A finite deformation nonlinear thermo-elastic model that mimics plasticity during monotonic loading

A. Goel, A. Sherafati, M. Negahban, A. Azizinamini, Yenan Wang

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We present and study a nonlinear thermo-elastic constitutive model that under monotonic loading closely reproduces the response seen in plasticity, showing the initial stiff elastic response, kneeing as if yielding, and then showing response resembling post-yield hardening. The proposed large deformation thermo-elastic response model is constructed based on four physically identifiable mechanical parameters, that are closely related to the parameters used to construct plasticity models, thermal expansion parameters and two thermodynamic parameters. The four mechanical parameters are the initial elastic shear and bulk moduli, the yield point in shear, the hardening slope in shear. The thermodynamic parameters are the heat capacity at a reference temperature and its rate of change with changes of temperature. The model can be considered an alternate to deformation plasticity models currently used and, as such, can be used as a lightweight substitute for plasticity modeling in certain analysis. Since the proposed model is thermodynamically based, not only thermal effects are integrated into the model, but also the stress is calculated in terms of the applied deformation, allowing the model to be integrated with other models when conducting numerical analysis. We study the response of the proposed model under simple shear, uniaxial extension, confined compression, partially-confined compression, and biaxial extension. We incorporate the elastic model into ABAQUS using its UMAT subroutine for solid elements and using UHYPER for shell elements. We compare the large deformation response from the proposed elastic model with J2-plasticity, and with plasticity and deformation plasticity models implemented in ABAQUS. The model in most cases compares very favorably to all such models. This comparison is done for both homogeneous and non-homogeneous problems including the case of a cantilever beam under tip loading. We show that for the problems that it applies to, the models run in approximately one tenth the computational time and with one tenth the number of iterations needed to conduct the analysis using the plasticity model in ABAQUS.

Original languageEnglish (US)
Pages (from-to)2977-2986
Number of pages10
JournalInternational Journal of Solids and Structures
Volume48
Issue number20
DOIs
StatePublished - Oct 1 2011

Fingerprint

Finite Deformation
Thermoelastic
plastic properties
Plasticity
Monotonic
Model
ABAQUS
shear
Large Deformation
Hardening
hardening
Thermodynamics
Compression
Elastic moduli
Bulk Modulus
subroutines
Cantilever Beam
thermodynamics
Shell Element
Thermal Expansion

Keywords

  • Bridge analysis
  • Deformation plasticity
  • Elasticity
  • Finite element analysis
  • Limit load capacity
  • Nonlinear thermo-elasticity
  • Plasticity

ASJC Scopus subject areas

  • Modeling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Cite this

A finite deformation nonlinear thermo-elastic model that mimics plasticity during monotonic loading. / Goel, A.; Sherafati, A.; Negahban, M.; Azizinamini, A.; Wang, Yenan.

In: International Journal of Solids and Structures, Vol. 48, No. 20, 01.10.2011, p. 2977-2986.

Research output: Contribution to journalArticle

@article{df1fc2a41f3f47f5a3df8597f800d140,
title = "A finite deformation nonlinear thermo-elastic model that mimics plasticity during monotonic loading",
abstract = "We present and study a nonlinear thermo-elastic constitutive model that under monotonic loading closely reproduces the response seen in plasticity, showing the initial stiff elastic response, kneeing as if yielding, and then showing response resembling post-yield hardening. The proposed large deformation thermo-elastic response model is constructed based on four physically identifiable mechanical parameters, that are closely related to the parameters used to construct plasticity models, thermal expansion parameters and two thermodynamic parameters. The four mechanical parameters are the initial elastic shear and bulk moduli, the yield point in shear, the hardening slope in shear. The thermodynamic parameters are the heat capacity at a reference temperature and its rate of change with changes of temperature. The model can be considered an alternate to deformation plasticity models currently used and, as such, can be used as a lightweight substitute for plasticity modeling in certain analysis. Since the proposed model is thermodynamically based, not only thermal effects are integrated into the model, but also the stress is calculated in terms of the applied deformation, allowing the model to be integrated with other models when conducting numerical analysis. We study the response of the proposed model under simple shear, uniaxial extension, confined compression, partially-confined compression, and biaxial extension. We incorporate the elastic model into ABAQUS using its UMAT subroutine for solid elements and using UHYPER for shell elements. We compare the large deformation response from the proposed elastic model with J2-plasticity, and with plasticity and deformation plasticity models implemented in ABAQUS. The model in most cases compares very favorably to all such models. This comparison is done for both homogeneous and non-homogeneous problems including the case of a cantilever beam under tip loading. We show that for the problems that it applies to, the models run in approximately one tenth the computational time and with one tenth the number of iterations needed to conduct the analysis using the plasticity model in ABAQUS.",
keywords = "Bridge analysis, Deformation plasticity, Elasticity, Finite element analysis, Limit load capacity, Nonlinear thermo-elasticity, Plasticity",
author = "A. Goel and A. Sherafati and M. Negahban and A. Azizinamini and Yenan Wang",
year = "2011",
month = "10",
day = "1",
doi = "10.1016/j.ijsolstr.2011.06.015",
language = "English (US)",
volume = "48",
pages = "2977--2986",
journal = "International Journal of Solids and Structures",
issn = "0020-7683",
publisher = "Elsevier Limited",
number = "20",

