Efficient Nonlinear Solid Mechanics Computation via Krylov Subspace Methods in a Finite Volume Framework

This paper introduces a computationally efficient approach for solving nonlinear solid mechanics problems using the finite volume method. The method employs a Jacobianfree Newton-Krylov (JFNK) technique, which avoids the explicit formation and storage of the Jacobian matrix, thereby reducing memory requirements and computational cost. The implementation leverages Krylov subspace solvers, such as GMRES, in conjunction with a compact-stencil approximation of the Jacobian as a preconditioner. The performance of this JFNK approach is assessed and compared against a traditional segregated solution method across a range of benchmark problems, including linear elasticity, hyperelasticity, and elastoplasticity. Results demonstrate the method's superior performance, particularly in terms of computational speed, for linear and nonlinear elastic cases. The implementation is integrated into an open-source computational mechanics library, providing a foundation for further research and application in solid mechanics simulations.