Peridynamic Modeling of Nearly-Incompressible Soft Materials for Aerospace Systems

Soft materials are increasingly integrated into modern aerospace systems due to their unique ability to deform, adapt, and absorb energy under extreme conditions. Applications such as morphing wing skins, soft robotic components for extraterrestrial exploration, and impact-absorbing systems in UAVs and space capsules, to cite a few, rely on soft polymers and elastomers subjected to large deformations. A major concern in these applications is the initiation and evolution of cracks, which can arise from cyclic loading, environmental exposure, or sudden impacts, possibly leading to failures like tearing or puncture. Predicting such damage with advanced numerical tools is essential for ensuring structural integrity, reliability, and mission success. Peridynamics, a nonlocal continuum mechanics theory, is particularly well-suited to modeling discontinuities due to fracture phenomena as the integral formulation of the internal forces allows to easily remove interactions between points across the crack surface. Therefore, cracks are not required to propagate along predefined paths, but can evolve along the most energetically favorable paths. Furthermore, peridynamic correspondence models allow to embed into the peridynamic framework hyperelastic constitutive laws used in classical continuum mechanics to describe the behavior of soft materials. Correspondence models require a stabilization technique to avoid zero-energy modes, which can undermine numerical accuracy. However, when modeling nearly-incompressible soft materials, stabilized correspondence models exhibit a numerical issue which leads to unrealistically stiff responses and an incorrect reproduction of the strain energy density for non-homogeneous deformations. Therefore, we propose a robust yet simple method to mitigate this issue and validate it through numerical examples of benchmark problems involving hyperelastic materials.