}

TY - JOUR

T1 - A finite deformation nonlinear thermo-elastic model that mimics plasticity during monotonic loading

AU - Goel, A.

AU - Sherafati, A.

AU - Negahban, M.

AU - Azizinamini, A.

AU - Wang, Yenan

PY - 2011/10/1

Y1 - 2011/10/1

N2 - We present and study a nonlinear thermo-elastic constitutive model that under monotonic loading closely reproduces the response seen in plasticity, showing the initial stiff elastic response, kneeing as if yielding, and then showing response resembling post-yield hardening. The proposed large deformation thermo-elastic response model is constructed based on four physically identifiable mechanical parameters, that are closely related to the parameters used to construct plasticity models, thermal expansion parameters and two thermodynamic parameters. The four mechanical parameters are the initial elastic shear and bulk moduli, the yield point in shear, the hardening slope in shear. The thermodynamic parameters are the heat capacity at a reference temperature and its rate of change with changes of temperature. The model can be considered an alternate to deformation plasticity models currently used and, as such, can be used as a lightweight substitute for plasticity modeling in certain analysis. Since the proposed model is thermodynamically based, not only thermal effects are integrated into the model, but also the stress is calculated in terms of the applied deformation, allowing the model to be integrated with other models when conducting numerical analysis. We study the response of the proposed model under simple shear, uniaxial extension, confined compression, partially-confined compression, and biaxial extension. We incorporate the elastic model into ABAQUS using its UMAT subroutine for solid elements and using UHYPER for shell elements. We compare the large deformation response from the proposed elastic model with J2-plasticity, and with plasticity and deformation plasticity models implemented in ABAQUS. The model in most cases compares very favorably to all such models. This comparison is done for both homogeneous and non-homogeneous problems including the case of a cantilever beam under tip loading. We show that for the problems that it applies to, the models run in approximately one tenth the computational time and with one tenth the number of iterations needed to conduct the analysis using the plasticity model in ABAQUS.

AB - We present and study a nonlinear thermo-elastic constitutive model that under monotonic loading closely reproduces the response seen in plasticity, showing the initial stiff elastic response, kneeing as if yielding, and then showing response resembling post-yield hardening. The proposed large deformation thermo-elastic response model is constructed based on four physically identifiable mechanical parameters, that are closely related to the parameters used to construct plasticity models, thermal expansion parameters and two thermodynamic parameters. The four mechanical parameters are the initial elastic shear and bulk moduli, the yield point in shear, the hardening slope in shear. The thermodynamic parameters are the heat capacity at a reference temperature and its rate of change with changes of temperature. The model can be considered an alternate to deformation plasticity models currently used and, as such, can be used as a lightweight substitute for plasticity modeling in certain analysis. Since the proposed model is thermodynamically based, not only thermal effects are integrated into the model, but also the stress is calculated in terms of the applied deformation, allowing the model to be integrated with other models when conducting numerical analysis. We study the response of the proposed model under simple shear, uniaxial extension, confined compression, partially-confined compression, and biaxial extension. We incorporate the elastic model into ABAQUS using its UMAT subroutine for solid elements and using UHYPER for shell elements. We compare the large deformation response from the proposed elastic model with J2-plasticity, and with plasticity and deformation plasticity models implemented in ABAQUS. The model in most cases compares very favorably to all such models. This comparison is done for both homogeneous and non-homogeneous problems including the case of a cantilever beam under tip loading. We show that for the problems that it applies to, the models run in approximately one tenth the computational time and with one tenth the number of iterations needed to conduct the analysis using the plasticity model in ABAQUS.

KW - Bridge analysis

KW - Deformation plasticity

KW - Elasticity

KW - Finite element analysis

KW - Limit load capacity

KW - Nonlinear thermo-elasticity

KW - Plasticity

UR - http://www.scopus.com/inward/record.url?scp=79961027187&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79961027187&partnerID=8YFLogxK

U2 - 10.1016/j.ijsolstr.2011.06.015

DO - 10.1016/j.ijsolstr.2011.06.015

M3 - Article

AN - SCOPUS:79961027187

VL - 48

SP - 2977

EP - 2986

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

SN - 0020-7683

IS - 20

ER -