A finite volume method for large strain analysis of incompressible hyperelastic materials

This paper describes development of a displacement–pressure based finite volume formulation for modelling of large strain problems involving incompressible hyperelastic materials. The method is based on the solution of the integral conservation equations governing momentum balance in total Lagrangian description. The incompressibility constraint is enforced by employing the integral form of the mass conservation equation in deformed configurations of the body. A Mooney–Rivlin incompressible material model is used for material description. A collocated variable arrangement is used and the spatial domain is discretized using finite volumes of an arbitrary polyhedral shape. A segregated approach is employed to solve resulting set of coupled non-linear algebraic equations, utilizing a SIMPLE based algorithm for displacement–pressure coupling. Comparisons of numerical and analytical results show a very good agreement. For the limited range of cell topologies tested the developed method appears to be locking free