2014/12/30 by Roubicek, Tomas, Panagiotopoulos, Christos, Mantic, Vladislav
#35K85 #49S05 #65Z05 #74C05 #74M15 #74R20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1412.8593
The quasistatic rate-independent evolution of a delamination at small strains in the so-called mixed mode, i.e.~distinguishing opening (Mode I) from shearing (Mode II) is rigorously analyzed in the context of a concept of stress-driven local solutions. The model has separately convex stored energy and is associative, namely the 1-homogeneous potential of dissipative force driving the delamination depends only on rates of internal parameters. An efficient fractional-step-type semi-implicit discretisation in time is shown to converge to specific, stress-driven like) local solutions that may approximately obey the maximum-dissipation principle. Making still a spatial discretisation, this convergence as well as relevancy of such solution concept are demonstrated on a nontrivial 2-dimensional example.