Fracture of viscoelastic materials: FEM implementation of a non-local & rate form-based finite-deformation constitutive theory

T Prakash G. Thamburaja, K. Sarah, A. Srinivasa, J. N. Reddy

Research output: Contribution to journalArticle

Abstract

We derive a thermodynamically-consistent, three-dimensional, rate form-based finite-deformation constitutive theory and computational approach for damage & fracture in nonlinear viscoelastic materials. The key ingredient that allows us to develop a physical criterion for fracture is the use of a Gibbs potential-based multinetwork formulation of viscoelasticity. An approach that is based on the use of the criticality of the averaged Gibbs potential over a fracture process zone is used for the initiation & propagation of cracks in a body. The rate form-based constitutive theory and fracture criterion are implemented into the Abaqus (2018) finite-element program through a user-material subroutine interface. Crack propagation is modeled as the failure of elements leading to loss of mechanical resistance to deformation. The tearing & fracture response of a viscoelastic material using a notch-in-plate sample deformed in simple tension is also simulated. By comparing the simulation results for a local damage criterion versus a truly nonlocal damage criterion, we show how the spread of Gibbs free energy around the crack tip influences the nature of the crack growth. As expected, the material fracture response described by a local damage criterion exhibits pathological mesh dependence whereas the response obtained using the nonlocal damage criterion is mesh objective regardless of mesh density, element type and orientation. This work presents two major computational advances: (1) the conversion of the rate form-based finite-deformation constitutive theory into an objective time-integration procedure is straightforward because the material time derivative-based constitutive equations are frame-invariant, and (2) the physically-observed crack initiation & propagation process in solids can be accurately & robustly simulated using simple numerical techniques such as the element failure method if a truly nonlocal fracture criterion is utilized. Finally, we benchmark results obtained from our computational framework and numerical simulations for modeling crack initiation & propagation to physical experimental data of mixed-mode crack propagation in a viscoelastic material.

Original languageEnglish
Pages (from-to)871-903
Number of pages33
JournalComputer Methods in Applied Mechanics and Engineering
Volume354
DOIs
Publication statusPublished - 1 Sep 2019

Fingerprint

Finite element method
Crack propagation
damage
mesh
crack initiation
crack propagation
Crack initiation
propagation
cracks
subroutines
tearing
Subroutines
viscoelasticity
crack tips
Viscoelasticity
constitutive equations
Gibbs free energy
notches
Constitutive equations
ingredients

Keywords

  • Constitutive theory
  • Finite-element method
  • Non-local fracture criterion
  • Viscoelasticity

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

Cite this

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title = "Fracture of viscoelastic materials: FEM implementation of a non-local & rate form-based finite-deformation constitutive theory",
abstract = "We derive a thermodynamically-consistent, three-dimensional, rate form-based finite-deformation constitutive theory and computational approach for damage & fracture in nonlinear viscoelastic materials. The key ingredient that allows us to develop a physical criterion for fracture is the use of a Gibbs potential-based multinetwork formulation of viscoelasticity. An approach that is based on the use of the criticality of the averaged Gibbs potential over a fracture process zone is used for the initiation & propagation of cracks in a body. The rate form-based constitutive theory and fracture criterion are implemented into the Abaqus (2018) finite-element program through a user-material subroutine interface. Crack propagation is modeled as the failure of elements leading to loss of mechanical resistance to deformation. The tearing & fracture response of a viscoelastic material using a notch-in-plate sample deformed in simple tension is also simulated. By comparing the simulation results for a local damage criterion versus a truly nonlocal damage criterion, we show how the spread of Gibbs free energy around the crack tip influences the nature of the crack growth. As expected, the material fracture response described by a local damage criterion exhibits pathological mesh dependence whereas the response obtained using the nonlocal damage criterion is mesh objective regardless of mesh density, element type and orientation. This work presents two major computational advances: (1) the conversion of the rate form-based finite-deformation constitutive theory into an objective time-integration procedure is straightforward because the material time derivative-based constitutive equations are frame-invariant, and (2) the physically-observed crack initiation & propagation process in solids can be accurately & robustly simulated using simple numerical techniques such as the element failure method if a truly nonlocal fracture criterion is utilized. Finally, we benchmark results obtained from our computational framework and numerical simulations for modeling crack initiation & propagation to physical experimental data of mixed-mode crack propagation in a viscoelastic material.",
keywords = "Constitutive theory, Finite-element method, Non-local fracture criterion, Viscoelasticity",
author = "{G. Thamburaja}, {T Prakash} and K. Sarah and A. Srinivasa and Reddy, {J. N.}",
year = "2019",
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T1 - Fracture of viscoelastic materials

