Keywords: micro-mechanics, damage, cementitious composite, constitutive.

The present authors have recently developed two models for cementitious composite materials (CCM) based on micro-mechanical theories. In this first of these [1] the 'penny-shaped' crack solution [2] was adopted but with a new rough crack closure component. The interesting result from this work was that the biaxial failure envelope calculated using the model had the same characteristics as the established biaxial failure envelope for concrete. The second development [3] used a combination of Eshelby's solution for an ellipsoid inclusion in an elastic body and the penny-shaped crack solution in a Mori-Tanaka scheme [2] to derive a model component which could replace phenomenological fracture or damage components of plastic-fracture or plastic-damage models. The key aspect of the latter work is that it natural simulates the type of splitting cracks that occur in CCMs when they are loaded in uniaxial compression. The present paper briefly describes these two micro-mechanical models and then each model is critically appraised and a new formulation is presented that uses aspects from each of the other two models.

The first problem addressed in the development of the new model was that of the asymmetric secant constitutive tensor. This was solved by introducing an expression which ensures that the total inelastic work from the formation from all cracks equals that from the sum of the individual cracks in the matrix phase. Once this had been solved, a formulation was derived which uses the effective matrix stresses as a basis for computing the added strain tensor, in a manner that provides the same stability as that of the kinematically constrained model.

The new model has been implemented in a MATHCAD sheet and a number of single point simulations undertaken. These include unixaxial, biaxial compression and uniaxial tensile stress paths. The simulations produce responses which are typical for concrete and mortar. When compared with the model of reference [1], it proved easier to derive the material data and obtain strains at peak stress that matched typical experimental values for normal strength concrete and mortar.

1

A.D. Jefferson and T. Bennett, "Micro-mechanical damage and rough crack closure in cementitious composite materials", International Journal of Numerical and Analytical Methods in Geomechanics, 31, 133-146, 2007. doi:10.1002/nag.551

2

S. Nemat-Nasser and M. Hori, "Micromechanics: Overall properties of heterogeneous materials", North-Holland, 1999.

3

A.D. Jefferson and T. Bennett, "Modelling cross-cracking in cementitious composite materials with micro-mechanics, damage theory and continuum plasticity", Under consideration, International Journal of Solids and Structures, 2007.

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