Some observations on the regularizing field for gradient damage models
Starting with a stress-based damage model similar to the model adopted in plasticity, the authors obtain an elastic-degradation damage model with additive decomposition of total strain rate into an elastic and a damage part. The damage part is proportional to the elastic part multiplied by the scalar damage variable. Implicitly the authors perform a formalism encountered in plasticity, which includes an elastic-damage continuum tangent tensor. The damage model is isotropic, with a linear strain damage law. Next, the authors introduce a damage loading function which includes a homogeneous stress function, a free term as static-like internal variable which decreases the stress induced by damage growth, and an other term which stands for the initial threshold for the onset of damage. Further internal variable is assumed to accumulate the damage strain expressed through a damage-strain softening modulus multiplied by a time integral of the damage part of the strain rate. The flow conditions for stress and derivatives of internal variables are Kuhn-Tucker type loading/unloading conditions. Finally, the authors obtain expressions for damage loading function, a consistency parameter for the flow, and constitutive equation with the scalar damage variable. Applications are made for a bar with constant cross-section in pure tension with monotonically increasing displacements at the edges. Plotted diagrams illustrate numerical results for different stress levels and softening regimes. The study examines also the brittleness of local first peak regularized regime, and interprets the variation of damage band as localization process.
Kuhn-Tucker loading/unloading conditions
additive decomposition of total strain rate
scientific article; zbMATH DE number 1487291
scientific article