possess an increased flow strength along a particular axis, thereby exploiting the orientation induced anisotropy effects. The fully three-dimensional issues involved in the use of glassy polymer components include anisotropic flow strenghts, limiting extensibilities, and deformation patterns. These characteristics have been altered by the initial forming operation but are obviously not expected to be enhanced in all directions. The presence of anisotropy in structural components may also lead to premature failure or unexpected shear localization. In this report the effects of initial deformation and the associated anisotropies are investigated through uniaxial compression tests on preoriented polycarbonate (PC) and polymethylmethacrylate (PMMA) specimens. The evolving anisotropy is monitored by testing materials preoriented by various amounts of strain and under different states of deformation. The tensorial nature of the anisotropic material is characterized by examining the preoriented material response in three orthogonal directions. A model for the large strain deformation response of glassy polymers has been shown by Arruda and Boyce [in press] to be well predictive of the evolution of anisotropy during deformation in initially isotropic materials. Here the authors evaluate the ability of the model developed in Arruda and Boyce [in press] to predict several aspects of the anisotropic response of preoriented materials. Using material properties determined from the characterization of the isotropic material response and a knowledge of the anisotropic state of the preoriented material, model simulations are shown to accurately capture all aspects of the large strain anisotropic response including flow strengths, strain hardening characteristics, cross-sectional deformation patterns, and limiting extensibilities. Although anisotropy has been shown to evolve with temperature and strain rate in Boyce, Arruda and Jayachandran [in press] and also state of deformation in Arruda and Boyce [in press], we submit an experimental observation that the subsequent deformation response of preoriented polymers may be predicted using only a measure of optical anisotropy, and not the prior strain or thermal history. Optical anisotropy, as measured for example by birefringence, therefore represents a true internal variable indicative of the evolution of anisotropy with inelastic strain, state of strain, and temperature.     

Disorder,pre-stress and non-affinity in polymer 8-chain models

To assess the role of single-chain elasticity, non-affine strain fields and pre-stressed reference states we present and discuss the results of numerical and analytical analyses of a modified 8-chain Arruda–Boyce model for cross-linked polymer networks. This class of models has proved highly successful in modeling the finite-strain response of flexible rubbers. We extend it to include the effects of spatial disorder and the associated non-affinity, and use it to assess the validity of replacing the constituent chain's nonlinear elastic response with equivalent linear, Hookean springs. Surprisingly, we find that even in the regime of linear response, the full polymer model gives very different results from its linearized counterpart, even though none of the chains are stretched beyond their linear regime. We demonstrate that this effect is due to the fact that the polymer models are under considerable pre-stress in their ground state. We show that pre-stress strongly suppresses non-affinity in these unit cell models, resulting in a marked stiffening of the bulk response. Polymer networks with some degree of flexibility are thus intrinsically prestressed, and one effect of such prestresses is to reduce non-affine deformations. Combined, these findings may help explain why fully affine mechanical models, in many cases, predict the bulk mechanical response of disordered polymer networks so well.     

On modeling the micro-indentation response of an amorphous polymer

Interest in instrumented indentation experiments as a means to estimate mechanical properties has grown rapidly in recent years. Although numerous nano/micro-indentation experimental studies on polymeric materials have been reported in the literature, a corresponding methodology for extracting material property information from the experimental data does not exist. This situation for polymeric materials exists primarily because baseline numerical analyses of sharp indentation using appropriate large deformation constitutive models for the nonlinear viscoelastic–plastic response of these materials appear not to have been previously reported in the literature. An existing, widely used theory for amorphous polymers (e.g. [Boyce, M., Parks, D., Argon, A.S., 1988. Large inelastic deformation of glassy polymers. Part 1: Rate dependent constitutive model. Mechanics of Materials 7, 15–33; Arruda, E.M., Boyce, M.C., 1993. Evolution of plastic anisotropy in amorphous polymers during finite straining. International Journal of Plasticity 9, 697–720]) has been recently found to lack sufficient richness to enable one to quantitatively reproduce the major features of the indentation load-versus-depth curves for some common amorphous polymers [Gearing, B.P., 2002. Constitutive equations and failure criteria for amorphous polymeric solids. Ph.D. thesis, Massachusetts Institute of Technology].This study develops a new continuum model for the viscoelastic–plastic deformation of amorphous polymeric solids. We have applied the constitutive model to capture salient features of the mechanical response of the amorphous polymeric solid poly(methyl methacrylate) (PMMA) at ambient temperature and stress states under which this material does not exhibit crazing. We have conducted compression-tension strain-controlled experiments, as well as stress-controlled compression-creep experiments, and these experiments are used to calibrate the material parameters in the constitutive model for PMMA.We have implemented our constitutive model in a finite-element computer program, and using this finite-element program we have simulated micro-indentation experiments on PMMA. We show that our constitutive model and finite element simulations reproduce the experimentally-measured indentation load-versus-depth response with reasonable accuracy.     

