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

The present contribution is concerned with the incorporation of gradient-extended damage into reduced integration-based continuum finite elements. To this end, purely mechanical low-order solid and solid-shell elements based on isoparametric concept are combined a gradient extended two-surface plasticity model. Due to tailored combination integration hourglass stabilization, enhanced assumed strain (EAS) method in case natural (ANS) method, most dominant locking phenomena eliminated. A polynomial approximation strain-like as well stress-like quantities within weak forms enables definition suitable stabilization. In way, element stiffness contributions coming from stabilization can be determined analytically, since they represent polynomials respect Cartesian coordinates. Two representative numerical examples an elasto-plastic asymmetrically notched specimen elastic thin annular plate reveal accuracy efficiency proposed methodology. Besides ability deliver mesh independent results, framework especially for constrained situations which conventional suffer well-known phenomena.