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In this paper, an enriched FEM technique is employed for thermo-mechanical contact problem based on the extended finite element method. A fully coupled thermo-mechanical contact formulation is presented in the framework of X-FEM technique that takes into account the deformable continuum mechanics and the transient heat transfer analysis. The Coulomb frictional law is applied for the mechanical contact problem and a pressure dependent thermal contact model is employed through an explicit formulation in the weak form of X-FEM method. The equilibrium equations are discretized by the Newmark time splitting method and the final set of non-linear equations are solved based on the Newton-Raphson method using a staggered algorithm. Finally, in order to illustrate the capability of the proposed computational model several numerical examples are solved and the results are compared with those reported in literature. [ABSTRACT FROM AUTHOR]

This paper proposes the use of a specific combination of discrete and finite element methods for the simulation of systems of deformable bodies in order to reduce the computational cost, when certain assumptions can be made. In particular, the Updated Lagrangian finite element formulation and the central difference time integration method are employed together with certain simplifying assumptions in order to linearize this highly nonlinear contact problem and obtain solutions with realistic computational cost and sufficiently good accuracy. Furthermore, the paper discusses software implementation issues and the advantages that the Java technologies can offer in the development of such engineering applications. [ABSTRACT FROM AUTHOR]

A monolithic numerical solution of a partial differential equation (PDE) model for shear bands, which includes a thermal softening rate dependent plastic flow rule and finite thermal conductivity, is presented. The formulation accounts for large deformation kinematics and includes incrementally objective treatment of the hypoplastic constitutive relations. Regularization is achieved by including finite thermal conductivity, which informs the PDE system of a length scale, governed by competition between shear heating and thermal diffusion. The monolithic solution scheme is then used to eliminate splitting errors during the solution of the discretized system. The scheme is presented in a general, mixed formulation, which allows for many choices of shape functions. We study and compare two elements, which have been implemented with the monolithic nonlinear solver: the Irreducible Shear Band Quad (ISBQ) and the Pian Sumihara Shear Band Quad (PSSBQ). ISBQ employs the same interpolation as an irreducible four node quad while PSSBQ is a mixed, assumed stress element. The algorithmic approximations to the Lie derivative and Jaumann rate of Kirchhoff stress are available in the literature for ISBQ type elements, and are derived in this paper for the PSSBQ. These expressions are used to achieve an incrementally objective formulation. It is found that the PSSBQ converges faster than the ISBQ with mesh refinement, and that the convergence of the ISBQ can be improved with a remeshing procedure. [ABSTRACT FROM AUTHOR]