AbstractA precise iterative strategy to compute the polar decomposition of the three-dimensional deformation gradient tensor is presented for nonlinear solid mechanics analysis software. By exploiting relationships between various stretch tensors, polar decomposition is transformed into the solution of six nonlinear (quadratic) simultaneous equations, via Newton-Raphson (N-R), and a subsequent 3×3 matrix inversion and multiplication. The approach is easy to program and is versatile in its applicability to statics or dynamics. With only modest computational increases, the approximations and potential numerical drift of incremental decomposition schemes is avoided. Convergence can be accelerated using stretch histories, which, coupled with a modified N-R approach, can reduce computer times. Using an explicit central difference time integration scheme, convergence is shown to be attained in only a few iterations with very tight tolerances for severe deformations. Numerical examples compare different method v...