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 concrete in the general framework for elastic-plastic damaging models proposed by the authors in (Contrafatto and Cuomo 2006 J. Plast. 22 2273–300) is presented. The modification concerns the definition of the internal energy potential. In the original paper the expression of the elastic energy potential depends on the sign of the trace of the elastic strain tensor. In the new formulation a decomposition of the strain tensor in its positive and negative component by means of a basis-free representation in terms of eigenprojections is used. As a consequence a different evolution of damage, affecting in a different way the tensile and compressive component of the strain tensor, is obtained. The two models belong to the class of continuum scalar damage models and are developed within the context of simple materials. The new model, first formulated in an arbitrary cartesian coordinate system, is presented in a principal axes representation, in order to reduce the algebraic complexity of the expressions and to make easier the analysis of simple load processes, while the treatment of the constitutive equations for the general case will be an object of future developments. A comparison between the predictions of the two models is performed by means of the analysis of some loading processes. The new formulation is able to overcome some drawbacks of the original model, especially in the tensile regime. In contrast, in the compressive regime, for which already the original formulation yielded satisfactory results, no change was detected.

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