Speaker
Description
Hyperelastic materials play a crucial role in current applications due to their unique properties, especially their flexibility, stretchability, and resilience based on incompressibility. However, the incompressibility constraint is an unavoidable challenge in the modeling of most hyperelastic ma- terials, and makes it even more challenging to successfully explain or reproduce crack propagation via numerical simulations.
Mixed formulations, e.g. the so-called Q1P0 approach [1], are commonly used to avert locking issues due to incompressibility at finite deformations. In the present study, the Q1P0 approach is derived based on the Hu-Washizu three-field variational principle [2], yielding a single-field displacement formulation. Afterwards, the phase-field approach is incorporated to predict finite strain fracture of nearly incompressible hyperelastic materials.
Following the basic idea in [3], the phase-field is coupled to release the incompressibility con- straint in damaged material, while ensuring incompressibility for intact material. With a consis- tently derived and condensed description, the multi-field formulation is reduced into a standard displacement-phase-field approach. A special phase-field degradation function is particularly in- corporated into the volumetric contribution to release the pressure term faster and consequently to allow crack opening, which mediates the innate contradiction between incompressibility constraint and diffuse crack opening. Subsequently, several numerical examples are presented to illustrate the characteristics of the proposed formulation.
References
[1] J.C. Simo, R.L. Taylor and K.S. Pister, 1985, Variational and projection methods for the volume constraint in finite deformation elasto-plasticity, Computer Methodes in Applied Mechanics and Engineering 51, pp. 177–208.
[2] GA. Holzapfel, 2000, Nonlinear solid mechanics: a continuum approach for engineering, Wiley, Chichester.
[3] B. Li, N. Bouklas, 2020, A variational phase-field model for brittle fracture in polydisperse elastomer networks, International Journal of Solids and Structures 182, pp. 193–204.
