Abstract

The Hellinger-Reissner principle is applied to derive a hybrid-mixed quadrilateral finite element with embedded-discontinuity in displacements, which can model a discrete crack (interface) within the element, and its sliding (and opening). The chosen material models are elasto-plasticity with hardening for the bulk, and traction-separation plasticity with softening for the interface. The latter model describes localized material failure and relates cohesion degradation with the fracture energy. The fulfillment of the inelastic relations at the bulk’s integration points is performed by a stress-driven update algorithm. The stress and embedded-discontinuity kinematic parameters are condensed on the element level, allowing for an efficient implementation.

摘要

应用 Hellinger-Reissner 原理推导出具有嵌入不连续位移的混合混合四边形有限元，它可以模拟单元内的离散裂纹（界面）及其滑动（和开口）。选择的材料模型是弹塑性与块体硬化，以及牵引分离塑性与界面软化。后一种模型描述了局部材料破坏并将内聚力退化与断裂能联系起来。体积积分点处的非弹性关系的实现是通过应力驱动的更新算法来实现的。应力和嵌入不连续运动学参数在单元级别上进行了压缩，从而实现了高效的实施。