  Finite elasticity problems commonly include material and geometric
nonlinearities and are solved using various numerical methods. However, for
highly nonlinear problems, achieving convergence is relatively difficult and
requires small load step sizes. In this work, we present a new method to
transform the discretized governing equations so that the transformed problem
has significantly reduced nonlinearity and, therefore, Newton solvers exhibit
improved convergence properties. We study exponential-type nonlinearity in soft
tissues and geometric nonlinearity in compression, and propose novel
formulations for the two problems. We test the new formulations in several
numerical examples and show significant reduction in iterations required for
convergence, especially at large load steps. Notably, the proposed formulation
is capable of yielding convergent solution even when 10 to 100 times larger
load steps are applied. The proposed framework is generic and can be applied to
other types of nonlinearities as well.
