A mixed formulation of the plane-stress problem to facilitate reuse of constitutive models in finite-element programs

Hailong Chen; Wen Jiang; Benjamin W. Spencer

doi:10.1016/j.mechrescom.2024.104307

A mixed formulation of the plane-stress problem to facilitate reuse of constitutive models in finite-element programs

Hailong Chen, Wen Jiang, Benjamin W. Spencer

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The plane-stress assumption can be challenging to support in a finite element program because it traditionally requires separate implementations of constitutive models than those intended for three-dimensional or two-dimensional plane-strain simulations. As a solution to this issue, this paper presents a method to solve the plane-stress problem using a mixed formulation. In this formulation, the out-of-plane strain is treated as a field variable that is solved for in addition to the standard in-plane displacement variables, in a manner that weakly enforces the condition that the out-of-plane stress is zero. The proposed formulation is non-intrusive, requiring no modifications to the constitutive models in contrast to the conventional plane-stress formulation. The proposed mixed formulation has been benchmarked against analytical solutions and numerical solutions, with good performance and accuracy.

Original language	English
Article number	104307
Journal	Mechanics Research Communications
Volume	139
DOIs	https://doi.org/10.1016/j.mechrescom.2024.104307
State	Published - Aug 2024

Bibliographical note

Publisher Copyright:
© 2024 Elsevier Ltd

Funding

This research was supported by the Laboratory Directed Research and Development program at INL under projects 13-071 and 24A1081-203FP. This manuscript was authored by Battelle Energy Alliance, LLC under contract no. DE-AC07-05ID14517 with the U.S. Department of Energy. The U.S. Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for U.S. Government purposes.

Funders	Funder number
Laboratory Directed Research and Development
U.S. Department of Energy EPSCoR
Bureau of International Narcotics and Law Enforcement Affairs	DE-AC07-05ID14517, 13-071, 24A1081-203FP

Keywords

Elastoplasticity
Mixed formulation
Out-of-plane strain
Plane stress

ASJC Scopus subject areas

Civil and Structural Engineering
General Materials Science
Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering

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10.1016/j.mechrescom.2024.104307

Cite this

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title = "A mixed formulation of the plane-stress problem to facilitate reuse of constitutive models in finite-element programs",

abstract = "The plane-stress assumption can be challenging to support in a finite element program because it traditionally requires separate implementations of constitutive models than those intended for three-dimensional or two-dimensional plane-strain simulations. As a solution to this issue, this paper presents a method to solve the plane-stress problem using a mixed formulation. In this formulation, the out-of-plane strain is treated as a field variable that is solved for in addition to the standard in-plane displacement variables, in a manner that weakly enforces the condition that the out-of-plane stress is zero. The proposed formulation is non-intrusive, requiring no modifications to the constitutive models in contrast to the conventional plane-stress formulation. The proposed mixed formulation has been benchmarked against analytical solutions and numerical solutions, with good performance and accuracy.",

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doi = "10.1016/j.mechrescom.2024.104307",

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AU - Chen, Hailong

AU - Jiang, Wen

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N2 - The plane-stress assumption can be challenging to support in a finite element program because it traditionally requires separate implementations of constitutive models than those intended for three-dimensional or two-dimensional plane-strain simulations. As a solution to this issue, this paper presents a method to solve the plane-stress problem using a mixed formulation. In this formulation, the out-of-plane strain is treated as a field variable that is solved for in addition to the standard in-plane displacement variables, in a manner that weakly enforces the condition that the out-of-plane stress is zero. The proposed formulation is non-intrusive, requiring no modifications to the constitutive models in contrast to the conventional plane-stress formulation. The proposed mixed formulation has been benchmarked against analytical solutions and numerical solutions, with good performance and accuracy.

AB - The plane-stress assumption can be challenging to support in a finite element program because it traditionally requires separate implementations of constitutive models than those intended for three-dimensional or two-dimensional plane-strain simulations. As a solution to this issue, this paper presents a method to solve the plane-stress problem using a mixed formulation. In this formulation, the out-of-plane strain is treated as a field variable that is solved for in addition to the standard in-plane displacement variables, in a manner that weakly enforces the condition that the out-of-plane stress is zero. The proposed formulation is non-intrusive, requiring no modifications to the constitutive models in contrast to the conventional plane-stress formulation. The proposed mixed formulation has been benchmarked against analytical solutions and numerical solutions, with good performance and accuracy.

KW - Elastoplasticity

KW - Mixed formulation

KW - Out-of-plane strain

KW - Plane stress

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A mixed formulation of the plane-stress problem to facilitate reuse of constitutive models in finite-element programs

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

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