A gradient-enhanced damage approach for viscoplastic thin-shell structures subjected to shock waves

A finite element model of gradient-enhanced damage viscoplasticity for dynamic analysis of thin-walled shell structures is proposed. To take void nucleation and growth into account, the free-energy function is enhanced by introducing a non-local damage term, which is defined in terms of a new non-local variable and a local damage parameter. Local constitutive laws considering viscoplastic behavior, isotropic hardening and isotropic ductile damage leading to softening are used. The performance of the proposed model is demonstrated through numerical simulations of several examples including shock-wave loaded plates.