A new path-following constraint for strain-softening finite element simulations

The application of strain-softening constitutive relations to model the failure modes of real-life structures is faced to numerical difficulties related to instabilities that appear as sharp snap-backs of the structural response. A path-following method has to complement the solution algorithm to achieve convergence despite these critical points. Because of the sharpness of the snap-backs, it is believed essential that the path-following constraint distinguish between a purely elastic unloading and a dissipative path. For that purpose, a new constraint based on the maximal value of the elastic predictor for the yield function is proposed. As it is highly non linear, a specific solution algorithm is required. The robustness of this constraint is illustrated by three applications: the study of crack propagations by means of a cohesive zone model, the failure of a structure submitted to nonlocal damage and the simulation of a nonlocal strain-softening plastic specimen