Energy consistent algorithms for dynamic finite deformation plasticity

This paper addresses the theoretical development and numerical implementation of energy consistent algorithms for dynamic elastoplasticity, emphasizing finite strain constitutive formulations so that unconditional stability of the algorithms is assured even in the fully nonlinear regime. The key concept behind energy consistency is the requirement that the discretized system obey an a priori stability estimate, which may be derived in general using the first and second laws of thermodynamics. This approach to computational dynamic plasticity differs from typical application of traditional algorithms (such as Newmark or Hilber–Hughes–Taylor- α methods), where local time integration schemes for plasticity laws are developed somewhat independently from the global time integration scheme for the equations of motion, without explicit consideration of thermodynamical restrictions. Two algorithms based on both additive and multiplicative finite deformation plasticity model are formulated within the energy consistent framework. Both algorithms possess the desirable feature of nonlinear stability of previous energy–momentum algorithms for elastodynamics.