Numerical simulation of weakly compressible hyper-elastic solids using a conservative pressure-velocity formulation on arbitrary Lagrangian-Eulerian framework

Abstract

Abstract Unification of the numerical models and methods in computational solid and fluid dynamics has been a research objective with at least two major advantages in mind. The first benefit of such unification is the more efficient data transfer between fluid and solid media, and the second advantage is the possibility of developing a better solver as compared to the separate existing solid and fluid solvers. In this paper, a conservative fluid-like pressure-velocity-based formulation is proposed that simulates large deformation of a weakly compressible hyper-elastic solid on an Arbitrary Lagrangian-Eulerian (ALE) framework. The proposed solver, which is implemented in OpenFOAM software, allows for flexible grid movement, i.e. mesh points are not forced to follow material points, as well as for the employment of various material models such as Mooney-Rivlin and Neo-Hookean constitutive laws. Three challenging 2-D and 3-D test cases including torsion, bending and pressing of solid objects are presented to examine and discuss the accuracy and flexibility of the proposed solver. Furthermore, more light is shed on the concept of the pressure in compressible solids and appropriate boundary conditions at traction boundaries.