On homogenization of elasto-plasticity
Augusto Visintin · Journal of Physics Conference Series · 2005
Plasticity is a classic hysteresis phenomenon. We represent elasto-plasticity with kinematic strain-hardening for multiaxial systems via the differential inclusion a (dε/d t ) − b (dσ/d t ) ∊ ∂ I K ( c σ − d ε) (with a , b , c , d constants ≥ 0); here I K 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.