The particle finite element method (PFEM) in thermo-mechanical problems

Abstract

The aim of this work is to develop a numerical framework for accurately and robustly simulating the different conditions exhibited by thermo-mechanical problems. In particular, the work will focus on the analysis of problems involving large strains, rotations, multiple contacts, large boundary surface changes, and thermal effects. The framework of the numerical scheme is based on the particle finite element method (PFEM) in which the spatial domain is continuously redefined by a distinct nodal reconnection, generated by a Delaunay triangulation. In contrast to classical PFEM calculations, in which the free boundary is obtained by a geometrical procedure (a - shape method), in this work, the boundary is considered as a material surface, and the boundary nodes are removed or inserted by means of an error function. The description of the thermo-mechanical constitutive model is based on the concepts of large strains plasticity. The plastic flow condition is assumed nearly incompressible, so a u-p mixed formulation, with a stabilization of the pressure term via the polynomial pressure projection, is proposed. One of the novelties of this work is the use of a combination between the isothermal split and the so-called IMPL-EX hybrid integration technique to enhance the robustness and reduce the typical iteration number of the fully implicit Newton–Raphson solution algorithm. The new set of numerical tools implemented in the PFEM algorithm, including new discretization techniques, the use of a projection of the variables between meshes, and the insertion and removal of points allows us to eliminate the negative Jacobians present during large deformation problems, which is one of the drawbacks in the simulation of coupled thermo-mechanical problems. Finally, two sets of numerical results in 2D are stated. In the first one, the behavior of the proposed locking-free element type and different time integration schemes for thermo-mechanical problems is analyzed. The potential of the method for modeling more complex coupled problems as metal cutting and metal forming processes is explored in the last example.