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Erschienen in:
2018 | OriginalPaper | Buchkapitel
10. An Example of a Nonlinear Problem: Homogenization of Plasticity and Limit Loads
verfasst von : Leonid Berlyand, Volodymyr Rybalko
Erschienen in: Getting Acquainted with Homogenization and Multiscale
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Abstract
This chapter provides an example of a nonlinear two-scale problem that we study via a Γ-convergence type technique, which was introduced in Chapter 9. We consider a model of plastic deformations and study the asymptotic behavior of the so-called limit loads. We are not directly using the classical Γ-convergence approach (presented in Chapter 9) but rather develop a different technique inspired by Γ-convergence. In order to obtain an optimal lower bound, which is typically the most challenging part in the Γ-convergence approach, we use the convex duality approach. This parallels with the study of linear conductivity problem from Chapter 7 which also uses the idea of convex duality.