Numerical solution of perfect plastic problems with contact: part II - numerical realization

This contribution is a continuation of our contribution denoted as PART I, where the discretized contact problem for elasto-perfectly plastic bodies was studied and suitable numerical methods were introduced. In particular, frictionless contact boundary conditions and Hencky’s material model with the von Mises criterion are considered. Here we describe some implementation details and present several numerical examples

A simple and efficient BEM implementation of quasistatic linear visco-elasticity

A simple, yet efficient procedure to solve quasistatic problems of special linear visco-elastic solids at small strains with equal rheological response in all tensorial components, utilizing boundary element method (BEM), is introduced. This procedure is based on the implicit discretisation in time (the so-called Rothe method) combined with a simple "algebraic" transformation of variables, leading to a numerically stable procedure (proved explicitly by discrete energy estimates), which can be easily implemented in a BEM code to solve initial-boundary value visco-elastic problems by using the Kelvin elastostatic fundamental solution only. It is worth mentioning that no inverse Laplace transform is required here. The formulation is straightforward for both 2D and 3D problems involving unilateral frictionless contact. Although the focus is to the simplest Kelvin-Voigt rheology, a generalization to Maxwell, Boltzmann, Jeffreys, and Burgers rheologies is proposed, discussed, and implemented in the BEM code too. A few 2D and 3D initial-boundary value problems, one of them with unilateral frictionless contact, are solved numerically

An adaptive hierarchical domain decomposition method for parallel contact dynamics simulations of granular materials

A fully parallel version of the contact dynamics (CD) method is presented in this paper. For large enough systems, 100% efficiency has been demonstrated for up to 256 processors using a hierarchical domain decomposition with dynamic load balancing. The iterative scheme to calculate the contact forces is left domain-wise sequential, with data exchange after each iteration step, which ensures its stability. The number of additional iterations required for convergence by the partially parallel updates at the domain boundaries becomes negligible with increasing number of particles, which allows for an effective parallelization. Compared to the sequential implementation, we found no influence of the parallelization on simulation results.Comment: 19 pages, 15 figures, published in Journal of Computational Physics (2011

Numerical solution of perfect plastic problems with contact: part I - theory and numerical methods

The contribution deals with a static case of discretized elasto-perfectly plastic problems obeying Hencky’s law in combination with frictionless contact boundary conditions. The main interest is focused on the analysis of the formulation in terms of displacements, limit load analysis and related numerical methods. This covers the study of: i) the dependence of the solution set on the loading parameter ζ, ii) relation between ζ and the parameter α representing the work of external forces, iii) loading process controlled by ζ and by α, iv) numerical methods for solving problems with prescribed value of ζ and α

A coupled finite-volume CFD solver for two-dimensional elasto-hydrodynamic lubrication problems with particular application to rolling element bearings

This paper describes a new computational fluid dynamics methodology for modelling elastohydrodynamic contacts. A finite-volume technique is implemented in the ‘OpenFOAM’ package to solve the Navier-Stokes equations and resolve all gradients in a lubricated rolling-sliding contact. The method fully accounts for fluid-solid interactions and is stable over a wide range of contact conditions, including pressures representative of practical rolling bearing and gear applications. The elastic deformation of the solid, fluid cavitation and compressibility, as well as thermal effects are accounted for. Results are presented for rolling-sliding line contacts of an elastic cylinder on a rigid flat to validate the model predictions, illustrate its capabilities, and identify some example conditions under which the traditional Reynolds-based predictions deviate from the full CFD solution

An adaptive mesh refinement approach for solving nonHertzian elastic contact problems

Semi-analytical methods are a common way of solving non-hertzian contact problems when designing mechanical components. These methods require of the discretization of the domain into a set of pressure elements and their accuracy and computational cost are related to the number of elements in which the domain is discretized. But, while the accuracy increases as the pressure element mesh is refined, the computational cost increases quadratically with the number of pressure elements. So in the great majority of the cases, a commitment between accuracy and computational cost must be achieved. In this work, a new approach has been developed to improve the performance of semi-analytical methods for solving contact problems. This approach uses an adaptive mesh refinement strategy, based on the quadtree decomposition of the domain. As a result, the computational cost decreases, while the accuracy of the method remains constant