LOCAL SECOND GRADIENT MODELS AND DAMAGE MECHANICS: APPLICATION TO CONCRETE P. KOTRONIS 1 , R. CHAMBON 1 , J. MAZARS 1 and F. COLLIN 2 1 Laboratoire Sols Solides Structures C.N.R.S./I.N.P.G./U.J.F, France. 2 Geomac Department, Université de Liège, Belgium ABSTRACT The non linear behaviour of concrete is often simulated using local constitutive models based on the continuous damage mechanics theory. This approach however is not adequate for post-localisation studies with strain softening. It is well known that spurious mesh dependence appears in computations and cases of failure without energy dissipation. In order to improve computational performance second grade local models are chosen to include a meso scale in the continuous damage model. This approach differs from the nonlocal one in the sense that it is a local theory with higher order stresses depending only on the local cinematic history. 1D numerical computations with concrete specimens are presented. Using a random initialisation of the iterative solver of the equilibrium equation we search the existence of various solutions for the boundary value study and also to see if the second grade term regularise the problem giving results that are mesh insensitive and objective. 1 INTRODUCTION Experimentally, concrete specimens exhibit a network of microscopic cracks that nucleate parallel to the axis of loading. Due to the presence of heterogeneities in the material (aggregates surrounded by a cement matrix), tensile transverse strains generate a self-equilibrated stress field orthogonal to the loading direction, a pure mode I (extension) is thus considered to describe the behaviour in compression. A classical local model based on continuous damage mechanics is used hereafter allowing accounting for the asymmetric behaviour of concrete under tension and compression. The influence of microcracking due to the external loads is introduced via a single scalar damage variable d ranging from 0 for the undamaged material to 1 for a completely damaged material. In order to introduce the non-symmetric behaviour of concrete, the failure criterion is expressed in terms of the principal extensions. This approach however is not adequate for post-localisation studies where strain softening appears. Calculations performed with a local classical continuum model - which does not incorporate an internal length variable - are unable to model objectively intrinsic failure zones. It is now well known that a spurious mesh dependence appears in computations and cases of failure without energy dissipation. In order to improve computational performance the nonlocal damage approach is often used in the literature. A different solution is investigated within this work. Second grade local models are chosen to include a meso scale in the continuous damage model. This approach differs from the nonlocal one in the sense that it is a local theory with higher order stresses depending only on the local cinematic history. Details on the damage mechanics constitutive law are given at the first part of the paper. The second gradient local approach is then introduced and different numerical computations with 1D concrete specimens in traction are presented. Using a random initialisation of the iterative solver of the equilibrium equation we search the existence of various solutions for the boundary value study and also to see if the second grade term regularise the problem giving results that are mesh insensitive and objective.