A TFETI Domain Decomposition Solver for Elastoplastic Problems

We propose an algorithm for the efficient parallel implementation of elastoplastic problems with hardening based on the so-called TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method. We consider an associated elastoplastic model with the von Mises plastic criterion and the linear isotropic hardening law. Such a model is discretized by the implicit Euler method in time and the consequent one time step elastoplastic problem by the finite element method in space. The latter results in a system of nonlinear equations with a strongly semismooth and strongly monotone operator. The semismooth Newton method is applied to solve this nonlinear system. Corresponding linearized problems arising in the Newton iterations are solved in parallel by the above mentioned TFETI domain decomposition method. The proposed TFETI based algorithm was implemented in Matlab parallel environment and its performance was illustrated on a 3D elastoplastic benchmark. Numerical results for different time discretizations and mesh levels are presented and discussed and a local quadratic convergence of the semismooth Newton method is observed

Matlab parallel codes for 3D slope stability benchmarks

This contribution is focused on a description of implementation details for solver related to the slope stability benchmarks in 3D. Such problems are formulated by the standard elastoplastic models containing the Mohr-Coulomb yield criterion and by the limit analysis of collapse states. The implicit Euler method and higher order finite elements are used for discretization. The discretized problem is solved by non-smooth Newton-like methods in combination with incremental methods of limit load analysis. In this standard approach, we propose several innovative techniques. Firstly, we use recently developed sub-differential based constitutive solution schemes. Such an approach is suitable for non-smooth yield criteria, and leads better return-mapping algorithms. For example, a priori decision criteria for each return-type or simplified construction of consistent tangent operators are applied. The parallel codes are developed in MATLAB using Parallel Computing Toolbox. For parallel implementation of linear systems, we use the TFETI domain decomposition method. It is a non-overlapping method where the Lagrange multipliers are used to enforce continuity on the subdomain interfaces and satisfaction of the Dirichlet boundary conditions

An efficient feti based solver for elasto-plastic problems of mechanics

This paper illustrates how to implement effectively solvers for elasto-plastic problems. We consider the time step problems formulated by nonlinear variational equations in terms of displacements. To treat nonlinearity and nonsmoothnes we use semismooth Newton method. In each Newton iteration we have to solve linear system of algebraic equations and for the numerical solution of the linear systems we use TFETI algorithm. In our benchmark we compute von Misses plasticity with isotropic hardening and use return mapping concept

Scalability Improvement of the Projected Conjugate Gradient Method used in FETI Domain Decomposition Algorithms

This report summarizes the results of the scalability improvements of the algorithms used in Total FETI (TFETI). A performance evaluation of two new techniques is presented in this report: (1) a novel pipelined implementation of CG method in PETSc and (2) a MAGMA LU solver running on following many-cores accelerators: GPU Nvidia Tesla K20m and Intel MIC Xeon Phi 5110P

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

An improved return-mapping scheme for nonsmooth yield surfaces: PART I - the Haigh-Westergaard coordinates

The paper is devoted to the numerical solution of elastoplastic constitutive initial value problems. An improved form of the implicit return-mapping scheme for nonsmooth yield surfaces is proposed that systematically builds on a subdifferential formulation of the flow rule. The main advantage of this approach is that the treatment of singular points, such as apices or edges at which the flow direction is multivalued involves only a uniquely defined set of non-linear equations, similarly to smooth yield surfaces. This paper (PART I) is focused on isotropic models containing: $a)$ yield surfaces with one or two apices (singular points) laying on the hydrostatic axis; $b)$ plastic pseudo-potentials that are independent of the Lode angle; $c)$ nonlinear isotropic hardening (optionally). It is shown that for some models the improved integration scheme also enables to a priori decide about a type of the return and investigate existence, uniqueness and semismoothness of discretized constitutive operators in implicit form. Further, the semismooth Newton method is introduced to solve incremental boundary-value problems. The paper also contains numerical examples related to slope stability with available Matlab implementation.Comment: 25 pages, 10 figure

How to simplify return-mapping algorithms in computational plasticity: part 2 –implementation details and experiments

The paper is devoted to numerical solution of a small-strain quasi-static elastoplastic problem. It is considered an isotropic model containing the Drucker-Prager yield criterion, a non-associative flow rule and a nonlinear hardening law. The problem is discretized by the implicit Euler and finite element methods. It is used an improved return-mapping scheme introduced in ”PART 1” and the semismooth Newton method. Algorithmic solution is described and efficiency of the improved scheme is illustrated on numerical examples