Papers by Keyword: Variational Approach

Abstract: Metal forming processes involve continuous strain path changes inducing plastic anisotropywhich could result in the failure of the material. It has been often observed that the formation andevolution of meso-scale dislocation microstructures under monotonic and non-proportional loading have substantial effect on the induced anisotropy. It is therefore quite crucial to study the microstructureevolution to understand the underlying physics of the macroscopic transient plastic behavior. In thiscontext the deformation patterning induced by the non-convex plastic energies is investigated in amulti-slip crystal plasticity framework. An incremental variational approach is followed, which resultsin a rate-independent model exhibiting a number of similarities to the rate-dependent formulationproposed in [Yalcinkaya, Brekelmans, Geers, Int. J. of Solids and Structures, 49, 2625-2636, 2012].However there is a pronounced difference in the dissipative character of the models. The influenceof the plastic potential on the evolution of dislocation microstructures is studied through a Landau-Devonshire double-well plastic potential. Numerical simulations are performed and the results arediscussed with respect to the observed microstructure evolution in metals.

Abstract: Fracture mechanics has been revisited by proposing different models of quasi static brittle fracture. In this work, the problem of the quasi static crack propagation is based on variational approach. It requires no prior knowledge of the crack path or of its topology. Moreover, it is capable of modeling crack initiation. In the numerical experiments, we use a standard linear (P1) Lagrange finite element method for discretization. We perform numerical simulations of a piece of brittle material without initial crack. An alternate minimizations algorithm is used. Based on these numerical results, we determine the influence of numerical parameters on the evolution of energies and crack propagation. We show also the necessity of considering the kinetic term and the crack propagation becomes dynamic.

Abstract: Fracture mechanics has been revisited aimed at modeling brittle fracture based on Griffith viewpoint. The purpose of this work is to present a numerical computational method for solving the quasi static crack propagation based on the variational theory. It requires no prior knowledge of the crack path or of its topology. Moreover, it is capable of modeling crack initiation. At the numerical level, we use a standard linear (P1) Lagrange finite element method for space discretization. We perform numerical simulations of a piece of brittle material without initial crack. We show also the necessity of adding the backtracking algorithm to alternate minimizations algorithm to ensure the convergence of the alternate minimizations algorithm to a global minimizer.

Abstract: Severe damage is produced in tissues by freezing and thawing. Until now, a great majority of the studies are performed qualitatively, lacking any quantitative approach. An important step is to choose the best option among different freezing methods. To approach the complex problem of damage produced in tissues by freezing, in this paper we present the classical mechanics approach and a quantitative study making use of a fractal methodology (evaluation of fractal dimension by box-counting method). A comparative fractal analysis between two different steps of freezing the human thoracic diaphragm muscle has been performed to quantify the voids and cracks produced by freezing (samples were placed in a cryostat chamber). Moreover, a standard Euclidean morphometry was performed to determine area and shape of the muscle nuclei after the two steps of freezing. Fractal dimension of the ice-tissue interface structures increased with decreasing temperature (p<0.0001), percentage of cell muscle decreased (p<0.01), while standard morphometry of the nuclei didnt show any modifications. Our results show the ability of the fractal approach to accurately quantify the damage produced by freezing and reveals that the lowest temperature produces the most damage.