On homogenization of elasto-plasticity

Plasticity is a classic hysteresis phenomenon. We represent elasto-plasticity with kinematic strain-hardening for multiaxial systems via the differential inclusion a(d?/dt) ? b(d?/dt) ?IK(c? ? d?)???(with a, b, c, d constants ? 0); here IK is the indicator function of a (nonempty) closed convex set K of the space of symmetric 3 ? 3-deviators. We formulate a hyperbolic initial- and boundary-value problem, and provide a well-posedness result. We then assume that the material coefficients rapidly oscillate w.r.t. space, formulate a corresponding two-scale problem, and discuss the homogenization.