Elastoplastic models and oscillators solved by a Lie-group differential algebraic equations method

Author-Highlights
• Index-one di erential algebraic equations are derived for plasticity equations.
• A Lie-group GL(n,R)GL(n,R) algorithm is developed.
• A Lie-group di erential algebraic equations (LGDAE) method is developed.
• Yield-surface can be preserved long-term.
• Elastoplastic oscillator and frictional oscillator are solve by the LGDAE.

In this paper, the viewpoint of non-linear complementarity problem (NCP) is adopted to derive a system of index-one differential algebraic equations (DAEs) for elastoplastic models, by recasting the complementary trio to an algebraic equation through the Fischer–Burmeister NCP-function. Then, we develop a novel algorithm based on the Lie-group GL(n,R)GL(n,R) to iteratively solve the resultant DAEs at each time marching step. The Lie-group differential algebraic equations (LGDAE) method is convergent very fast, rendering efficient numerical schemes which can long-term preserve the yield-surface for plasticity models, without resorting on two-phase equations and on-off switching criteria. Several examples, including two non-linear elastoplastic oscillators whose restoring forces are modeled by elastoplastic constitutive equations, are used to assess the performance of the presently developed index-one formulation of elastoplasticity and test the efficiency and accuracy of LGDAE.