Comparison of two forms of strain decomposition in an elastic-plastic damaging model for concrete

In the paper a new modified form of the constitutive equations for concretein the general framework for elastic-plastic damaging models proposed by theauthors in (Contrafatto and Cuomo 2006 J. Plast. 22 2273–300) is presented.The modification concerns the definition of the internal energy potential. In theoriginal paper the expression of the elastic energy potential depends on the signof the trace of the elastic strain tensor. In the new formulation a decompositionof the strain tensor in its positive and negative component by means of a basisfreerepresentation in terms of eigenprojections is used. As a consequencea different evolution of damage, affecting in a different way the tensile andcompressive component of the strain tensor, is obtained. The two models belongto the class of continuum scalar damage models and are developed within thecontext of simple materials. The new model, first formulated in an arbitrarycartesian coordinate system, is presented in a principal axes representation, inorder to reduce the algebraic complexity of the expressions and to make easierthe analysis of simple load processes, while the treatment of the constitutiveequations for the general case will be an object of future developments. Acomparison between the predictions of the two models is performed by meansof the analysis of some loading processes. The new formulation is able toovercome some drawbacks of the original model, especially in the tensileregime. In contrast, in the compressive regime, for which already the originalformulation yielded satisfactory results, no change was detected.