An 8-chain Model for Rubber-like Materials Accounting for Non-affine Chain Deformations and Topological Constraints

Several industrial applications involve rubber and rubber-like materials, and it is important to be able to predict the constitutive response of these materials. In the present paper, a new constitutive model for rubber-like solids is proposed. The model is based on the 8-chain concept introduced by Arruda and Boyce (J. Mech. Phys. Solids 41, 389–412, 1993) to which two new components are added. Real polymer networks do not deform affinely, and in the proposed model this is accounted for by the inclusion of an elastic spring, acting in series with the representative polymer chain. Furthermore, real polymer chains are not completely free to move, which is modelled by imposing a topological constraint on the transverse motions of the representative polymer chain. The model contains five model parameters and these need to be determined on the basis of experimental data. Three experimental studies from the literature were used to assess the proposed model. The model was able to reproduce experimental data performed under conditions of uniaxial tension, generalised plane deformation, and biaxial tension with an excellent accuracy. The strong predictive abilities together with the numerically efficient structure of the model make it suitable for implementation in a finite element context.     

Modelling large deformation behaviour under loading–unloading of semicrystalline polymers: Application to a high density polyethylene

In this work, the large deformation behaviour under monotonic loading and unloading of a high density polyethylene (HDPE) is studied. To analyze the nonlinear time-dependent response of the material, mechanical tests were conducted at room temperature under constant true strain rates and stress relaxation conditions. A physically-based inelastic model written under finite strain formulation is proposed to describe the mechanical behaviour of HDPE. In the model, the inelastic mechanisms involve two parallel elements: a visco-hyperelastic network resistance acting in parallel with a viscoelastic–viscoplastic intermolecular resistance where the amorphous and crystalline phases are explicitly taken into consideration. The semicrystalline polymer is considered as a two-phase composite. The influence of the crystallinity on the loading and unloading behaviour is investigated. Numerical results are compared to experimental data. It is shown that the model is able to accurately reproduce the experimental observations corresponding to monotonic loading, unloading and stress relaxation behaviours at different strain levels. Finally, the model capabilities to capture cyclic loading–unloading behaviour up to large strains are discussed. To demonstrate the improved modelling capabilities, simulations are also performed using the original model of Boyce et al. [Boyce, M.C., Socrate, S., Llana, P.G., 2000. Constitutive model for the finite deformation stress–strain behavior of poly(ethylene terephthalate) above the glass transition. Polymer 41, 2183–2201] modified by Ahzi et al. [Ahzi, S., Makradi, A., Gregory, R.V., Edie, D.D., 2003. Modeling of deformation behavior and strain-induced crystallization in poly(ethylene terephthalate) above the glass transition temperature. Mechanics of Materials 35, 1139–1148].     

Modeling morphology evolution and mechanical behavior during thermo-mechanical processing of semi-crystalline polymers

A new model is proposed that combines statistical mechanics and thermodynamic aspects to characterize orientation development, nucleation and growth of crystallites, and chain entanglement slippage with interdependent relationships necessary to accurately correlate and in some cases predict the morphology and mechanical behavior of semi-crystalline polymers during various thermo-mechanical processes in the rubbery state, close to the glass transition temperature. Internal state variables (ISVs) that directly represent the underlying microstructure state are used to characterize polymer morphology and the resulting properties throughout deformation. The model uses fundamental thermodynamic coefficients for polyethylene terephthalate (PET) and is correlated to experimental data at various strain rates and temperatures just above the glass transition temperature. Experimental data are used that measure the stress, amorphous orientation, and crystallinity during uniaxial deformation of PET. The model is found to correlate well to these experimental data.     

