Using a second gradient model to simulate the behaviour of concrete structural elements

Being a quasi-brittle material, concrete under tensile loading exhibits a strain softening behaviour that cannot be accurately reproduced with classical (without an internal length parameter) continuum mechanics models. An internal length parameter must be introduced to regularize the problem, as in the case of the so-called second gradient model. In this approach, an enriched kinematic description of the continuum is adopted considering higher (second) order gradients of the displacements following the work of Cosserat, Toupin, Mindlin and Germain. The model has been developed by Chambon and co-workers and has been mainly used with plasticity constitutive laws to reproduce the non-linear behaviour of soils. It is here applied for the first time to concrete and reinforced concrete specimens considering material laws based on the damage mechanics theory. The advantages and limitations of the approach are discussed, and possible improvements towards more realistic responses are suggested.