An improved contact algorithm for multi-material Arbitrary Lagranian-Eulerian hydrocodes in three-dimensions. (2017) - Walls, Kenneth C.; Littlefield, David L.
Abstract: Realistic and accurate modeling of contact for problems involving large deformations and severe distortions presents a host of computational challenges. Due to their natural description of surfaces, Lagrangian finite element methods are traditionally used for problems where the accuracy of behavior along contact interfaces is important. However, problems such as those involving ballistic penetrations and perforations, blast-structure interactions, and vehicular crash dynamics, can result in elements developing large aspect ratios, twisting, or even inverting. For this reason, Eulerian, and by extension Arbitrary Lagrangian-Eulerian (ALE), frameworks have become popular when modeling events that involve large deformations. However, additional complexities arise when these frameworks permit multiple materials to occupy a single finite element. Multi-material Eulerian formulations in computational structural mechanics are traditionally approached using mixed-element thermodynamic or constitutive models. These traditional approaches replace contacting materials in an element with an approximated single material. However, this approximation often has little basis in the actual physics taking place at the contacting boundary and can easily lead to unphysical behavior due to bonding that takes place along the interface boundary. This work presents a significant departure from traditional Eulerian treatment of contact by adding a separate velocity field and solving the conservation equations separately for each material and then imposing inequality constraints associated with contact to the solutions with the appropriate traction integrals included. This results in natural treatment of contacting surfaces in an Eulerian framework and eliminates the need for mixture theory. The advantages of this method will be demonstrated with several computational examples.