Methods for selective scaling of strain and inertia for explicit dynamics with tetrahedral finite elements

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Purpose of the proposed research project is the development of variational methods for selective scaling of inertia and strain for explicit dynamic finite element analysis to develop efficient and accurate tetrahedral finite elements for non-linear dynamics and wave propagation. For complex geometries, tetrahedral finite elements are often indispensable in finite element meshes. Existing tetrahedral finite elements are limited in their performance due to the following issues: Locking, high CPU cost, high numerical dispersion and large reflection-transmission errors in heterogeneous media. So far, the universal accurate high-performance tetrahedral does not exist. To reduce locking effects and CPU cost, which are important issues in non-linear structural dynamics, variational selective inertia and strain scaling is proposed. The basic hypothesis is that the application of strain scaling for tetrahedral elements prone to locking and the application of inertia scaling for computationally expensive elements like elements with Allmans rotations and composite finite elements enables the development of efficient and at the same time accurate elements. For wave propagation problems, an optimized dispersion behavior of higher-order tetrahedral elements may be obtained by inertia customization. Finally, the accuracy for simulation in heterogeneous media is improved by a reduction of the reflection-transmission-error.