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 hy perelasticity. The proposed method is featuring the principal axis represen tation of the theory, facilitating the choice of the strain energy function (in terms of the principal stretches) and simplifying the stress computati on. The choice of the spatial Cauchy-Green strain measure, leading to a ver y sparse structure of the strain-displacement operators, and the operator s plit solution of equilibrium equations, leading to reduced secondary storag e requirements, further increase the computational efficiency. A set of num erical examples is used to illustrate a robust performance of the construct ed plane strain element with a single incompatible mode in quasi-incompress ible deformation patterns.