A friction interface model for multi-material interactions in a Eulerian framework

A friction model for hyper-elastic solid materials was proposed for the simulation of complex shear impacts in a Eulerian framework. The interfacial status of multi-material interactions was obtained in Harten, Lax, and van Leer discontinuity (HLLD) Riemann solver. The inverse deformation gradient tensor was utilized in governing equations to describe the shape change of hyper-elastic solid materials. The level set method (LSM) was used to identify multiple materials in computational domain and the interface boundary condition was applied using the real ghost fluid method (RGFM). A uniform eigensystem of hyperbolic equations was derived using the fifth-order characteristic-wise weighted essentially non-oscillatory (WENO) scheme. Six numerical tests of one-dimensional problems were used to illustrate the robustness of the 5th order WENO scheme. The proposed friction model was evaluated for impact cases in both one and two dimensions with three-dimensional components. The redistribution of strain and kinetic energy during solid-solid interactions was represented using the proposed friction model, while both ‘slip’ and ‘stick’ interface showed unphysical approximations. We believe that the friction interface model completes the theory of multi-material interaction and provide a more appropriate way to model the complex dynamic behavior in Eulerian framework for solid materials.