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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. 

Shape sensing is an emerging technique for the reconstruction of deformed shapes using data from a discrete network of strain sensors. The prominence is due to its suitability in promising applications such as structural health monitoring in multiple engineering fields and shape capturing in the medical field. In this work, a physics-informed deep learning model, named SenseNet, was developed for shape sensing applications. Unlike existing neural network approaches for shape sensing, SenseNet incorporates the knowledge of the physics of the problem, so its performance does not rely on the choices of the training data. Compared with numerical physics-based approaches, SenseNet is a mesh-free method, and therefore it offers convenience to problems with complex geometries. SenseNet is composed of two parts: a neural network to predict displacements at the given input coordinates, and a physics part to compute the loss using a function incorporated with physics information. The prior knowledge considered in the loss function includes the boundary conditions and physics relations such as the strain–displacement relation, material constitutive equation, and the governing equation obtained from the law of balance of linear momentum.SenseNet was validated with finite-element solutions for cases with nonlinear displacement fields and stress fields using bending and fixed tension tests, respectively, in both two and three dimensions. A study of the sensor density effects illustrated the fact that the accuracy of the model can be improved using a larger amount of strain data. Because general three dimensional governing equations are incorporated in the model, it was found that SenseNet is capable of reconstructing deformations in volumes with reasonable accuracy using just the surface strain data. Hence, unlike most existing models, SenseNet is not specialized for certain types of elements, and can be extended universally for even thick-body applications.