This thesis concerns the study of the yield criterion of the porous materials using the homogenei... more This thesis concerns the study of the yield criterion of the porous materials using the homogeneization, the limit analysis and the interior point optimization. The yield criterion of a porous material using Gurson's model, the most widely accepted for such materials in elasto-platic codes, is investigated. The Gurson model idealizes the porous material as a single cavity in a homothetic cell composed of a rigid plastic Mises material, called the Representative Volume Element (RVE) in the following. In this model, the cavities don't have any interactions or coalescence. Then we use the two limit analysis approaches, via a discretization of the model in finite elements. They lead to non-linear optimization problems, solved either by two commercial (???j'ai change le “cormmecial”)codes, XA or MOSEK, both optimization codes based on so-called interior point methods. For porous materials with cylindrical cavities, the Gurson criterion appears to be insufficient. In the generalized plane strain case, an analytical expression of this true criterion must take the form of a function of the loading parameters, at least in a three-dimensional representation. Conversely, for a porous material with spherical cavities, a full 3D model is worked out. The Gurson approach is slightly improved and, for the first time, it is validated by our rigorous static and kinematic approaches. The study of a RVE with 35 cylindrical random cavities confirms a bimodal criterion in generalized plane strain. In plane stress loading, the RVE is not representative. A nonlinear interior point method for solving stress based upper bound problems is proposed. To solve the problem, we used a convex optimizer, written on Matlab, developed at CORE (Centre of Operation Research and Econometrics) of Louvain la Neuve in Belgium. Assuming a linear, continuous or discontinuous virtual velocity field, the method appears to be efficient and general. This method is straightforward, needing only the yield criterion as information on the material
This thesis concerns the study of the yield criterion of the porous materials using the homogenei... more This thesis concerns the study of the yield criterion of the porous materials using the homogeneization, the limit analysis and the interior point optimization. The yield criterion of a porous material using Gurson's model, the most widely accepted for such materials in elasto-platic codes, is investigated. The Gurson model idealizes the porous material as a single cavity in a homothetic cell composed of a rigid plastic Mises material, called the Representative Volume Element (RVE) in the following. In this model, the cavities don't have any interactions or coalescence. Then we use the two limit analysis approaches, via a discretization of the model in finite elements. They lead to non-linear optimization problems, solved either by two commercial (???j'ai change le “cormmecial”)codes, XA or MOSEK, both optimization codes based on so-called interior point methods. For porous materials with cylindrical cavities, the Gurson criterion appears to be insufficient. In the gener...
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European Journal of Mechanics A-solids, Jan 1, 2005
The yield criterion of a porous material using Gurson's model [Gurson, A.L., 1977. Continuum theo... more The yield criterion of a porous material using Gurson's model [Gurson, A.L., 1977. Continuum theory of ductile rupture by void nucleation and growth – Part I: Yield criteria and flow rules for porous ductile media. ASME J. Engrg. Mater. Technol. 99, 2–15] is investigated herein. Both methods of Limit Analysis are applied using linear and conic programming codes for solving resulting non-linear optimization problems. First, the results obtained for a porous media with cylindrical cavities [Francescato, P., Pastor, J., Riveill-Reydet, B., 2004. Ductile failure of cylindrically porous materials. Part 1: Plane stress problem and experimental results. Eur. J. Mech. A Solids 23, 181–190; Pastor, J., Francescato, P., Trillat, M., Loute, E., Rousselier, G., 2004. Ductile failure of cylindrically porous materials. Part 2: Other cases of symmetry. Eur. J. Mech. A Solids 23, 191–201] are summarized, showing that the Gurson expression is too restrictive in this case. Then the hollow sphere problem is investigated, in the axisymmetrical and in the three-dimensional (3D) cases. A plane mesh of discontinuous triangular elements is used to model the hollow sphere as RVE in the axisymmetrical example. This first model does not provide a very precise yield criterion. Then a full 3D model is applied (using discontinuous tetrahedral elements), thus solving nearly exactly the general three-dimensional problem. Several examples of loadings are investigated in order to test the final criterion in a variety of situations. As a result, the Gurson approach is slightly improved and, for the first time, it is validated by our rigorous static and kinematic approaches.
The yield criterion of a porous material satisfying Gurson criterion conditions is studied here. ... more The yield criterion of a porous material satisfying Gurson criterion conditions is studied here. We use the twofold limit analysis approach applied to a representative volume element of the porous media and recent optimization codes. Both upper and lower bounds are very close, and they give quasi-exact solutions. As a result, the Gurson approach is slightly improved and, for the first time, validated by a rigorous, full 3D static approach.
The yield criterion of a porous material satisfying Gurson criterion conditions is studied here. ... more The yield criterion of a porous material satisfying Gurson criterion conditions is studied here. We use the twofold limit analysis approach applied to a representative volume element of the porous media and recent optimization codes. Both upper and lower bounds are very close, and they give quasi-exact solutions. As a result, the Gurson approach is slightly improved and, for the first time, validated by a rigorous, full 3D static approach.
