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

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

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

Natural Graphite Sheet Heat Sinks with Embedded Heat Pipes

Natural graphite sheet (NGS) is a candidate material for lightweight, high-performance heat sinks. We show that the low through–plane thermal conductivity can be mitigated by using heat pipes. In the measured configuration, the thermal resistance of an NGS heat sink with embedded heat pipes is comparable to that of a geometrically-identical aluminum one. The achieved weight reduction is 37 %. When electrical insulation of a heat sink is not required, soft and conforming NGS does not require thermal grease at the interface between the heat source and the heat sink. The low electrical conductivity of NGS does not lead to a decrease in common mode conducted emissions, but the potential to reduce the radiated emissions was quantified to be 12 to 97 % based on an analogy with antennas. In practical applications, replacing an existing heat sink with a geometrically identical NGS one is not recommended because it limits the achievable improvements in thermal performance, weight, and cost. Instead, we suggest using an optimization algorithm to determine the optimal heat sink geometry

Parameter identification of chaboche material model using indantation test data and inverse approach

In this paper genetic algorithm and sensitivity analysis are used to identify 6 parameters of Chaboche kinematic hardening model using repeated Finite element (FE) simulations of indentation test. Five of them are material constants of Chaboche kinematic hardening model itself. The last one represents the stiffness of the foundation and the indenter. To obtain experimental data indentation test under cyclic loading on universal tensile testing machine was performed. Because for sensitivity analysis to obtain all possible combinations of parameters and its values large number of simulation have to be performed supercomputer Anselm hosted by IT4Innovation has been used. Advantage of using supercomputer is that every simulation could use multiple cores which will reduce computational time. Moreover, since each simulation is independent, computational time could be further reduced by performing multiple simulations at the same time. It is clear from the comparison of both methods that the genetic algorithm is very good choice for the parameter estimation

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