Computationally efficient explicit nonlinear analyses using reduced integration-based solid-shell finite elements

Solid-shell formulations based on reduced integration with hourglass stabilization have several advantages. Among these are the smaller number of Gauss points and the direct modelling of the thickness stretch, a feature which is usually not present in standard degenerated shell elements. The latter issue is especially important for applications where contact is involved, e.g. for almost all relevant systems in production technology. Obviously this makes solid-shell formulations very attractive for their use in industrial design. A major disadvantage in the context of explicit analyses is, however, the fact that the critical time step is determined by the thickness of the solid-shell element which is usually smaller than the smallest in-plane dimension. Therefore, four-node shells (where the critical time step is determined by the in-plane dimensions) are still often preferred for explicit analysis. In the present paper we suggest several techniques to overcome this difficulty, also in the case of problems dominated by nonlinearities such as finite deformations, elastoplasticity and contact. Reference is made to an 8-node hexahedron solid-shell element recently proposed by Schwarze and Reese (2011) [32] in an implicit context. First of all, the time steps in explicit analyses are so small that it may be not necessary to update the hourglass stabilization and the implicit computation of the internal element degrees-of-freedom in every time step. Performing the update in only every hundredth step or computing an explicit rather than implicit update can reduce the computational effort up to about 50%. Another important issue is selective mass scaling which means to modify the mass matrix in such a way that the speed of sound in thickness direction is reduced. This enables the choice of a larger time step. The CPU effort can be finally noticeably decreased without changing the structural response significantly. This makes the presently used solid-shell formulation competitive to four-node shells, also for explicit analysis.