A new locking-free hexahedral element with adaptive subdivision for explicit coining simulation

In this paper, an 8-node hexahedral element based on multi-point integration is proposed in the dynamic explicit framework, with a new adaptive subdivision method adopted. By taking advantages of the assumed strain method, the volumetric and the shear locking of the element are successfully avoided. The locking-free hexahedral element is further applied to coining simulations. Due to large-scale elements and high non-linearity, it's difficult to carry out coining simulations in the context of the implicit framework, especially for a commemorative coin with fine patterns. Thus, an explicit algorithm for coining simulations is developed, which avoids time-consuming iterations and guarantees the computational convergence. Aiming at improving the simulation efficiency furtherly, a multi-layer one-to-four adaptive element subdivision strategy is proposed, with two subdivision criteria with respect to element geometry considered. In this way, the element number in the simulation is dramatically decreased, while the fine patterns of the coin are described exactly. Based on several numerical examples, the locking-free and hourglass-free properties of the proposed hexahedral element are validated, and the accuracy of the coining simulation algorithm is also demonstrated.