Fast estimation of localized plasticity and damage by energetic methods

Structural failure often follows the initiation of cracks occurring at corners, free edges or interfaces. Continuum damage mechanics gives quantitative information about such cracking. But when used in a fully coupled manner (with elasticity and plasticity), it leads to costly computations. In order to obtain helpful results for a fine and fast design, we propose to determine localized plasticity and damage by use of local post-calculations, which follow a simple elastic finite element computation. Energetic methods such as Neuber’s, such as the strain energy density or as the complementary energy density methods, are justified for small scale yielding by use of path-independent integrals. They are extended to cyclic loading inducing fatigue and the case of thermal stresses is considered. For plane problems, these methods are completed by the analytical determination of the stress triaxiality along free edges or rigid inclusions. The crack initiation conditions are then quickly estimated by the time-integration of Lemaitre’s damage law. Cal- culations made for a holed plate (plane strain) and for a bi-axial testing specimen (plane stress) validate the meth- ods.