An endochronic plasticity formulation for filled rubber

The nature of elastomeric material demands the consideration of finite deformations, nonlinear elasticity including damage as well as rate-dependent and rate-independent dissipative properties. While many models accounting for these effects have been refined over time to do better justice to the real behavior of rubber-like materials, the realistic simulation of the elastoplastic characteristics for filled rubber remains challenging.The classical elastic-ideal-plastic formulation exhibits a distinct yield-surface, whereas the elastoplastic material behavior of filled rubber components shows a yield-surface free plasticity. In order to describe this elastoplastic deformation of a material point adequately, a physically based endochronic plasticity model was developed and implemented into a Finite Element code. The formulation of the ground state elastic characteristics is based on Arruda and Boyce (1993) eight-chain model. The evolution of the constitutive equations for the nonlinear endochronic elastoplastic response are derived in analogy to the Bergström–Boyce finite viscoelasticity model discussed by Dal and Kaliske (2009).     

A physically-based constitutive model for anisotropic damage in rubber-toughened glassy polymers during finite deformation

The present work focuses on the development of a physically-based model for large deformation stress-strain response and anisotropic damage in rubber-toughened glassy polymers. The main features leading to a microstructural evolution (regarding cavitation, void aspect ratio, matrix plastic anisotropy and rubbery phase deformation) in rubber-toughened glassy polymers are introduced in the proposed constitutive model. The constitutive response of the glassy polymer matrix is modelled using the hyperelastic-viscoplastic model of [Boyce et al., 1988] and [Boyce et al., 2000]. The deformation mechanisms of the matrix material are accounted for by two resistances: an elastic-viscoplastic isotropic intermolecular resistance acting in parallel with a visco-hyperelastic anisotropic network resistance, each resistance being modified to account for damage effects by void growth with a variation of the void aspect ratio. The effective contribution of the hyperelastic particles to the overall composite behaviour is taken into account by treating the overall system in a composite scheme framework. The capabilities of the proposed constitutive model are checked by comparing experimental data with numerical simulations. The deformation behaviour of rubber-toughened poly(methyl methacrylate) was investigated experimentally in tension at a temperature of 80 °C and for different constant true strain rates monitored by a video-controlled technique. The reinforcing phase is of the soft core-hard shell type and its diameter is of the order of one hundred nanometers. The particle volume fraction was adjusted from 15% to 45% by increments of 5%. The stress-strain response and the inelastic volumetric strain are found to depend markedly on particle volume fraction. For a wide range of rubber volume fractions, the model simulations are in good agreement with the experimental results. Finally, a parametric analysis demonstrates the importance of accounting for void shape, matrix plastic anisotropy and rubber content.     

HIA: A Hybrid Integral Approach to model incompressible isotropic hyperelastic materials—Part 1: Theory

This paper provides a new constitutive model for rubber-like materials. The model adds to the 8-chain density introduced by Arruda and Boyce, two phenomenological components: an original part made of an integral density and an interleaving constraint part represented by a logarithmic function as proposed by Gent and Thomas. The model contains six rheological parameters connected to the polymer chemistry and to the macroscopic behavior. Four sets of experimental data from the literature are used to identify the rheological parameters and to assess the proposed model. The model is able to reproduce with a good accuracy experimental data performed under different loading conditions such as uniaxial and equibiaxial tension, uniaxial compression, pure and simple shear as well as the Mooney plot.     

Effects of crystal content on the mechanical behaviour of polyethylene under finite strains: Experiments and constitutive modelling

