Wavelet Based Methods in Elastoplasticity and Damage Analysis

In this work we review some applications of wavelet bases for the discretization of non linear problems arising in engineering materials. In particular, we will consider aWavelet-Galerkin method coupling with interpolating bases for the numerical treatement of elastoplasticity problems. Here, we use an elastic predictor/ plastic corrector method in terms of a stress correction. This correction has to be done pointwise. We use interpolatory wavelets in the correction step and perform (fast) change of bases to switch between the different representations. We show the basic properties of the new numerical approach by some numerical test both in dynamical case. Moreover,we consider the possibility to state adaptive algorithms for the computation of the plastic wave. A simple one dimensional problem is used, both in hardening and softening case, for numerical test.