T2 - FEM implementation of a non-local & rate form-based finite-deformation constitutive theory

AU - G. Thamburaja, T Prakash

AU - Sarah, K.

AU - Srinivasa, A.

AU - Reddy, J. N.

PY - 2019/9/1

Y1 - 2019/9/1

N2 - We derive a thermodynamically-consistent, three-dimensional, rate form-based finite-deformation constitutive theory and computational approach for damage & fracture in nonlinear viscoelastic materials. The key ingredient that allows us to develop a physical criterion for fracture is the use of a Gibbs potential-based multinetwork formulation of viscoelasticity. An approach that is based on the use of the criticality of the averaged Gibbs potential over a fracture process zone is used for the initiation & propagation of cracks in a body. The rate form-based constitutive theory and fracture criterion are implemented into the Abaqus (2018) finite-element program through a user-material subroutine interface. Crack propagation is modeled as the failure of elements leading to loss of mechanical resistance to deformation. The tearing & fracture response of a viscoelastic material using a notch-in-plate sample deformed in simple tension is also simulated. By comparing the simulation results for a local damage criterion versus a truly nonlocal damage criterion, we show how the spread of Gibbs free energy around the crack tip influences the nature of the crack growth. As expected, the material fracture response described by a local damage criterion exhibits pathological mesh dependence whereas the response obtained using the nonlocal damage criterion is mesh objective regardless of mesh density, element type and orientation. This work presents two major computational advances: (1) the conversion of the rate form-based finite-deformation constitutive theory into an objective time-integration procedure is straightforward because the material time derivative-based constitutive equations are frame-invariant, and (2) the physically-observed crack initiation & propagation process in solids can be accurately & robustly simulated using simple numerical techniques such as the element failure method if a truly nonlocal fracture criterion is utilized. Finally, we benchmark results obtained from our computational framework and numerical simulations for modeling crack initiation & propagation to physical experimental data of mixed-mode crack propagation in a viscoelastic material.

AB - We derive a thermodynamically-consistent, three-dimensional, rate form-based finite-deformation constitutive theory and computational approach for damage & fracture in nonlinear viscoelastic materials. The key ingredient that allows us to develop a physical criterion for fracture is the use of a Gibbs potential-based multinetwork formulation of viscoelasticity. An approach that is based on the use of the criticality of the averaged Gibbs potential over a fracture process zone is used for the initiation & propagation of cracks in a body. The rate form-based constitutive theory and fracture criterion are implemented into the Abaqus (2018) finite-element program through a user-material subroutine interface. Crack propagation is modeled as the failure of elements leading to loss of mechanical resistance to deformation. The tearing & fracture response of a viscoelastic material using a notch-in-plate sample deformed in simple tension is also simulated. By comparing the simulation results for a local damage criterion versus a truly nonlocal damage criterion, we show how the spread of Gibbs free energy around the crack tip influences the nature of the crack growth. As expected, the material fracture response described by a local damage criterion exhibits pathological mesh dependence whereas the response obtained using the nonlocal damage criterion is mesh objective regardless of mesh density, element type and orientation. This work presents two major computational advances: (1) the conversion of the rate form-based finite-deformation constitutive theory into an objective time-integration procedure is straightforward because the material time derivative-based constitutive equations are frame-invariant, and (2) the physically-observed crack initiation & propagation process in solids can be accurately & robustly simulated using simple numerical techniques such as the element failure method if a truly nonlocal fracture criterion is utilized. Finally, we benchmark results obtained from our computational framework and numerical simulations for modeling crack initiation & propagation to physical experimental data of mixed-mode crack propagation in a viscoelastic material.

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