The nonlinear elastic response of suspensions of rigid inclusions in rubber: II—A simple explicit approximation for finite-concentration suspensions

Lopez-Pamies, Oscar; Goudarzi, Taha; Danas, Kostas

doi:10.1016/j.jmps.2012.08.013

Cited by 88 publications

(104 citation statements)

References 43 publications

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“…The periodic unit cell is a cube with edge size L and is constructed using the method presented by Segurado and Llorca [39] (see also [10]) and extended to polydisperse inclusion distributions by Lopez-Pamies et al [21]. The virtual microstructure contains a dispersion of a sufficiently large number of non-overlapping spheres of uniform (monodisperse) or different (polydisperse) size.…”

Section: Unit Cell Finite Element Calculations and Assessment Of The mentioning

confidence: 99%

“…For the two-phase composite and for c (2) ≤ 0.20 monodisperse spheres are used; for higher volume fractions polydisperse (variable size) distributions are used. In the present study, the two-phase polydisperse approach of Lopez-Pamies et al [21] is readily extended to obtain virtual microstructures with three-phases or more. For instance, denoting the matrix phase with 1 and the two inclusion phases with 2 and 3, the extension is straightforward and requires the continuous alternation of spheres of phase 2 and spheres of phase 3 during the RSA process.…”

Section: Unit Cell Finite Element Calculations and Assessment Of The mentioning

confidence: 99%

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A methodology for the estimation of the effective yield function of isotropic composites

Papadioti

Danas

Aravas

2016

International Journal of Solids and Structures

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In this work we derive a general model for N −phase isotropic, incompressible, rateindependent elasto-plastic materials at finite strains. The model is based on the nonlinear homogenization variational (or modified secant) method which makes use of a linear comparison composite (LCC) material to estimate the effective flow stress of the nonlinear composite material. The homogenization approach leads to an optimization problem which needs to be solved numerically for the general case of a N −phase composite. In the special case of a two-phase composite an analytical result is obtained for the effective flow stress of the elasto-plastic composite material. Next, the model is validated by periodic three-dimensional unit cell calculations comprising a large number of spherical inclusions (of various sizes and of two different types) distributed randomly 1 in a matrix phase. We find that the use of the lower Hashin-Shtrikman bound for the LCC gives the best predictions by comparison with the unit cell calculations for both the macroscopic stress-strain response as well as for the average strains in each of the phases. The formulation is subsequently extended to include hardening of the different phases. Interestingly, the model is found to be in excellent agreement even in the case where each of the phases follows a rather different hardening response.Keywords: Homogenization; Elasto-plasticity; Composite materials; Finite strains * Corresponding author. Fax: +30 2421 074009. E-mail addresses: aravas@uth.gr (N. Aravas), kdanas@lms.polytechnique.fr (K. Danas). 1 IntroductionThe present work deals with the analytical and numerical estimation of the effective as well as the phase average response of N−phase incompressible isotropic elasto-plastic metallic composites. Special attention is given to particulate microstructures, i.e., composite materials which can be considered to comprise a distinct matrix phase and an isotropic distribution of spherical particles [46] (or in a more general setting an isotropic distribution of phases [45]). In the present study, the particles are considered to be stiffer than the matrix phase, which is the case in most metallic materials of interest, such as TRIP steels, dual phase steels, aluminum alloys and others. Such materials, usually contain second-phase particles (e.g., intermetallics, carbon particles) or just second and third phase variants (e.g., retained austenite, bainite, martensitic phases). In addition, these phases/particles tend to reinforce the yield strength of the composite while they usually have different strength and hardening behavior than the host matrix phase.In the literature of nonlinear homogenization there exists a large number of studies for twophase composite materials. The reader is referred to Ponte Castañeda and Suquet [33], Ponte Castañeda [32], Idiart et al. [15], and Idiart [16] for a review of the nonlinear homogenization schemes such as the ones used in the present work and relevant estimates. Nonetheless, very few studies exist in the conte...

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Section: Unit Cell Finite Element Calculations and Assessment Of The mentioning

confidence: 99%

Section: Unit Cell Finite Element Calculations and Assessment Of The mentioning

confidence: 99%

A methodology for the estimation of the effective yield function of isotropic composites

Papadioti

Danas

Aravas

2016

International Journal of Solids and Structures

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“…This is achieved by use of an Random Sequential Adsorption (RSA) algorithm as described in Lopez-Pamies et al (2013). In Fig.2, we show three different realizations comprising 30 monodisperse voids with a total initial porosity f 0 = 5% 4 .…”

Section: Assessment Of the Mvarx Model With Fem Simulationsmentioning

confidence: 99%

A homogenization model for porous ductile solids under cyclic loads comprising a matrix with isotropic and linear kinematic hardening

