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 (with-out 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 (sec-ond) 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 rst
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.