Homogenization of the Prager model in one-dimensional plasticity

Abstract

We propose a new method for the homogenization of hysteresis models of plasticity. For the one-dimensional wave equation with an elasto-plastic stress-strain relation we derive averaged equations and perform the homogenization limit for stochastic material parameters. This generalizes results of the seminal paper by Franců and Krejčí. Our approach rests on energy methods for partial differential equations and provides short proofs without recurrence to hysteresis operator theory. It has the potential to be extended to the higher dimensional case.

Dispersive Effective Models for Waves in Heterogeneous Media

“…This principle is flexible and can be applied in complex applications, e.g. to another three-scale problem in [13] or to problems with hysteresis in [14,15,16].…”

Homogenization of plasticity equations with two-scale convergence methods

“…The stochastic homogenization of the system was treated in [24] in one space dimension. In this stochastic setting, a problem appears that is closely related to the problems here: for g = g(x, y), the weak convergence of a sequence of functions g η (x) = g(x, χ η (x)) must be analyzed.…”

“…In this stochastic setting, a problem appears that is closely related to the problems here: for g = g(x, y), the weak convergence of a sequence of functions g η (x) = g(x, χ η (x)) must be analyzed. This has been possible in [24] with the notion of two-scale ergodicity. We emphasize that one space dimension permits control of the stress and is therefore very different from the higher dimensional case.…”

Periodic Homogenization of the Prandtl–reuss Model With Hardening

“…This concept of variational solutions, which was already exploited in [29], uses an energy inequality in the characterization of solutions. It will actually turn out to be equivalent to the first concept, but it can be verified more easily for weak limits.…”