JUSTIFICATION OF HOMOGENIZATION IN VISCOPLASTICITY: FROM CONVERGENCE ON TWO SCALES TO AN ASYMPTOTIC SOLUTION IN L2(Ω)

Abstract

A homogenized material model can be used effectively for simulation, if the difference of the solutions of this model and the microscopic model converges to zero in a strong norm when the microstructure is scaled. The second author recently showed for the quasistatic initial-boundary value problem with internal variables modeling an inelastic solid body Ω at small strain that this convergence holds in an averaged sense over phase shifts of the microstructure. Based on this result, we construct an asymptotic solution, which converges to the solution of the microscopic problem in the L2(Ω)-norm, thus avoiding the averaging.