High-order FEMs for thermo-hyperelasticity at finite strains

Zohar Yosibash; Danny Weiss; Stefan Hartmann

doi:10.1016/j.camwa.2013.11.003

High-order FEMs for thermo-hyperelasticity at finite strains

Zohar Yosibash^*, Danny Weiss, Stefan Hartmann

^*Corresponding author for this work

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

11 Scopus citations

Abstract

Thermo-hyperelastic problems at finite strains belong to a category of non-linear coupled problems that impose challenges on their numerical treatment. We present the weak-form for a 1-D coupled, stationary, thermo-hyperelastic system with constant or temperature-dependent material properties. The coupled system is discretized by a 'monolithic' high-order finite element method (p-FEM) based on hierarchical shape-functions. To verify the accuracy and to investigate the convergence rates of the p-FEM for the non-linear coupled problem, exact solutions are derived that are compared to the numerical results. These demonstrate the accuracy and efficiency of the applied p-FEMs.

Original language	English
Pages (from-to)	477-496
Number of pages	20
Journal	Computers and Mathematics with Applications
Volume	67
Issue number	3
DOIs	https://doi.org/10.1016/j.camwa.2013.11.003
State	Published - Feb 2014
Externally published	Yes

Funding

Funders	Funder number
Deutsche Forschungsgemeinschaft	RA 624/19-1, HA 2024/7-2

Keywords

Coupled FEM
Monolithic scheme
Thermo-hyperelasticity
p-FEM

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10.1016/j.camwa.2013.11.003

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title = "High-order FEMs for thermo-hyperelasticity at finite strains",

abstract = "Thermo-hyperelastic problems at finite strains belong to a category of non-linear coupled problems that impose challenges on their numerical treatment. We present the weak-form for a 1-D coupled, stationary, thermo-hyperelastic system with constant or temperature-dependent material properties. The coupled system is discretized by a 'monolithic' high-order finite element method (p-FEM) based on hierarchical shape-functions. To verify the accuracy and to investigate the convergence rates of the p-FEM for the non-linear coupled problem, exact solutions are derived that are compared to the numerical results. These demonstrate the accuracy and efficiency of the applied p-FEMs.",

keywords = "Coupled FEM, Monolithic scheme, Thermo-hyperelasticity, p-FEM",

author = "Zohar Yosibash and Danny Weiss and Stefan Hartmann",

note = "Funding Information: The authors thank Mr. Hagen Wille (Technical University of Munich, Germany) for his help. The authors gratefully acknowledge the financial support of the German Research Foundation (DFG) under the grants RA 624/19-1 and HA 2024/7-2 . ",

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doi = "10.1016/j.camwa.2013.11.003",

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AU - Yosibash, Zohar

AU - Weiss, Danny

AU - Hartmann, Stefan

N1 - Funding Information: The authors thank Mr. Hagen Wille (Technical University of Munich, Germany) for his help. The authors gratefully acknowledge the financial support of the German Research Foundation (DFG) under the grants RA 624/19-1 and HA 2024/7-2 .

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N2 - Thermo-hyperelastic problems at finite strains belong to a category of non-linear coupled problems that impose challenges on their numerical treatment. We present the weak-form for a 1-D coupled, stationary, thermo-hyperelastic system with constant or temperature-dependent material properties. The coupled system is discretized by a 'monolithic' high-order finite element method (p-FEM) based on hierarchical shape-functions. To verify the accuracy and to investigate the convergence rates of the p-FEM for the non-linear coupled problem, exact solutions are derived that are compared to the numerical results. These demonstrate the accuracy and efficiency of the applied p-FEMs.

AB - Thermo-hyperelastic problems at finite strains belong to a category of non-linear coupled problems that impose challenges on their numerical treatment. We present the weak-form for a 1-D coupled, stationary, thermo-hyperelastic system with constant or temperature-dependent material properties. The coupled system is discretized by a 'monolithic' high-order finite element method (p-FEM) based on hierarchical shape-functions. To verify the accuracy and to investigate the convergence rates of the p-FEM for the non-linear coupled problem, exact solutions are derived that are compared to the numerical results. These demonstrate the accuracy and efficiency of the applied p-FEMs.

KW - Coupled FEM

KW - Monolithic scheme

KW - Thermo-hyperelasticity

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JO - Computers and Mathematics with Applications

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ER -

High-order FEMs for thermo-hyperelasticity at finite strains

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