An adaptive wavelet-Galerkin method for an elastic-plastic-damage constitutive model: 1D problem Original Research Article

We present a wavelet-Galerkin method for the analysis of elastic-plastic-damage systems. Juʹs model (J.W. Ju, Int. J. Solids Struct. 25 (1989) 803) is explicitly considered and numerically tested but the method applies equally well to a broad range of damage-mechanics models. A three-step elastic-predictor, plastic-corrector, damage-corrector strategy is the core of the proposed approach. We use a displacement approach with wavelet interpolating functions instead of classical polynomials. This allows to clearly locate those sites in the system where damage is taking place, thanks to the high-pass filtering action operated by the wavelets. This opens the way to inexpensive self-adaptive strategies that are introduced and preliminary tested herein.