Towards forming simulations by means of reduced integration-based solid-shell elements considering gradient-extended damage

Abstract

Abstract The present contribution is concerned with the non-local damage analysis of geometrically non-linear shells. To this end, a low-order displacement-based solid-shell finite element formulation is combined with a gradient-extended damage-plasticity model. Due to a tailored combination of reduced integration with hourglass stabilization, the enhanced assumed strain (EAS) method and the assumed natural strain (ANS) method, the most dominant locking phenomena are eliminated. A polynomial approximation of the strain-like as well as the stress-like quantities within the weak forms enables the definition of a suitable and efficient hourglass stabilization. In this way, the internal element force vectors as well as the element stiffness contributions coming from the hourglass stabilization can be determined analytically. A numerical example of a circumferentially notched cylinder considering plasticity coupled with damage reveals the potential of the proposed methodology. Besides the ability to deliver mesh independent results within the softening regime, the framework is especially suitable for thin-walled structures, in which conventional low-order continuum elements suffer from well-known locking phenomena.