The mechanical stress-strain behaviour of polyethylene (PE) materials under finite strains is studied both experimentally and theoretically. In order to gain insight into the structure and physical properties of investigated PE materials, a series of thermal (DSC and DMTA) and microstructural (small-angle X-ray scattering and AFM) characterizations have been undertaken. The influence of crystallinity on the various features of the tensile stress-strain response is considered over a large strain range, implying thermoplastic-like to elastomer-like mechanical behaviour. A physically-based hyperelastic-viscoplastic approach was adopted to develop a pertinent model for describing the mechanical behaviour of PE materials under finite strains. The semicrystalline polymer is being treated as a heterogeneous medium, and the model is based on a two-phase representation of the microstructure. The effective contribution of the crystalline and amorphous phases to the overall intermolecular resistance to deformation is treated in a composite framework, and coupled to a molecular network resistance to stretching and chain orientation capturing the overall strain hardening response. In order to extract the individual constitutive response of crystalline and amorphous phases, a proper identification scheme based on a deterministic approach was elaborated using the tensile test data of PE materials under different strain rates. Comparisons between the constitutive model and experiments show fair agreement over a wide range of crystallinities (from 15% to 72%) and strain rates. The constitutive model is found to successfully capture the important features of the observed monotonic stress-strain response: the thermoplastic-like behaviour for high crystallinity includes a stiff initial response, a yield-like event followed by a gradual increase of strain hardening at very large strains; for the elastomer-like behaviour observed in the low crystallinity material, the strain hardening response is largely predominant. Strain recovery upon unloading increases with decreasing crystallinity: this is quantitatively well reproduced for high crystallinity materials, whereas predictions significantly deviate from experiments at low crystallinity. Model refinements are finally proposed in order to improve the ability of the constitutive equations to predict the nonlinear unloading response whatever the crystal content.     

Cyclic stress-softening model for the Mullins effect in compression

This paper models the cyclic stress softening of an elastomer in compression. After the initial compression the material is described as being transversely isotropic. We derive non-linear transversely isotropic constitutive equations for the elastic response, stress relaxation, residual strain, and creep of residual strain in order to model accurately the inelastic features associated with cyclic stress softening. These equations are combined with a transversely isotropic version of the Arruda–Boyce eight-chain model to develop a constitutive relation that is capable of accurately representing the Mullins effect during cyclic stress softening for a transversely isotropic, hyperelastic material, in particular a carbon-filled rubber vulcanizate. To establish the validity of the model we compare it with two test samples, one for filled vulcanized styrene–butadiene rubber and the other for filled vulcanized natural rubber. The model is found to fit this experimental data extremely well.     

Polyconvexity of generalized polynomial-type hyperelastic strain energy functions for near-incompressibility

In this article we investigate several models contained in the literature in the case of near-incompressibility based on invariants in terms of polyconvexity and coerciveness inequality, which are sufficient to guarantee the existence of a solution. These models are due to Rivlin and Saunders, namely the generalized polynomial-type elasticity, and Arruda and Boyce. The extension to near-incompressibility is usually carried out by an additive decomposition of the strain energy into a volume-changing and a volume-preserving part, where the volume-changing part depends on the determinant of the deformation gradient and the volume-preserving part on the invariants of the unimodular right Cauchy–Green tensor. It will be shown that the Arruda–Boyce model satisfies the polyconvexity condition, whereas the polynomial-type elasticity does not. Therefore, we propose a new class of strain-energy functions depending on invariants. Moreover, we focus our attention on the structure of further isotropic strain-energy functions.     

A dynamic finite element method for inhomogeneous deformation and electromechanical instability of dielectric elastomer transducers

We present a three-dimensional nonlinear finite element formulation for dielectric elastomers. The mechanical and electrical governing equations are solved monolithically using an implicit time integrator, where the governing finite element equations are given for both static and dynamic cases. By accounting for inertial terms in conjunction with the Arruda–Boyce rubber hyperelastic constitutive model, we demonstrate the ability to capture the various modes of inhomogeneous deformation, including pull-in instability and wrinkling, that may result in dielectric elastomers that are subject to various forms of electrostatic loading. The formulation presented here forms the basis for needed computational tools that can elucidate the electromechanical behavior and properties of dielectric elastomers that are used for engineering applications.     

Correlation between swift effects and tension–compression asymmetry in various polycrystalline materials

