A space-time finite element method for elasto-plastic shock dynamics

A space-time finite element method (STFEM) for elastoplastic dynamic analysis is proposed in this paper. A weak form of the governing equation which corresponds to the conservation of impulse-momentum (the shockmomentum equation) is established, based on which STFEM equations are derived. A family of linear temporal shape functions is studied, which for linear elasticity, the ensuing STFEM algorithm is equivalent to the Newmark algorithm with gamma = 0.5. Rate-independent plasticity is incorporated into the model. As a numerical example, a cantilever beam under shock loading is analyzed. The results show that the propagation of shock waves is drastically slowed down by the presence of plasticity. Also, because the plastic deformation tends to be localized in the vicinity of the impact, a full transient analysis is essential, in order to accurately determine the locations of the: plastic hinges. (C) 1999 Academic Press.