Gradient flow model of mode-III fracture in Maxwell-type viscoelastic materials

TL;DR

This paper develops a phase field model for mode III fracture in Maxwell-type viscoelastic materials, capturing crack growth influenced by viscoelastic relaxation without relying on linear assumptions.

Contribution

It introduces a novel gradient flow-based phase field model for viscoelastic fracture that avoids additional assumptions used in previous models.

Findings

Crack propagation depends on the balance between loading and viscoelastic relaxation.

Numerical simulations demonstrate the model's ability to predict crack growth.

Energetic analysis provides insights into fracture dynamics.

Abstract

We formulate a phase field crack growth model for mode III fracture in a Maxwell-type viscoelastic material. To describe viscoelastic relaxation, a field variable of viscously flowed strain is employed in addition to a displacement field and damage phase field used in the original elastic model. Unlike preceding models constructed in the mechanical engineering community, our model is based only on the generic procedure for driving (uni-directional) gradient flow system from a physically natural system energy and employ no additional assumption such as the super-imposed relations for stress and strain (and their time derivatives) valid only for linear viscoelasticity. Numerical simulations indicate that the competition between increase in deformation by applied loading and the viscoelastic relaxation determines whether a distinct crack propagation has occurred from an initial crack. Furthermore, we consider the numerical results from an energetic perspective.