Static gradient damage simulations using stabilized finite elements

The hourglass control of two-field finite elements for the coupled problem of gradient damage is analyzed. For the equilibrium equations, stabilization is introduced according to the least-square method. For the additional averaging equation, three proposals of stabilization are considered, however only the gamma operator method performs well. Attention is focused on the formulation, implementation and spectral analysis of four-noded elements in two-dimensional simulations. Basic benchmarks of a tensile bar with an imperfection and a beam in four-point bending are computed and discussed.