Numerical simulations of damage and fracture in viscoelastic solids using a nonlocal fracture criterion

Abstract

We present a recently developed three-dimensional-finite-deformation-rate form-based constitutive theory to describe the deformation and fracture of viscoelastic solids. The constitutive theory was also implemented into a commercial finite-element program. Damage and fracture in viscoelastic solids is simulated using the element failure method coupled with a Gibbs free energy-based nonlocal fracture criterion. By numerically simulating selected boundary value problems, we show that our newly developed computational framework is able to reproduce the correct stress-strain response, force–displacement response and crack propagation characteristics in viscoelastic solids undergoing fracture, when compared to the response obtained using the extended finite-element method implementation in a commercially available finite element program.

Keywords:

• Viscoelastic solid
• constitutive theory
• fracture
• finite element method
• boundary value problem

Notes

1 In the literature, the element failure method is inaccurately termed as the element deletion method.

2 With reference to the strain-time responses shown in Fig. 2c, let ϵ_present and ϵ_abaqus represent the value of the strain at a given simulation time for a given value of σ_max, obtained from using our present theory and the Abaqus [19] viscoelastic Prony-series model, respectively. Furthermore, let the error at a given simulation time for a given value of σ_max be defined as $\left\{|{ϵ}_{\mathit{abaqus}}-{ϵ}_{\mathit{present}}|/\left|{ϵ}_{\mathit{present}}\right|\right\}\times$ 100 %. From the simulated strain-time responses shown in Fig. 2c, we can determine that the error is lesser than 5 %.

3 We have chosen to use a maximum principal stress damage initiation criterion because an energy type damage initiation criterion is not present in the Abaqus [19] implementation of the XFEM method.

Additional information

Funding

P.T. acknowledges the funding sup;port received from the Ministry of Education, Malaysia under Research Grant No. FRGS/1/2017/TK03/UKM/01/1. S.K. acknowledges the funding support received from UKM under Research Grant No. GUP-2015-054. A.S. acknowledges the partial support provided by the Holdredge/Paul Chaired Professorship. Partial support by the Oscar S. Wyatt Chair to P.T and J.N.R. are also gratefully acknowledged.