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

• A fluid-like solver is implemented in OpenFOAM to simulate hyperelastic deformations of a weakly compressible material. • Three benchmark cases including torsion, pressing, and bending for 2-D and 3-D geometries are successfully simulated. • At traction boundaries, applying pressure condition deduced from the conservation of mass gives promising results. • Some simplified constitutive laws violate the compatibility between pressure, density and stress. • Compared to Lagrangian, Eulerian approach has computational merits in the case of pure rotation of a cylinder. 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. [ABSTRACT FROM AUTHOR]