On Static and Evolutionary Homogenization in Crystal Plasticity for Stratified Composites

Davoli, Elisa; Kreisbeck, Carolin

doi:10.1007/978-3-031-04496-0_7

Cited by 4 publications

(1 citation statement)

References 25 publications

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“…The mathematical literature on high-contrast materials is vast. To keep our presentation concise, we only point out that, besides results for stratified elastoplastic composites [14,15,22,25], the only additional available contributions in the inelastic setting concern the study of brittle fracture problems [5,6,42]. For the modeling of nonlinear elastic high-contrast composites we single out the works [10,13].…”

Section: Introductionmentioning

confidence: 99%

Homogenization of high-contrast media in finite-strain elastoplasticity

Davoli¹,

Gavioli²,

Pagliari³

2023

Preprint

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This work is devoted to the analysis of the interplay between internal variables and high-contrast microstructure in inelastic solids. As a concrete case-study, by means of variational techniques, we derive a macroscopic description for an elastoplastic medium. Specifically, we consider a composite obtained by filling the voids of a periodically perforated stiff matrix by soft inclusions. We study the Γ-convergence of the related energy functionals as the periodicity tends to zero. The main challenge is posed by the lack of coercivity brought about by the degeneracy of the material properties in the soft part. We prove that the Γ-limit, which we compute with respect to a suitable notion of convergence, is the sum of the contributions resulting from each of the two components separately. Eventually, convergence of the energy minimizing configurations is obtained.

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Section: Introductionmentioning

confidence: 99%

Homogenization of high-contrast media in finite-strain elastoplasticity

Davoli¹,

Gavioli²,

Pagliari³

2023

Preprint

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A homogenization result in finite plasticity

Davoli,

Gavioli,

Pagliari

2024

Calc. Var.

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We carry out a variational study for integral functionals that model the stored energy of a heterogeneous material governed by finite-strain elastoplasticity with hardening. Assuming that the composite has a periodic microscopic structure, we establish the $$\Gamma $$ Γ -convergence of the energies in the limiting of vanishing periodicity. The constraint that plastic deformations belong to $$\textsf{SL}(3)$$ SL ( 3 ) poses the biggest hurdle to the analysis, and we address it by regarding $$\textsf{SL}(3)$$ SL ( 3 ) as a Finsler manifold.

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