Mixed and selective reduced integration procedures in large strain hyperelastic analysis of nearly incompressible solids

Abstract

We compare a mixed method and a displacement method with selective reduced integration for the finite element analysis of finite, nearly incompressible, hyperelasticity. The Simo-Taylor three-field variational formulation is extended to a general description which includes volumetric-deviatoric coupling and can readily be specialized to particular cases, such as the strain energy functions due to Rivlin or Ogden. The displacement formulation is obtained as a special case. Emphasis is placed on the treatment of incompressibility and the avoidance of volumetric locking. Classical incompressible strain energy functions, extended to include the effect of compressibility at the nearly incompressible limit, result in a penalty type algorithm for the imposition of near incompressibility. This is accomplished through the decomposition of strain into distortional and volumetric components. Shear locking is prevented through the use of higher order elements. All integrals are evaluated in the current configuration. The two methods have been implemented into the finite element code MSC/NASTRAN i . It is shown that the methods,