Multiscale Methods For Accelerating Explicit Dynamics Computations In Solid Mechanics

Abstract

In this work we tackle two novel approaches for the solution of multiscale solid mechanics problems. In the first one a selective mass scaling approach is presented that can significantly reduce the computational cost in explicit dynamic simulations, while maintaining accuracy. One of the main computational issues with traditional explicit dynamics simulations is the significant reduction of the critical time step as the spatial resolution of the finite element mesh increases. The proposed method is based on a multiscale decomposition approach that separates the dynamics of the system into low (coarse scales) and high frequencies (fine scales). Here, the critical time step is increased by selectively applying mass scaling on the fine scale component only. In problems where the response is dominated by the coarse (low frequency) scales, significant increases in the stable time step can be realized. In this work, we use the Proper Orthogonal Decomposition (POD) method to build the coarse scale space. The main idea behind POD is to obtain an optimal low-dimensional orthogonal basis for representing an ensemble of high-dimensional data. In our proposed method, the POD space is generated with snapshots of the solution obtained from early times of the full-scale simulation. The example problems addressed in this work show significant improvements in computational time, without heavily compromising the accuracy of the results. The second approach uses POD in a similar manner, but adopts an equation-free central difference projective integration scheme to observe and advance dynamics of the coarse scales. This equationfree approach is adopted in order to circumvent some of the drawbacks of the Galerkin projection of the momentum equations on the coarse scales, for model reduction. Proven consistency and accuracy properties make this method attractive for tackling transient dynamics problems.