Incompatible mode method for finite deformation quasi-incompressible elasticity

In this work we develop a geometrically nonlinear version of the method of incompatible modes, suitable for quasi-incompressible finite deformation hyperelasticity. The proposed method is featuring the principal axis representation of the theory, facilitating the choice of the strain energy function (in terms of the principal stretches) and simplifying the stress computation. The choice of the spatial Cauchy-Green strain measure, leading to a very sparse structure of the strain-displacement operators, and the operator split solution of equilibrium equations, leading to reduced secondary storage requirements, further increase the computational efficiency. A set of numerical examples is used to illustrate a robust performance of the constructed plane strain element with a single incompatible mode in quasi-incompressible deformation patterns. Received 14 December 1998