The Swift phenomenon, which refers to the occurrence of permanent axial deformation during monotonic free-end torsion, has been known for a very long time. While plastic anisotropy is considered to be its main cause, there is no explanation as to why in certain materials irreversible elongation occurs while in others permanent shortening is observed.In this paper, a correlation between Swift effects and the stress–strain behavior in uniaxial tension and compression is established. It is based on an elastic–plastic model that accounts for the combined influence of anisotropy and tension–compression asymmetry. It is shown that, if for a given orientation the uniaxial yield stress in tension is larger than that in compression, the specimen will shorten when twisted about that direction; however, if the yield stress in uniaxial compression is larger than that in uniaxial tension, axial elongation will occur. Furthermore, it is shown that on the basis of a few simple mechanical tests it is possible to predict the particularities of the plastic response in torsion for both isotropic and initially anisotropic materials. Unlike other previous interpretations of the Swift effects, which were mainly based on crystal plasticity and/or texture evolution, it is explained the occurrence of Swift effects at small to moderate plastic strains. In particular, the very good quantitative agreement between model and data for a strongly anisotropic AZ31–Mg alloy confirm the correlation established in this work between tension–compression asymmetry and Swift effects. Furthermore, it is explained why the sign of the axial plastic strains that develop depends on the twisting direction.     

Heuristic search for a predictive strain-energy function in nonlinear elasticity

In this work, a new, quasi-structural model – bootstrapped eight-chain model – is proposed as a modification to the strain energy of eight-chain model [Arruda, E.M., Boyce, M.C., 1993. A three-dimensional constitutive model for the large stretch behaviour of rubber elastic materials. J. Mech. Phys. Solids 41, 389—412] that invokes the Langevin chain statistics. This development has been led to by our heuristic search into how the strain energy of eight-chain model may be adapted in order to account better for the mechanical behaviour of elastomeric materials in both linear and nonlinear elastic regimes [Treloar, L.R.G., 1944. Stress–strain data for vulcanised rubber under various types of deformation. Trans. Faraday Soc. 40, 59–70]. The eight-chain model appears to produce very similar results in predicting biaxial stress to those of a first stretch-invariant model that gives a good fit in uniaxial extension and, thus, it is shown that the former can not be significantly enhanced within the limitation of the latter. Evaluation of predictive capability for an additive invariant-separated form of strain energy shows that an explicit inclusion of a second stretch-invariant function would not work and that any thus added term ought to be dependent on both the first and second stretch-invariants of deformation tensor, and hints that an improvement is possibly needed at low strain. The composite and filament models [Miroshnychenko, D., Green, W.A., Turner, D.M., 2005. Composite and filament models for the mechanical behaviour of elastomeric materials. J. Mech. Phys. Solids 53 (4), 748–770] have their strain-energy functions in that suggested form and cope very well with predicting the experimental data of Treloar (1944). We use the form of strain energy for the filament model, that proved to be successful, to bootstrap the strain energy of eight-chain model in order to improve the performance of the latter at low strain. Thus, we derive a new model – bootstrapped eight-chain model – that requires only two material parameters – a rubber modulus and a limiting chain extensibility. The proposed model is quasi-structural due to bootstrapping and it retains the best traits and corrects the faults of the eight-chain model, conforming more closely to the classical experimental data of Treloar (1944).     

Mechanical response of a short fiber-reinforced thermoplastic: Experimental investigation and continuum mechanical modeling

The present work can be regarded as a first step toward an integrated modeling of mold filling during injection molding process of polymer composites and the resulting material behavior under service loading conditions. More precisely, the emphasis of the present paper is laid on how to account for local fiber orientation in the ground matrix on the prediction of the mechanical response of the composite at its final solid state. To this end, a set of experiments which captures the mechanical behavior of an injection molded short fiber-reinforced thermoplastic under different strain histories is described. It is shown that the material exhibits complex response mainly due to non-linearity, anisotropy, time/rate-dependence, hysteresis and permanent strain. Furthermore, the relaxed state of the material is characterized by the existence of an equilibrium hysteresis independently of the applied strain rate. A three-dimensional phenomenological model to represent experimentally observed response is developed. The microstructure configuration of the material is simplified and assumed to be entirely represented by a distributed fiber orientation in the ground matrix. In order to account for distributed short fiber orientations in a continuum sense, a concept of (symmetric) generalized structural tensor (tensor of orientation) of second order is adopted. The proposed model is based on assumption that the strain energy function of the composite is given by a linear mixture of the strain energy of each constituent: an isotropic part representing Phase 1 which is essentially related to the ground matrix and an anisotropic part describing Phase 2 which is mainly related to the fibers and the interphase as a whole. Hence, taking into account the fiber content and orientation, the efficiency of the model is assessed and perspectives are drawn.     

