A multiscale anisotropic polymer network model coupled with phase field fracture
Prajwal Kammardi Arunachala
Department of Civil and Environmental Engineering, Stanford University, Stanford, California, USA
Search for more papers by this authorSina Abrari Vajari
Department of Civil and Environmental Engineering, Stanford University, Stanford, California, USA
Search for more papers by this authorMatthias Neuner
Unit of Strength of Materials and Structural Analysis, University of Innsbruck, Innsbruck, Austria
Search for more papers by this authorJay Sejin Sim
Department of Mechanical Engineering, Stanford University, Stanford, California, USA
Search for more papers by this authorRenee Zhao
Department of Mechanical Engineering, Stanford University, Stanford, California, USA
Search for more papers by this authorCorresponding Author
Christian Linder
Department of Civil and Environmental Engineering, Stanford University, Stanford, California, USA
Correspondence
Christian Linder, Department of Civil and Environmental Engineering, Stanford University, Stanford, CA, USA.
Email: [email protected]
Search for more papers by this authorPrajwal Kammardi Arunachala
Department of Civil and Environmental Engineering, Stanford University, Stanford, California, USA
Search for more papers by this authorSina Abrari Vajari
Department of Civil and Environmental Engineering, Stanford University, Stanford, California, USA
Search for more papers by this authorMatthias Neuner
Unit of Strength of Materials and Structural Analysis, University of Innsbruck, Innsbruck, Austria
Search for more papers by this authorJay Sejin Sim
Department of Mechanical Engineering, Stanford University, Stanford, California, USA
Search for more papers by this authorRenee Zhao
Department of Mechanical Engineering, Stanford University, Stanford, California, USA
Search for more papers by this authorCorresponding Author
Christian Linder
Department of Civil and Environmental Engineering, Stanford University, Stanford, California, USA
Correspondence
Christian Linder, Department of Civil and Environmental Engineering, Stanford University, Stanford, CA, USA.
Email: [email protected]
Search for more papers by this authorAbstract
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 dissipation in the system is considered to be mainly due to the breaking of the molecular bonds at the microscale. To validate our model, we employ the double-edge notched tensile test as a benchmark, comparing simulation predictions with existing experimental data. Additionally, to enhance our understanding of the fracturing process, we conduct uniaxial tensile experiments on a square film made up of polydimethylsiloxane (PDMS) rubber embedded with a hole and notches and then compare our simulation predictions with the experimental observations. Furthermore, we visualize the evolution of stretch and damage values in chains oriented along different directions to assess the predictive capacity of the model. The results are also compared with another existing model to evaluate the utility of our model in accurately simulating the fracture behavior of rubber-like materials.
CONFLICT OF INTEREST STATEMENT
The authors declare no potential conflict of interests.
Open Research
DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available upon reasonable request.
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