A computational approach for thermo-elasto-plastic frictional contact based on a monolithic formulation using non-smooth nonlinear complementarity functions

Abstract

A new monolithic solution scheme for thermo-elasto-plasticity and thermo-elasto-plastic frictional contact with finite deformations and finite strains is presented. A key feature is the reformulation of all involved inequality constraints, namely those of Hill's orthotropic yield criterion as well as the normal and tangential contact constraints, in terms of non-smooth nonlinear complementarity functions. Using a consistent linearization, this system of equations can be solved with a non-smooth variant of Newton's method. A quadrature point-wise decoupled plastic constraint enforcement and the use of so-called dual basis functions in the mortar contact formulation allow for a condensation of all additionally introduced variables, thus resulting in an efficient formulation that contains discrete displacement and temperature degrees of freedom only, while, at the same time, an exact constraint enforcement is assured. Numerical examples from thermo-plasticity, thermo-elastic frictional contact and thermo-elasto-plastic frictional contact demonstrate the wide range of applications covered by the presented method.

Nodally integrated thermomechanical RKPM: Part II—generalized thermoelasticity and hyperbolic finite-strain thermoplasticity

“…11 are L 0 = 5.334 cm, a 0 = 0.6298 cm, and a 1 = 0.6413 cm. 3 m/s with the time step t = 1 × 10 −8 s. The maximum value of the equivalent plastic strain in this study is close to the numerical results by other methods [27,46].…”

“…Figure 14 shows the evolution of the radius at the center of the bar and the force-displacement relationship, along with experimental data. It can be seen that RKPM agrees with the reference FEM results (denoted as Seitz et al) [46], and the experimental data in [42]. For the reduction in radius, RKPM is in better agreement with experimental data than the reference.…”

“…For thermoplasticity, we decompose the free energy function into an elastic energy φ e , a plastic energy φ p due to work hardening, and thermal energy φ θ following [46]:…”

A mortar finite element approach for point, line, and surface contact

“…[6][7][8][9][10][11] These methods have already been successfully extended to resolve complex interface phenomena such as wear, [12][13][14] lubrication, 15 and thermal effects. 16,17 Despite the superior robustness of mortar methods, their applicability is strongly restricted by the requirement of smooth geometries (ie, surface-to-surface contact). From an illustrative, slightly unmathematical perspective, this is due to their weak enforcement of the contact constraints, which results in a surface-based weighting of the gap function.…”

A multi-scale FEM-BEM formulation for contact mechanics between rough surfaces

“…Moreover, it is prone to be extended for the solution of nonlinear multi-field problems involved in heat transfer or in reaction-diffusion systems [32,33,34], for which the boundary element method has not been applied so far. Last but not least, new robust contact discretization schemes and solution strategies have been advanced within the framework of the FEM in recent years, including nonlinear thermomechanics and wear [35,36,37,38,39].…”