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This paper deals with the computational modeling and numerical simulation of contact problems at finite deformations using the finite element method. Quasi-static and dynamic problems are considered and two particular frictional conditions, full stick friction and frictionless cases, are addressed. Lagrange multipliers and regularized formulations of the contact problem, such as penalty or augmented Lagrangian methods, are avoided and a new direct elimination method is proposed. Conserving algorithms are also introduced for the proposed formulation for dynamic contact problems. An assessment of the performance of the resulting formulation is shown in a number of selected benchmark tests and numerical examples, including both quasi-static and dynamic contact problems under full stick friction and frictionless contact conditions. Conservation of key discrete properties exhibited by the time stepping algorithm used for dynamic contact problems is also shown in an example. [ABSTRACT FROM AUTHOR]

This paper investigates the computational performance of S-CLAY1S constitutive model by varying its yield function equation. S-CLAY1S is an advanced anisotropic elasto-plastic model that has been developed based on the extension of conventional critical state theory. In addition to modified Cam-Clay׳s hardening law, S-CLAY1S also accounts for inherent and evolving plastic anisotropy, interparticle bonding and degradation of bonds during plastic straining. A modified Newton–Raphson stress update algorithm has been adopted for the implementation of the model and it was found that the algorithm׳s convergence performance is sensitive to the expression of the yield function. It is shown that for an elasto-plastic model which is developed based on the critical state theory, it is possible to improve the performance of the numerical implementation by changing the form of the yield function. The results of this work can provide a new perspective for computationally cost-effective implementation of complex constitutive models in finite element analysis that can yield in more efficient boundary value level simulations. [ABSTRACT FROM AUTHOR]