The Large-Deformation Performance of Lagrangian Higher-Order Elements for Explicit Dynamics

  • Beissel, Stephen (Southwest Research Intstitute)

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Finite-element analysis that resolves the wave motion in nonlinear solid dynamics is most effectively performed using explicit time integration on a Lagrangian mesh. Until recently, such analyses have been performed predominantly with first-order elements. The second-order [1,2] and higher-order [3] formulations introduced recently for explicit dynamics exhibit several advantages over the traditional first-order formulations, such as the improved representation of curved surfaces, the avoidance of both volumetric locking and zero-energy modes of deformation, and the superior accuracy in modelling wave motion. This presentation evaluates the performance of these second- and higher-order elements under the large deformations that are characteristic of severe loading. Simulation results are presented that probe the large-deformation accuracy and efficiency of the elements by comparison with standard first-order elements. The results include convergence with mesh refinement and the effects of increasing element order. The simulations incorporate element deformations through either increasing material strains or the isoparametric mappings of the elements from their parent domains. The conclusions of this evaluation include the beneficial effects of element order and the importance of maintaining an accurate estimate of the critical stable time step, both of which increase with increasing order. REFERENCES [1] K.T. Danielson and J.L. O’Daniel. Reliable second-order hexahedral elements for explicit methods in nonlinear solid dynamics. Int. J. Numer. Methods Eng. 85 (9), pp. 1073-1102, 2011. [2] K.T. Danielson. Fifteen node tetrahedral elements for explicit methods in nonlinear solid dynamics. Comput. Methods Appl. Mech. Eng. 272, pp. 160-180, 2014. [3] S.R. Beissel, T.J. Holmquist, C.A. Gerlach and G.R. Johnson. Modeling High-Frequency Wave Propagation in Solids Using Higher-Order Finite Elements in the EPIC Code. Southwest Research Institute Report 18.19018/022 on contract W56HZV-17-C-0047 with the U.S. Army REDECOM-TARDEC, Nov. 2016.