Numerical Simulation of Elastic-Plastic Non-Conforming Contact

Abstract

A fast algorithm for elastic-plastic non-conforming contact simulation is presented in this work. While the elastic response of a material subjected to load application is reversible, plasticity theory describes the irreversible behavior of the material in reaction to loading beyond the limit of elastic domain. Therefore, elastic-plastic response of contacting bodies to loading beyond yield strength is needed to assess the load-carrying capacity of the mechanical contact. The modern approach in simulating elastic-plastic contact is based on the algorithm originally proposed by Mayeur, (Mayeur, 1996), employing Betti’s reciprocal theorem. Although Mayeur developed a model for the three-dimensional problem, numerical implementation was restricted to two-dimensional case, due to lack of formulas for the influence coefficients. Problem generalization is due to Jacq, (Jacq, 2001), and to Jacq et al. (Jacq et al., 2002), who advanced a complete semi-analytical formulation for the three-dimensional elastic-plastic contact. The algorithm was later refined by these authors, (Wang & Keer, 2005), who improved the convergence of residual and elastic loops. The main idea of their Fast Convergence Method (FCM) is to use the convergence values for the current loop as initial guess values for the next loop. This approach reduces the number of iterations if the loading increments are small. Nelias, Boucly, and Brunet, (Nelias et al., 2006), further improved the convergence of the residual loop. They assessed plastic strain increment with the aid of a universal algorithm for integration of elastoplasticity constitutive equations, originally proposed by Fotiu and Nemat-Nasser, (Fotiu & Nemat-Nasser, 1996), as opposed to existing formulation, based on Prandtl-Reuss equations, (Jacq, 2001). As stated in (Nelias et al., 2006), this results in a decrease of one order of magnitude in the CPU time. Influence of a tangential loading in elastic-plastic contact was investigated by Antaluca, (Antaluca, 2005). Kinematic hardening was added by Chen, Wang, Wang, Keer, and Cao, (Chen et al.,2008), who advanced a three-dimensional numerical model for simulating the repeated rolling or sliding contact of a rigid sphere over an elastic-plastic half-space. The efficiency of existing elastic-plastic contact solvers, (Jacq et al., 2002; Wang & Keer, 2005) is impaired by two shortcomings. Firstly, the algorithms are based on several levels of iteration, with the innermost level having a slow convergence. Secondly, the effect of a three-dimensional distribution in a three-dimensional domain, namely residual stresses related to plastic strains, is computed using two-dimensional spectral algorithms.