G. Meschke, R. Lackner, H.A. Mang:
"An Anisotropic Material Model for Cracked Concrete Based on Plasticity- and Damage Theory";
ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, 77 (1997), S1; S. S217 - S218.
Tensile loading of plain concrete induces a growth and coalescene of microcracks which results in the formation of macroscopic cracks and progressiv degradation of the elastic moduli. This deterioration process prevents a complete closure of microcracks in unloading processes. As a consequence, permanent strains develop. The proposed material model for plain concrete  is based on an anisotropic damage evolution law  and formulated within the framework of multisurface damage-elastoplasticity allowing for stiffness degredation as well as for the modelling of inelastic deformations. Cracking under tension as well as the nonlinear response of concrete in compression is taken into account.
 G. MESCHKE, R. LACKNER, H.A. MANG: An anisotropic elastoplastic-damage model for plain concrete, J. for Num. Methods in Eng. (42), 703-727, 1998
 S. GOVINDJEE, G.J. KAY, J.C. SIMO: Anisotropic modelling and numerical simulation of brittle damage in concrete, Int. J. Num. Meth. Eng 38 (1995), 3611-3634.
Keywords: crack, damage, softening, plasticity, anisotropic, multisurface