On a Class of Continuum Damage Mechanics Theories

A thermodynamically consistent continuum damage mechanics formula tion in the stress space is outlined. Damage is reflected in the fourth-order material com pliance tensor involving a damage parameter whose increment is obtained from the consis tency condition of the damage surface. A new damage function and an alternate damage response tensor in mode I are formulated by means of which a smooth transition from the cleavage damage mode to the compressive damage mode is achieved and nonlinear re sponses in the lateral directions are predicted. Furthermore, the permanent deformation in damage mode I is predicted by using a simple evolutionary equation. The tangent compli ance tensor is also given in terms of the response tensors and the first variation of the damage function with respect to state variables. The model is illustrated for different stress paths in mortar and concrete.