Hybrid geometric-dissipative arc-length methods for the quasi-static analysis of delamination problems

This paper presents a class of arc-length methods for the quasi-static analysis of problems involving material and geometric nonlinearities. A constraint equation accounting for geometric and dissipative requirements is adopted: the geometric part refers to the Riks and Crisfield equations, while the dissipative one refers to the dissipated energy. The approach allows for a continuous variation of the nature of the constraint, and a switch criterion is not needed to trace the elastic and the dissipative parts of the equilibrium paths. To illustrate the robustness and the efficiency of the methods, three examples involving geometric and material nonlinearities are discussed.