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Description
Understanding the fracture mechanism of elastomeric materials is essential for ensuring the reliability and durability of numerous engineering applications. Rubbers, which exhibit large elastic deformations and energy-dissipative behavior, are susceptible to crack initiation and propagation under monotonic and cyclic loading. So, this work presents a mathematical formulation of the mixed formulation of the multi-field (u, p, d) framework through a phase-field fracture in nearly incompressible hyperelasticity undergoing failure. Here, we rely on the phase-field approach to fracture which is a widely adopted framework for modeling and computing the fracture failure phenomena in solids. We incorporate a hybrid formulation with an additive strain energy decomposition to account for different behaviors in tension and compression. A mixed displacement and pressure formulations must satisfy the inf-sup condition for solution stability. Hence, we utilize a mixed formulation with a perturbed Lagrangian formulation which enforces the incompressibility constraint in the undamaged material and reduces the pressure effect in the damaged material. So that the proposed formulation guarantee that the discrete Ladyshenskaya-Babuska-Brezzi (LBB) condition is not violated. In this work, we also present crack propagation experiments, evaluated by digital image correlation (DIC), for an SBR elastomer and compare them with the proposed numerical approach. Two numerical examples are provided to illustrate the capability and efficiency of the model, thereby capturing complex fracture behavior under realistic loading conditions. Experimental verification of quasi-statically driven crack growth was performed under fully relaxed conditions. An experimental calibration was first conducted to determine the hyperelastic constitutive parameters and the material’s fracture toughness. Finally, the effectiveness of the scheme is further evaluated by comparing the crack paths, maximum force response, and force-displacement curves obtained from both experimental and numerical results.
