A finite element formulation based on non-associated plasticity for sheet metal forming

In the present paper, a finite element formulation based on non-associated plasticity is developed. In the constitutive formulation, isotropic hardening is assumed and an evolution equation for the hardening parameter consistent with the principle of plastic work equivalence is introduced. The yield function and plastic potential function are considered as two different functions with functional form as the yield function of Hill [Hill, R., 1948. Theory of yielding and plastic flow of anisotropic metals. Proc. Roy. Soc. A 193, 281–297] or Karafillis–Boyce associated model [Karafillis, A.P. Boyce, M., 1993. A general anisotropic yield criterion using bounds and a transformation weighting tensor. J. Mech. Phys. Solids 41, 1859–1886]. Algorithmic formulations of constitutive models that utilize associated or non-associated flow rule coupled with Hill or Karafillis–Boyce stress functions are derived by application of implicit return mapping procedure. Capabilities in predicting planar anisotropy of the Hill and Karafillis–Boyce stress functions are investigated considering material data of Al2008-T4 and Al2090-T3 sheet samples. The accuracy of the derived stress integration procedures is investigated by calculating iso-error maps.     

A theory of network alteration for the Mullins effect

This paper reports on the development of a new network alteration theory to describe the Mullins effect. The stress-softening phenomenon that occurs in rubber-like materials during cyclic loading is analysed from a physical point of view. The Mullins effect is considered to be a consequence of the breakage of links inside the material. Both filler-matrix and chain interaction links are involved in the phenomenon. This new alteration theory is implemented by modifying the eight-chains constitutive equation of Arruda and Boyce (J. Mech. Phys. Solids 41 (2) (1993) 389). In the present method the parameters of the eight-chains model, denoted C_R and N in the bibliography, become functions of the maximum chain stretch ratio. The accuracy of the resulting constitutive equation is demonstrated on cyclic uniaxial experiments for both natural rubbers and synthetic elastomers.     

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).     

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.     

Modeling of polycrystals using a gradient crystal plasticity theory that includes dissipative micro-stresses

This study investigates thermodynamically consistent dissipative hardening in gradient crystal plasticity in a large-deformation context. A viscoplastic model which accounts for constitutive dependence on the slip, the slip gradient as well as the slip rate gradient is presented. The model is an extension of that due to Gurtin (Gurtin, M. E., J. Mech. Phys. Solids, 52 (2004) 2545–2568 and Gurtin, M. E., J. Mech. Phys. Solids, 56 (2008) 640–662)), and is guided by the viscoplastic model and algorithm of Ekh et al. (Ekh, M., Grymer, M., Runesson, K. and Svedberg, T., Int. J. Numer. Meths Engng, 72 (2007) 197–220) whose governing equations are equivalent to those of Gurtin for the purely energetic case. In contrast to the Gurtin formulation and in line with that due to Ekh et al., viscoplasticity in the present model is accounted for through a Perzyna-type regularization. The resulting theory includes three different types of hardening: standard isotropic hardening is incorporated as well as energetic hardening driven by the slip gradient. In addition, as a third type, dissipative hardening associated with plastic strain rate gradients is included. Numerical computations are carried out and discussed for the large strain, viscoplastic model with non-zero dissipative backstress.     

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.     

Generalized self-consistent estimation of the apparent isotropic elastic moduli and minimum representative volume element size of heterogeneous media

Under investigation is a heterogeneous material consisting of an elastic homogeneous isotropic matrix in which layered elastic isotropic inclusions or pores are embedded. The generalized self-consistent model (GSCM) is extended so as to be capable of estimating the apparent elastic properties of a finite-size specimen smaller than a representative volume element (RVE). The kinematical or static apparent shear modulus is determined as a root of a cubic polynomial equation instead of a quadratic polynomial equation as in the classical GSCM of Christensen and Lo [Christensen, R.M., Lo, K.H., 1979. Solutions for effective shear properties in three phase sphere and cylinder models. J. Mech. Phys. Solids 27, 315–330]. It turns out that the extended GSCM establishes a link between the composite sphere assemblage model (CSAM) of Hashin [Hashin, Z., 1962. The elastic moduli of heterogeneous materials. J. Appl. Mech. 29, 143–150] and the classical GSCM. Demanding that the normalized distance between the kinematical and static apparent moduli of a finite-size specimen be smaller than a certain tolerance, the minimum RVE size is estimated in a closed form.     

