A Fixed Grid Finite Element Method (FGFEM) in addition to a Mooney-Rivlin hyperelastic model is introduced. This method uses the mixed finite element formulation to treat the elements, but classifying these in a fixed cartesian grid that is superimposed over the model geometry -- In order to do this, the boundary tracking is achieved by solving the level set equation -- A numerical extrapolation of the displacement field from the solid domain to the entire fixed grid domain is done -- The system of equations are solved by the use of an incremental Newton-Raphson scheme -- Finally, some numerical examples are implemented and good convergence results are obtained for the displacement field, showing that FGFEM for the hyperelastic model is suitable for mechanical problems undergoing large strains and large displacement