Incorporating the effects of fabric in the dilatant double shearing model for planar deformation of granular materials

The objective of this paper is to incorporate the effects of fabric and its evolution into the Dilatant Double Shearing Model [Mehrabadi, M.M., Cowin, S.C., 1978. Initial planar deformation of dilatant granular materials. J. Mech. Phys. Solids 26, 269–284] for granular materials in order to capture the anisotropic behavior and the complex response of granular materials in cyclic shear loading. An important consequence of considering the fabric is that one can have unequal shearing rates along the two slip directions. This property leads to the non-coaxiality of the principal axes of stress and strain rate, which is more appropriate for a material that exhibits initial and induced anisotropy. In addition, we employ a fabric-dependent elasticity tensor with orthotropic symmetry. The model developed in this paper also predicts one of the experimentally observed characteristics of granular materials: the gradual concentration of the contact normals towards the maximum principal stress direction.We implement the constitutive equations into ABAQUS/Explicit by writing a user material subroutine in order to predict the strength anisotropy of granular materials in a plane strain biaxial compression test and investigate the mechanical behavior of granular materials under the cyclic shear loading conditions. The predictions from this model show good quantitative agreement with the experiments of [Park, C.S., 1990. Anisotropy in deformation and strength properties of sands in plane strain compression, Masters Thesis, University of Tokyo; Park, C.S., Tatsuoka, F., 1994. Anisotropic strength and deformation of sands in plane strain compression. In: XIII ICSMFE, New Delhi, India; Okada, N., 1992. Energy dissipation in inelastic flow of cohesionless granular media. Ph.D. Thesis, University of California, San Diego].     

材料三维微结构表征及其晶体塑性有限元模拟

材料的力学性能，尤其是在有限变形下所呈现的宏观各向异性，是材料结构设计和服役寿命考虑的关键因素。由于宏观模型不能较好地反映材料微观结构（晶粒的形貌和取向等）对宏观塑性各向异性的影响，因此，本文建立了能实际反映晶粒形貌的三维Voronoi模型，并基于晶体塑性理论对铝合金在有限变形下的响应进行计算。首先，建立反映材料微结构的代表性体积单元RVE模型进行计算，并与实验结果进行对比验证。然后，以单向拉伸为例，分析了有限变形过程中试件的晶粒形貌和取向分布等微观因素对宏观各向异性演化的影响，并从材料和结构两个层面讨论了微观结构对宏观力学性能的影响。结果表明，本文模型能够反映微观结构对宏观力学性能的影响，为实际生产制造领域构件的力学性能提供可靠的预测。     

Global and local large-deformation response of sub-micron,soft- and hard-particle filled polycarbonate

Since polymers play an increasingly important role in both structural and tribological applications, understanding their intrinsic mechanical response is key. Therefore in the last few decades much effort has been devoted into the development of constitutive models that capture the polymers' intrinsic mechanical response quantitatively. An example is the Eindhoven Glassy Polymer model. In practice most polymers are filled, e.g. with hard particles or fibers, with colorants, or with soft particles that serve as impact modifiers. To characterize the influence of type and amount of filler particles on the intrinsic mechanical response, we designed model systems of polycarbonate with different volume fractions of small, order 100 nm sized, either hard or soft particles, and tested them in lubricated uniaxial compression experiments. To reveal the local effects on interparticle level, three-dimensional representative volume elements (RVEs) were constructed. The matrix material is modeled with the EGP model and the fillers with their individual mechanical properties. It is first shown that (only) 32 particles are sufficient to capture the statistical variations in these systems. Comparing the simulated response of the RVEs with the experiments demonstrates that in the small strain regime the stress is under-predicted since the polymer matrix is modeled by using only one single relaxation time. The yield- and the large strain response is captured well for the soft-particle filled systems while, for the hard-particles at increased filler loadings, the predictions are less accurate. This is likely caused by polymer–filler interactions that result in accelerated physical aging of the polymer matrix close to the surfaces. Modifying the S_a-parameter, that captures the thermodynamic state of the polymer matrix, allows us to correctly predict the macroscopic response after yield. The simulations reveal that all rate-dependencies of the different filled systems originate from that of the polymer matrix. Finally, an onset is presented to predict local and global failure based on critical events on the microlevel, that are likely to cause the over-prediction in the large-strain response of the hard-particle filled systems.