A multiscale phase field fracture approach based on the non-affine microsphere model for rubber-like materials

• Published in: Computer methods in applied mechanics and engineering 2023-05, Vol.410 (C), p.115982, Article 115982
• Main Authors: Arunachala, Prajwal Kammardi, Abrari Vajari, Sina, Neuner, Matthias, Linder, Christian
• Format: Article
• Language: English
• Subjects: Fracture propagation; Multiscale model; Non-affine microsphere model; Phase field fracture approach; Rubber-like materials
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2023.115982

Rubber-like materials have a broad scope of applications due to their unique properties like high stretchability and increased toughness. Hence, computational models for simulating their fracture behavior are paramount for designing them against failures. In this study, the phase field fracture approach is integrated with a multiscale polymer model for predicting the fracture behavior in elastomers. At the microscale, damaged polymer chains are modeled to be made up of a number of elastic chain segments pinned together. Using the phase field approach, the damage in the chains is represented using a continuous variable. Both the bond stretch internal energy and the entropic free energy of the chain are assumed to drive the damage, and the advantages of this assumption are expounded. A framework for utilizing the non-affine microsphere model for damaged systems is proposed by considering the minimization of a hypothetical undamaged free energy, ultimately connecting the chain stretch to the macroscale deformation gradient. At the macroscale, a thermodynamically consistent formulation is derived in which the total dissipation is assumed to be mainly due to the rupture of molecular bonds. Using a monolithic scheme, the proposed model is numerically implemented and the resulting three-dimensional simulation predictions are compared with existing experimental data. The capability of the model to qualitatively predict the propagation of complex crack paths and quantitatively estimate the overall fracture behavior is verified. Additionally, the effect of the length scale parameter on the predicted fracture behavior is studied for an inhomogeneous system.