A multiscale anisotropic polymer network model coupled with phase field fracture

The study of polymers has continued to gain substantial attention due to their expanding range of applications, spanning essential engineering fields to emerging domains like stretchable electronics, soft robotics, and implantable sensors. These materials exhibit remarkable properties, primarily stemming from their intricate polymer chain network, which, in turn, increases the complexity of precisely modeling their behavior. Especially for modeling elastomers and their fracture behavior, accurately accounting for the deformations of the polymer chains is vital for predicting the rupture in highly stretched chains. Despite the importance, many robust multiscale continuum frameworks for modeling elastomer fracture tend to simplify network deformations by assuming uniform behavior among chains in all directions. Recognizing this limitation, our study proposes a multiscale fracture model that accounts for the anisotropic nature of elastomer network responses. At the microscale, damage in the chains is assumed to be driven by both the chain's entropy and the internal energy due to molecular bond distortions. In order to bridge the stretching in the chains to the macroscale deformation, we employ the maximal advance path constraint network model, inherently accommodating anisotropic network responses. As a result, chains oriented differently can be predicted to exhibit varying stretch and, consequently, different damage levels. To drive macroscale fracture based on damages in these chains, we utilize the micromorphic regularization theory, which involves the introduction of dual local-global damage variables at the macroscale. The macroscale local damage variable is obtained through the homogenization of the chain damage values, resulting in the prediction of an isotropic material response. The macroscale global damage variable is subjected to nonlocal effects and boundary conditions in a thermodynamically consistent phase field continuum formulation. Moreover, the total . Authors: Arunachala, Prajwal Kammardi [Stanford Univ., CA (United States)] (ORCID:0000000278916786); Vajari, Sina Abrari [Stanford Univ., CA (United States)] (ORCID:0000000182545984); Neuner, Matthias [Univ. Innsbruck (Austria)]; Sim, Jay Sejin [Stanford Univ., CA (United States)]; Zhao, Renee [Stanford Univ., CA (United States)]. DOE Contract: NA0003962. Subjects: Engineering; Mathematics; anisotropic network response; fracture propagation; micromorphic regularization; multiscale model; phase field fracture; polymer network model; rubber-like materials