Numerical treatment of small strain single crystal plasticity based on the infeasible primal-dual interior point method

Journal article (2021)

Authors

L. Scheunemann Universität Duisburg-Essen
P.S. Britto Nigro Team Tamas Keviczky - Mechanical, Maritime and Materials Engineering
J. Schröder Universität Duisburg-Essen
Research Group
Team Tamas Keviczky (Mechanical, Maritime and Materials Engineering) (TU Delft)
Crystal plasticity Complex step derivative approximation Consistent tangent formulation Infeasible primal dual interior point method Nonlinear optimization with constraints Numerical Differentiation
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Published Date

2021

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Tamas Keviczky

Abstract

In this contribution, a small strain single crystal plasticity framework in the context of an infeasible primal–dual interior point method (IPDIPM) is discussed with a focus on the numerical treatment. Related to rate-independent algorithms in the field of single-crystal plasticity, the use of the IPDIPM to solve the constrained optimization problem offers the advantage that it handles the naturally arising redundancy in the slip system intrisically through a barrier term. This formulation penalizes the approach of the unfeasible domain, whereas the penalization term gradually approaches zero in the algorithm. This paper focusses on the numerical treatment and presents different tangent operator formulations and compares their convergency behavior in a numerical example.