Cheng

Danas

Constantinescu

et al. 2017

International Journal of Solids and Structures

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International audienceIn this work, we propose an semi-analytical micromechanical model to study the elasto-plastic response of porous materials subjected to cyclic loading with isotropic and linear kinematic hardening at finite strains. To this end, we use an approximate but numerically efficient decoupled homogenization strategy between the elastic and plastic parts. The resulting effective back stress in the porous solid, similar to the macroscopic stress and plastic strain, has non-zero hydrostatic terms and depends on the porosity, the void shape and orientation as a result of the homogenization process. Subsequently, a complete set of equations is defined to describe the evolution of the microstructure, i.e., void volume fraction (porosity), (ellipsoidal) void shape and orientation both in the elastic and the plastic regimes. The model is then numerically implemented in a general purpose user-material subroutine. Full field finite element simulations of multi-void periodic unit cells are used to assess the predictions of the proposed model. The latter is found to be in good qualitative and quantitative agreement with the finite element results for most of the loading types, hardening parameters and porosities considered in this study, but is less accurate for very small porosities. The combined analytical and numerical study shows that elasticity is an important mechanism for porosity ratcheting in addition to strain hardening. Specifically, in order to recover the main qualitative features of porosity ratcheting for all cyclic loads considered in the present study, it is shown to be critical to take into account the evolution of the microstructure not only during the plastic loading, as is the usual hypothesis, but also during elastic loading. Finally, the effect of isotropic and linear kinematic hardening is found to be highly non-monotonic and non-trivial upon porosity ratcheting for most cases considered here

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“…The analysis of random composites with a high volume fraction of spherical particles, even though theoretically possible (see for instance Lopez-Pamies et al (2013), albeit at lower particle volume fractions), is beyond the scope of current numerical tools for two reasons: the analysis will require (i) the modelling of large representative volume elements and many millions of degrees of freedom to adequately represent the porous matrix and the particles and (ii) the inclusion of the very thin matrix films in between particles that are touching each other; accurate FE modelling of the deformation of such thin porous films that undergo very large local deformations further complicates the FE modelling. A more appropriate discrete particle model is presented in the following section that is free of such disadvantages.…”

Section: Summary Of Predictions For the Periodic Compositesmentioning

confidence: 99%

Deformation mechanisms of idealised cermets under multi-axial loading

Bele

Goel

Pickering

et al. 2017

Journal of the Mechanics and Physics of Solids

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The response of idealised cermets comprising approximately 60% by volume steel spheres in a Sn/Pb solder matrix is investigated under a range of axisymmetric compressive stress states. Digital volume correlation (DVC) analysis of X-ray microcomputed tomography scans (μ-CT), and the measured macroscopic stress-strain curves of the specimens revealed two deformation mechanisms. At low triaxialities the deformation is granular in nature, with dilation occurring within shear bands. Under higher imposed hydrostatic pressures, the deformation mechanism transitions to a more homogeneous incompressible mode. However, DVC analyses revealed that under all triaxialities there are regions with local dilatory and compaction responses, with the magnitude of dilation and the number of zones wherein dilation occurs decreasing with increasing triaxiality. Two numerical models are presented in order to clarify these mechanisms: (i) a periodic unit cell model comprising nearly rigid spherical particles in a porous metal matrix and (ii) a discrete element model comprising a large random aggregate of spheres connected by non-linear normal and tangential "springs". The periodic unit cell model captured the measured stress-strain response with reasonable accuracy but under-predicted the observed dilation at the lower triaxialities, because the kinematic constraints imposed by the skeleton of rigid particles were not accurately accounted for in this model. By contrast, the discrete element model captured the kinematics and predicted both the overall levels of dilation and the simultaneous presence of both local compaction and dilatory regions with the specimens. However, the levels of dilation in this model are dependent on the assumed contact law between the spheres. Moreover, since the matrix is not explicitly included in the analysis, this model cannot be used to predict the stress-strain responses. These analyses have revealed that the complete constitutive response of cermets depends both on the kinematic constraints imposed by the particle aggregate skeleton, and the constraints imposed by the metal matrix filling the interstitial spaces in that skeleton.

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The nonlinear elastic response of suspensions of rigid inclusions in rubber: II—A simple explicit approximation for finite-concentration suspensions

Cited by 88 publications

References 43 publications

A methodology for the estimation of the effective yield function of isotropic composites

A methodology for the estimation of the effective yield function of isotropic composites

A homogenization model for porous ductile solids under cyclic loads comprising a matrix with isotropic and linear kinematic hardening

Deformation mechanisms of idealised cermets under multi-axial loading

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