Shock enhancement of cellular structures under impact loading: Part II analysis

Numerical simulations of two distinct testing configurations using a Hopkinson bar (pressure bar behind/ahead of the shock front) are performed with an explicit finite element code. It allows us to confirm the observed test data such as velocity and force time histories at the measurement surface. A comparison of the simulated local strain fields during shock front propagation with those measured by image correlation provides an additional proof of the validity of such simulations.Very simple rate insensitive phenomenological constitutive model are used in such simulations. It shows that the shock effect is captured numerically with a basic densification feature. It means that strength enhancement due to shock should not be integrated in the constitutive model of foam-like materials used in industrial FE codes.In order to separate shock enhancement from entire strength enhancement, an improvement of an existing model with easily identifiable parameters for shock enhancement prediction is proposed. For a quick estimate of the shock enhancement level, a simple power law densification model is proposed instead of the classical RPPL model proposed by Reid and co-workers [Tan et al., 2005. Dynamic compressive strength properties of aluminium foams. Part I—experimental data and observations. J. Mech. Phys. Solids 53, 2174-2205]. It is aimed at eliminating the parameter identification uncertainty of the RPPL model. Such an improved model is easily identifiable and gives a good prediction of the shock enhancement level.     

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.     

Overspeed burst of elastoviscoplastic rotating disks – Part I: Analytical and numerical stability analyses

Burst of rotating disks in case of overspeed is investigated. The certification of turbo-engines requires to demonstrate the integrity of disks at higher rotation speeds than the maximum rotation speed reachable in service. The determination of the burst speed by analysis can help to reduce the number of tests required for the certification. This prediction can be established by non-linear stability analyses of finite element simulations. Non-linearities originate from (i) the material behaviour described by elastoviscoplastic constitutive equations, (ii) geometric changes accounted for by the finite strain formulation. In this work, loss of uniqueness and loss of stability criteria from [Hill, R., 1958. A general theory of uniqueness and stability in elastic-plastic solids. J. Mech. Phys. Solids 6, 236–249] are applied. The loss of stability criterion is restricted to the case of rotating disks and compared to several simple widely used material based failure criteria. 3D simulations of rotating metal disks are performed for a given elastoviscoplastic behaviour and the stability criteria are evaluated. The sensitivity of disk stability to material parameters, such as yield criterion, hardening and viscosity is evaluated in the case of a nickel based superalloy.     

Evolution of plastic anisotropy in amorphous polymers during finite straining

The large strain deformation response of amorphous polymers results primarily from orientation of the molecular chains within the polymeric material during plastic straining. Molecular network orientation is a highly anisotropic process, thus the observed mechanical response is strongly a function of the anisotropic state of these materials. Through mechanical testing and material characterization, the nature of the evolution of molecular orientation under different conditions of state of strain is developed. The role of developing anisotropy on the mechanical response of these materials is discussed in the context of assessing the capabilities of several models to predict the state of deformation-dependent response. A three-dimensional rubber elasticity spring system that is capable of capturing the state of deformation dependence of strain hardening is used to develop a tensorial internal state variable model of the evolving anisotropic polymer response. This fully three-dimensional constitutive model is shown to be successfully predictive of the true stress vs. true strain data obtained in our isothermal uniaxial compression and plane strain compression experiments on amorphous polycarbonate (PC) and polymethylmethacrylate (PMMA) at moderate strain rates. A basis is established for providing the polymer designer with the ability to predict the flow strengths and deformation patterns of highly anisotropic materials. A companion paper by Arruda, Boyce, and Quintus-Bosz [in press] shows how the model developed herein is used to predict various anisotropic aspects of the large strain mechanical response of preoriented materials. Additional work has been done to extend the model to include the effects of strain rate and temperature in Arruda, Jayachandran, and Boyce [in press].     

Constitutive and damage model for 63Sn37Pb solder under uniaxial and torsional cyclic loading

A constitutive model with Ohno–Wang kinematic hardening rule is developed and employed to simulate the isothermal cyclic behavior of Sn–Pb solder under uniaxial and torsional loading. An implicit constitutive integration scheme is presented for inelastic flow of solder. Then a modified low cycle fatigue life prediction model is put forward in which the sum of maximum shear strain range and normal strain range based on the critical plane concept is adopted to replace the uniaxial strain range used by Stolkarts et al. [Stolkarts, V., Keer, L.M., Fine, M.E., 1999. Damage evolution governed by microcrack nucleation with application to the fatigue of 63Sn–37Pb solder. J. Mech. Phys. Solids 47, 2451–2468]. Comparison of the experimental results and simulation verifies that the stress strain hysteresis loops and peak stress decline curve of solder can be reasonably modeled over a wide range of loading conditions with implement of damage coupled constitutive model, and the lifetime estimations of 63Sn37Pb solder based on the assumption of microcrack nucleation governed damage is effective to provide a conservative prediction.     

