A new adaptive peridynamic framework for modeling large deformation and fracture behavior of hyperelastic materials

Accurate prediction of deformation and fracture behaviors of hyperelastic materials is crucial in engineering applications and industry. The paper presents a new three-dimensional computational model to simulate large deformations and fractures in hyperelastic materials using the peridynamic method. The main innovation of the proposed three-dimensional hyperelastic peridynamic (3D-HPD) model lies in its incorporation of the stress-strain relationship of hyperelastic materials into the peridynamic framework. Therefore, the peridynamic parameters, such as bond stiffness and strength, are dynamically updated based on the instantaneous value of Young's modulus derived from the stress-strain relation of hyperelastic materials. The 3D-HPD model highlights the following novelties: 1) The 3D-HPD model directly employs the stress-strain relation for each peridynamic bond. Thus, the large deformations and fractures in hyperelastic materials are accurately captured in three dimensions by integrating the responses in all peridynamic bonds; 2) Unlike other models that may require specific hyperelastic formulations, the 3D-HPD model offers a more straightforward application, enhancing usability and reducing complexity; 3) The 3D-HPD model is capable of simulating the response of hyperelastic materials under various loading conditions, including tensile, torsional, and lateral loadings. We confirm the validity of the 3D-HPD model by evaluating it against experimental measurements and observations. For the first time, the model examines hyperelastic materials' fracture and deformation behaviors under combined loading conditions. The new findings of the mechanical performance of hyperelastic materials under multi-axial stresses provide new insights to enhance their design and usage.