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A robust explicit integration of elasto-plastic constitutive models, based on simple subincrement size estimation

Miroslav Halilovic (Faculty of Mechanical Engineering, University of Ljubljana, Ljubljana, Slovenia)
Bojan Starman (Faculty of Mechanical Engineering, University of Ljubljana, Ljubljana, Slovenia)
Marko Vrh (Faculty of Mechanical Engineering, University of Ljubljana, Ljubljana, Slovenia)
Boris Stok (Faculty of Mechanical Engineering, University of Ljubljana, Ljubljana, Slovenia)

Engineering Computations

ISSN: 0264-4401

Article publication date: 7 August 2017

Abstract

Purpose

The purpose of this study, which is designed for the implementation of models in the implicit finite element framework, is to propose a robust, stable and efficient explicit integration algorithm for rate-independent elasto-plastic constitutive models.

Design/methodology/approach

The proposed automatic substepping algorithm is founded on an explicit integration scheme. The estimation of the maximal subincrement size is based on the stability analysis.

Findings

In contrast to other explicit substepping schemes, the algorithm is self-correcting by definition and generates no cumulative drift. Although the integration proceeds with maximal possible subincrements, high level of accuracy is attained. Algorithmic tangent stiffness is calculated in explicit form and optionally no analytical second-order derivatives are needed.

Research limitations/implications

The algorithm is convenient for elasto-plastic constitutive models, described with an algebraic constraint and a set of differential equations. This covers a large family of materials in the field of metal plasticity, damage mechanics, etc. However, it cannot be directly used for a general material model, because the presented algorithm is convenient for solving a set of equations of a particular type.

Practical implications

The estimation of the maximal stable subincrement size is computationally cheap. All expressions in the algorithm are in explicit form, thus the implementation is simple and straightforward. The overall performance of the approach (i.e. accuracy, time consumption) is fully comparable with a default (built-in) ABAQUS/Standard algorithm.

Originality/value

The estimated maximal subincrement size enables the algorithm to be stable by definition. Subincrements are much larger than those in conventional substepping algorithms. No error control, error correction or local iterations are required even in the case of large increments.

Keywords

Citation

Halilovic, M., Starman, B., Vrh, M. and Stok, B. (2017), "A robust explicit integration of elasto-plastic constitutive models, based on simple subincrement size estimation", Engineering Computations, Vol. 34 No. 6, pp. 1774-1806. https://doi.org/10.1108/EC-03-2016-0103

Publisher

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Emerald Publishing Limited

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