Constitutive model for uniaxial transformation ratchetting of super-elastic NiTi shape memory alloy at room temperature

The transformation ratchetting of super-elastic NiTi shape memory alloy was observed by the uniaxial stress-controlled cyclic tests [Kang, G.Z., Kan, Q.H., Qian, L.M., Liu, Y.J, 2009a. Ratchetting deformation of super-elastic and shape memory NiTi Alloys. Mech. Mater. 41, 139–153]. It is concluded that the NiTi alloy presents apparent ratchetting behaviour, and the ratchetting is collectively caused by the cyclic accumulation of residual induced-martensite and the transformation-induced plastic deformation (i.e., namely transformation ratchetting). Based on the experimental results, a cyclic constitutive model was constructed in the framework of generalized plasticity [Lubliner, J., Auricchio, F., 1996. Generalized plasticity and shape memory alloys. Int. J. Solids Struct. 33, 991–1003] to describe the transformation ratchetting of super-elastic NiTi alloy. The proposed model simultaneously accounts for the evolutions of residual induced-martensite and transformation-induced plastic strain during the stress-controlled cyclic loading by introducing an internal variable z_c, i.e., cumulated induced-martensite volume fraction. The dependence of transformation ratchetting on the applied stress levels and the phase transformation hardening behaviour of the NiTi alloy are also considered in the developed model. The anisotropic phase transformation behaviours of the alloy presented in the tension and compression cases are described by employing a Drucker–Prager-typed transformation surface. It is shown that the simulated results of transformation ratchetting obtained by the proposed model are in good agreement with the corresponding experiments, since the typical features of transformation ratchetting are reasonably captured by the proposed model.     

Distribution based model for the grain boundaries in polycrystalline plasticity

This contribution focuses on the development of constitutive models for the grain boundary region between two crystals, relying on the dislocation based polycrystalline model documented in (Evers, L.P., Parks, D.M., Brekelmans, W.A.M., Geers, M.G.D., 2002. Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation. J. Mech. Phys. Solids 50, 2403–2424; Evers, L.P., Brekelmans, W.A.M., Geers, M.G.D., 2004a. Non-local crystal plasticity model with intrinsic SSD and GND effects. J. Mech. Phys. Solids 52, 2379–2401; Evers, L.P., Brekelmans, W.A.M., Geers, M.G.D., 2004b. Scale dependent crystal plasticity framework with dislocation density and grain boundary effects. Int. J. Solids Struct. 41, 5209–5230). The grain boundary is first viewed as a geometrical surface endowed with its own fields, which are treated here as distributions from a mathematical point of view. Regular and singular dislocation tensors are introduced, defining the grain equilibrium, both in the grain core and at the boundary of both grains. Balance equations for the grain core and grain boundary are derived, that involve the dislocation density distribution tensor, in both its regular and singular contributions. The driving force for the motion of the geometrically necessary dislocations is identified from the pull-back to the lattice configuration of the quasi-static balance of momentum, that reveals the duality between the stress and the curl of the elastic gradient. Criteria that govern the flow of mobile geometrically necessary dislocations (GNDs) through the grain boundary are next elaborated on these bases. Specifically, the sign of the projection of a lattice microtraction on the glide velocity defines a necessary condition for the transmission of incoming GNDs, thereby rendering the set of active slip systems for the glide of outgoing dislocations. Viewing the grain boundary as adjacent bands in each grain with a constant GND density in each, the driving force for the grain boundary slip is further expressed in terms of the GND densities and the differently oriented slip systems in each grain. A semi-analytical solution is developed in the case of symmetrical slip in a bicrystal under plane strain conditions. It is shown that the transmission of plastic slip occurs when the angle made by the slip direction relative to the grain boundary normal is less than a critical value, depending on the ratio of the GND densities and the orientation of the transmitted dislocations.     

A micro-macro approach to rubber-like materials. Part III: The micro-sphere model of anisotropic Mullins-type damage

A micromechanically based non-affine network model for finite rubber elasticity and viscoelasticity was discussed in Parts I and II [Miehe, C., Göktepe, S., Lulei, F., 2004. A micro-macro approach to rubber-like materials. Part I: The non-affine micro-sphere model of rubber elasticity. J. Mech. Phys. Solids 52, 2617-2660; Miehe, C., Göktepe, S., 2005. A micro-macro approach to rubber-like materials. Part II: Viscoelasticity model for polymer networks. J. Mech. Phys. Solids, published on-line, doi:10.1016/j.jmps.2005.04.006.] of this work. In this follow-up contribution, we further extend the micro-sphere network model such that it incorporates a deformation-induced softening commonly referred to as the Mullins effect. To this end, a continuum formulation is constructed by a superimposed modeling of a crosslink-to-crosslink (CC) and a particle-to-particle (PP) network. The former is described by the non-affine elastic network model proposed in Part I. The Mullins-type damage phenomenon is embedded into the PP network and micromechanically motivated by a breakdown of bonds between chains and filler particles. Key idea of the constitutive approach is a two-step procedure that includes (i) the set up of micromechanically based constitutive models for a single chain orientation and (ii) the definition of the macroscopic stress response by a directly evaluated homogenization of state variables defined on a micro-sphere of space orientations. In contrast to previous works on the Mullins effect, our formulation inherently describes a deformation-induced anisotropy of the damage as observed in experiments. We show that the experimentally observed permanent set in stress-strain diagrams is achieved by our model in a natural way as an anisotropy effect. The performance of the model is demonstrated by means of several numerical experiments including the solution of boundary-value problems.     

