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We present the application of simultaneous diagonalization and minimum energy(SDME) high-order finite element modal bases for simulation of transientnon-linear elastodynamic problem, including impact cases with neo-hookeanhyperelastic materials. The bases are constructed using procedures forsimultaneous diagonalization of the internal modes and Schur complement of theboundary modes from the standard nodal and modal bases, constructed usingLagrange and Jacobi polynomials, respectively. The implementation of thesebases in a high-order finite element code is straightforward, since theprocedure is applied only to the one-dimensional expansion bases. Non-lineartransient structural problems with large deformation, hyperelastic materialsand impact are solved using the obtained bases with explicit and implicit timeintegration procedures. Iterative solutions based on preconditioned conjugategradient methods are considered. The performance of the proposed bases in termsof the number of iterations of pre-conditioned conjugate gradient methods andcomputational time are compared with the standard nodal and modal bases. Ournumerical tests obtained speedups up to 41 using the considered bases whencompared to the standard ones.

Simulation of non-linear structural elastodynamic and impact problems using minimum energy and simultaneous diagonalization high-order bases