The present contribution is concerned with the incorporation of gradient-extended damage into a reduced integration-based solid-shell finite element formulation. To this end, a purely mechanical low-order solid-shell element based on the isoparametric concept is combined with a gradient-extended two-surface damage plasticity model. Due to a tailored combination of the assumed natural strain (ANS) as well as the enhanced assumed strain (EAS) method, the most important locking phenomena are eliminated. A polynomial approximation of the kinematic as well as the constitutively dependent quantities within the weak forms enables the definition of a suitable hourglass stabilization. In this way, the element stiffness contributions coming from the hourglass stabilization can be determined analytically, since they represent polynomials with respect to Cartesian coordinates. Several numerical examples on elastic as well as elasto-plastic plates and shells under various loading scenarios show the ability of the present methodology to predict various degradation processes such as damage initiation, propagation, merging as well as branching.

本贡献涉及将梯度扩展的损伤合并到减少的基于积分的固体壳有限元公式中。为此，将基于等参概念的纯机械低阶固体壳单元与梯度扩展的两面损伤可塑性模型相结合。由于假定的自然应变（ANS）和增强的假定的应变（EAS）方法的量身定制的组合，最重要的锁定现象被淘汰。弱形式内的运动量以及与本构有关的量的多项式逼近使得可以定义合适的沙漏稳定性。以这种方式，由于它们代表关于笛卡尔坐标的多项式，因此可以分析地确定来自沙漏稳定性的单元刚度贡献。在各种载荷情况下的弹性以及弹塑性板和壳上的几个数值示例表明，本方法论能够预测各种降解过程，例如破坏的开始，扩散，合并以及分支。