Abstract
Plasticity is a classic hysteresis phenomenon. We represent elasto-plasticity with kinematic strain-hardening for multiaxial systems via the differential inclusiona(dε/dt) − b(dσ/dt) ∊ ∂IK(cσ − dε) (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.
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