Locking treatment of penalty-based gradient-enhanced damage formulation for failure of compressible and nearly incompressible hyperelastic materials

Abstract

Soft materials are of major interest for biomechanics applications due to their high deformability and susceptibility to experience damage events under different loading scenarios. The present study is concerned with modelling damage evolution processes in these nonlinear materials whose structural responses are prone to locking when low-order kinematic interpolation is employed in the context of nonlinear Finite Element schemes. For this reason, a pair of gradient-enhanced continuum damage schemes are proposed with the aim of tackling mechanical failure problems in applications that exhibit shear and volumetric locking. In particular, we present the consistent formulation and the assessment of the corresponding performance of (i) a mixed displacement-enhanced assumed strain employing a total Lagrangian formulation, and (ii) a three-field mixed displacement-pressure-Jacobian formulation. The novel and formulations are consistently derived and numerically implemented, providing a satisfactory agreement with respect to built-in elements handling the treatment of shear and volumetric locking, respectively, in conjunction to the modelling damage phenomena via the use of a penalty-based gradient-enhanced formulation. This performance is examined via several numerical applications. Furthermore, the final example justifies the need for a formulation combining both mixed FE approaches to simulate problems encompassing both locking issues (shear and volumetric locking), which can be performed using a combination of the and herein proposed.

A multiscale anisotropic polymer network model coupled with phase field fracture

“…Notably, there have been studies incorporating Monte Carlo simulations to assess failure uncertainties, 52 accounting for fracture nucleation in high-stress concentration regions for modeling crack propagation and healing in elastomers, 53 considering the strength of the material for predicting crack nucleation, 54 capturing the rate-dependent viscoelastic behavior of rubbers, 55,56 modeling high-speed crack instability, 57 and enforcing incompressibility. [58][59][60][61][62] To improve the robustness and convergence rate, the edge-based smoothed finite elements has been utilized for modeling fractures at large deformations. 63,64 Furthermore, a higher-order phase field theory has also been introduced for hyperelastic rubbers to enhance numerical efficiency.…”

“…For rubber‐like materials, many researchers have extended this framework based on Griffith's theory, using macroscale critical energy release rates. Notably, there have been studies incorporating Monte Carlo simulations to assess failure uncertainties, 52 accounting for fracture nucleation in high‐stress concentration regions for modeling crack propagation and healing in elastomers, 53 considering the strength of the material for predicting crack nucleation, 54 capturing the rate‐dependent viscoelastic behavior of rubbers, 55,56 modeling high‐speed crack instability, 57 and enforcing incompressibility 58–62 . To improve the robustness and convergence rate, the edge‐based smoothed finite elements has been utilized for modeling fractures at large deformations 63,64 .…”