07 Décembre – Thesis defense - Margaux Sage

14 h Amphi LRL - Building R - Arts et Métiers (Talence)

Discrete model of quasi-brittle fracture:proposal of a damage model for lattice beams.

Although much work has been done on modelling the failure mechanisms of brittle and quasi-brittle materials, gaps in the understanding of failure processes persist. In order to make progress on the comprehension of these mechanisms, the research work carried out within the framework of this thesis consists in combining several methods widely used to model fracture problems. Indeed, the model developed in this thesis is inspired by nonlinear fracture mechanics, in particular the cohesive zone models, coupled with a discrete numerical method. This model consists in particular in the introduction, in the discrete element code GranOO, of a cohesive link of the damageable beam type, whose damage and consequently the failure are energetically controlled. The equations derived from the Euler-Bernoulli beam theory governing the behaviour of the links are thus enriched with a softening phase, inspired by cohesive zone models, based on an equivalence between the kinematics of the Euler-Bernoulli beam and the conventional failure modes.  This equivalence leads to the definition of two pseudo failure modes. The first one, called pseudo Mode I, is based on the first order elongation of the lattice beam due to tensile stresses, while pseudo Mode II is based on the second order elongations generated by bending, shear and torsion stresses. The atypical character of this model led to a quick calibration and validation phase. In the first stage, the model is calibrated by means of two tests, a simple tensile test and a simple compression test on a quasi-fragile material of mortar type (sand concrete). The modelling of the compression test then shows a predisposition of the model to account for the effect of the test boundary conditions on the cracking paths, which will be further verified later. In a second step, the model is tested through the simulation of a tension-compression test and a Brazilian test, verifying the ability of the model to account for the unilateral effect and the kinetics of crack propagation respectively. Finally, the damageable lattice beam model is confronted with more complex experimental tests. On the one hand, the different tests proposed in the Carpiuc benchmark are simulated.  The simulation of notched mortar specimens subjected to simultaneous tensile, shear and bending stresses allows to evaluate the capacities of the model to describe cracking paths (bifurcation and branching) and kinetics of these paths consistent with the experimental results. Finally, a cyclic tension-compression test on a notched concrete specimen is simulated. The mechanisms of crack reclosure and the unilateral effect are described in a satisfactory manner.

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