hal-01395635
https://polytechnique.hal.science/hal-01395635
https://polytechnique.hal.science/hal-01395635/document
https://polytechnique.hal.science/hal-01395635/file/V4_Revised_Homogenization.pdf
doi:10.1016/j.ijsolstr.2016.02.022
[X] Ecole Polytechnique
[INSTITUT-TELECOM] Institut Mines Télécom
[ENSMP] MINES ParisTech
[CNRS] CNRS - Centre national de la recherche scientifique
[X-LMS] Laboratoire de Mécanique des Solides (LMS)
[X-DEP] Polytechnique
[X-DEP-MECA] Département de mécanique
[ENSMP_LMS] Mécanique des solides (LMS)
[PARISTECH] ParisTech
[PSL] Université Paris sciences et lettres
[UNIV-PARIS-SACLAY] Université Paris-Saclay
[X-SACLAY] X-SACLAY
[ENSMP_DEP_MM] Département Mécanique et Matériaux
[ENSMP-PSL] MINES ParisTech - École nationale supérieure des mines de Paris - PSL
A methodology for the estimation of the effective yield function of isotropic composites
Papadioti, I
Danas, Kostas
Aravas, N.
[PHYS.MECA.SOLID] Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph]
ART
Composite materials
Finite strains
Homogenization
Elasto-plasticity
In this work we derive a general model for N−phase isotropic, incompressible, rate-independent 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 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.
2016
2017-12-21
en
International Journal of Solids and Structures
Elsevier