Reduced integration‐based solid and solid‐shell finite elements for gradient‐extended damage

Abstract

AbstractThe present contribution is concerned with the incorporation of gradient‐extended damage into reduced integration‐based continuum finite elements. To this end, the purely mechanical low‐order solid and solid‐shell elements based on the isoparametric concept are combined with a gradient extended two‐surface damage plasticity model. Due to a tailored combination of reduced integration with hourglass stabilization, the enhanced assumed strain (EAS) method and in case of the solid‐shell 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 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. Two representative numerical examples of an elasto‐plastic asymmetrically notched specimen as well as an elastic thin annular plate reveal the accuracy and efficiency of the proposed methodology. Besides the ability to deliver mesh independent results, the framework is especially suitable for constrained situations in which conventional low‐order finite elements suffer from well‐known locking phenomena.