Three-dimensional cohesive fracture modeling of non-planar crack growth using adaptive FE technique

In this paper, the three-dimensional adaptive finite element modeling is presented for cohesive fracture analysis of non-planer crack growth. The technique is performed based on the Zienkiewicz–Zhu error estimator by employing the modified superconvergent patch recovery procedure for the stress recovery. The Espinosa–Zavattieri bilinear constitutive equation is used to describe the cohesive tractions and displacement jumps. The 3D cohesive fracture element is employed to simulate the crack growth in a non-planar curved pattern. The crack growth criterion is proposed in terms of the principal stress and its direction. Finally, several numerical examples are analyzed to demonstrate the validity and capability of proposed computational algorithm. The predicted crack growth simulation and corresponding load-displacement curves are compared with the experimental and other numerical results reported in literature.     

Two-subsystem thermodynamics for the mechanics of aging amorphous solids

The effect of physical aging on the mechanics of amorphous solids as well as mechanical rejuvenation is modeled with nonequilibrium thermodynamics, using the concept of two thermal subsystems, namely a kinetic one and a configurational one. Earlier work (Semkiv and Hütter in J Non-Equilib Thermodyn 41(2):79–88, 2016) is extended to account for a fully general coupling of the two thermal subsystems. This coupling gives rise to hypoelastic-type contributions in the expression for the Cauchy stress tensor, that reduces to the more common hyperelastic case for sufficiently long aging. The general model, particularly the reversible and irreversible couplings between the thermal subsystems, is compared in detail with models in the literature (Boyce et al. in Mech Mater 7:15–33, 1988; Buckley et al. in J Mech Phys Solids 52:2355–2377, 2004; Klompen et al. in Macromolecules 38:6997–7008, 2005; Kamrin and Bouchbinder in J Mech Phys Solids 73:269–288 2014; Xiao and Nguyen in J Mech Phys Solids 82:62–81, 2015). It is found that only for the case of Kamrin and Bouchbinder (J Mech Phys Solids 73:269–288, 2014) there is a nontrivial coupling between the thermal subsystems in the reversible dynamics, for which the Jacobi identity is automatically satisfied. Moreover, in their work as well as in Boyce et al. (Mech Mater 7:15–33, 1988), viscoplastic deformation is driven by the deviatoric part of the Cauchy stress tensor, while for Buckley et al. (J Mech Phys Solids 52:2355–2377, 2004) and Xiao and Nguyen (J Mech Phys Solids 82:62–81, 2015) this is not the case.     

On the mechanics of mother-of-pearl: A key feature in the material hierarchical structure

Mother-of-pearl, also known as nacre, is the iridescent material which forms the inner layer of seashells from gastropods and bivalves. It is mostly made of microscopic ceramic tablets densely packed and bonded together by a thin layer of biopolymer. The hierarchical microstructure of this biological material is the result of millions of years of evolution, and it is so well organized that its strength and toughness are far superior to the ceramic it is made of. In this work the structure of nacre is described over several length scales. The tablets were found to have wavy surfaces, which were observed and quantified using various experimental techniques. Tensile and shear tests performed on small samples revealed that nacre can withstand relatively large inelastic strains and exhibits strain hardening. In this article we argue that the inelastic mechanism responsible for this behavior is sliding of the tablets on one another accompanied by transverse expansion in the direction perpendicular to the tablet planes. Three dimensional representative volume elements, based on the identified nacre microstructure and incorporating cohesive elements with a constitutive response consistent with the interface material and nanoscale features were numerically analyzed. The simulations revealed that even in the absence of nanoscale hardening mechanism at the interfaces, the microscale waviness of the tablets could generate strain hardening, thereby spreading the inelastic deformation and suppressing damage localization leading to material instability. The formation of large regions of inelastic deformations around cracks and defects in nacre are believed to be an important contribution to its toughness. In addition, it was shown that the tablet junctions (vertical junctions between tablets) strengthen the microstructure but do not contribute to the overall material hardening. Statistical variations within the microstructure were found to be beneficial to hardening and to the overall mechanical stability of nacre. These results provide new insights into the microstructural features that make nacre tough and damage tolerant. Based on these findings, some design guidelines for composites mimicking nacre are proposed.