A finite volume method for incompressible linear elasticity

This paper describes development of a finite volume based method for modelling of incompressible linear elastic body problems. The method is based on the solution of the integral form of conservation equations governing momentum balance and the introduction of pressure as an additional variable. The incompressibility is enforced by employing the volumetric constraint equation. A collocated variable arrangement is used and the spatial domain is discretised using finite volumes of arbitrary polyhedral shapes. A segregated approach is employed to solve resulting set of coupled linear algebraic equations, embedding a SIMPLE based algorithm for displacement–pressure coupling. Numerical experiments showed that the developed method appears to be locking free.