This thesis concerns the study of the yield criterion of the porous materials using the homogenei... more This thesis concerns the study of the yield criterion of the porous materials using the homogeneization, the limit analysis and the interior point optimization. The yield criterion of a porous material using Gurson's model, the most widely accepted for such materials in elasto-platic codes, is investigated. The Gurson model idealizes the porous material as a single cavity in a homothetic cell composed of a rigid plastic Mises material, called the Representative Volume Element (RVE) in the following. In this model, the cavities don't have any interactions or coalescence. Then we use the two limit analysis approaches, via a discretization of the model in finite elements. They lead to non-linear optimization problems, solved either by two commercial (???j'ai change le “cormmecial”)codes, XA or MOSEK, both optimization codes based on so-called interior point methods. For porous materials with cylindrical cavities, the Gurson criterion appears to be insufficient. In the generalized plane strain case, an analytical expression of this true criterion must take the form of a function of the loading parameters, at least in a three-dimensional representation. Conversely, for a porous material with spherical cavities, a full 3D model is worked out. The Gurson approach is slightly improved and, for the first time, it is validated by our rigorous static and kinematic approaches. The study of a RVE with 35 cylindrical random cavities confirms a bimodal criterion in generalized plane strain. In plane stress loading, the RVE is not representative. A nonlinear interior point method for solving stress based upper bound problems is proposed. To solve the problem, we used a convex optimizer, written on Matlab, developed at CORE (Centre of Operation Research and Econometrics) of Louvain la Neuve in Belgium. Assuming a linear, continuous or discontinuous virtual velocity field, the method appears to be efficient and general. This method is straightforward, needing only the yield criterion as information on the material
This thesis concerns the study of the yield criterion of the porous materials using the homogenei... more This thesis concerns the study of the yield criterion of the porous materials using the homogeneization, the limit analysis and the interior point optimization. The yield criterion of a porous material using Gurson's model, the most widely accepted for such materials in elasto-platic codes, is investigated. The Gurson model idealizes the porous material as a single cavity in a homothetic cell composed of a rigid plastic Mises material, called the Representative Volume Element (RVE) in the following. In this model, the cavities don't have any interactions or coalescence. Then we use the two limit analysis approaches, via a discretization of the model in finite elements. They lead to non-linear optimization problems, solved either by two commercial (???j'ai change le “cormmecial”)codes, XA or MOSEK, both optimization codes based on so-called interior point methods. For porous materials with cylindrical cavities, the Gurson criterion appears to be insufficient. In the gener...
Please be patient while the object screen loads. Changez de vue : Choisir un site… UCL FUNDP FUSL... more Please be patient while the object screen loads. Changez de vue : Choisir un site… UCL FUNDP FUSL FUCaM. ...
Please be patient while the object screen loads. Change Site View : Select a site… UCL FUNDP FUSL... more Please be patient while the object screen loads. Change Site View : Select a site… UCL FUNDP FUSL FUCaM. ...
Please be patient while the object screen loads. Change Site View : Select a site… UCL FUNDP FUSL... more Please be patient while the object screen loads. Change Site View : Select a site… UCL FUNDP FUSL FUCaM. ...
Please be patient while the object screen loads. Change Site View : Select a site… UCL FUNDP FUSL... more Please be patient while the object screen loads. Change Site View : Select a site… UCL FUNDP FUSL FUCaM. ...
European Journal of Mechanics A-solids, Jan 1, 2005
The yield criterion of a porous material using Gurson's model [Gurson, A.L., 1977. Continuum theo... more The yield criterion of a porous material using Gurson's model [Gurson, A.L., 1977. Continuum theory of ductile rupture by void nucleation and growth – Part I: Yield criteria and flow rules for porous ductile media. ASME J. Engrg. Mater. Technol. 99, 2–15] is investigated herein. Both methods of Limit Analysis are applied using linear and conic programming codes for solving resulting non-linear optimization problems. First, the results obtained for a porous media with cylindrical cavities [Francescato, P., Pastor, J., Riveill-Reydet, B., 2004. Ductile failure of cylindrically porous materials. Part 1: Plane stress problem and experimental results. Eur. J. Mech. A Solids 23, 181–190; Pastor, J., Francescato, P., Trillat, M., Loute, E., Rousselier, G., 2004. Ductile failure of cylindrically porous materials. Part 2: Other cases of symmetry. Eur. J. Mech. A Solids 23, 191–201] are summarized, showing that the Gurson expression is too restrictive in this case. Then the hollow sphere problem is investigated, in the axisymmetrical and in the three-dimensional (3D) cases. A plane mesh of discontinuous triangular elements is used to model the hollow sphere as RVE in the axisymmetrical example. This first model does not provide a very precise yield criterion. Then a full 3D model is applied (using discontinuous tetrahedral elements), thus solving nearly exactly the general three-dimensional problem. Several examples of loadings are investigated in order to test the final criterion in a variety of situations. As a result, the Gurson approach is slightly improved and, for the first time, it is validated by our rigorous static and kinematic approaches.
The yield criterion of a porous material satisfying Gurson criterion conditions is studied here. ... more The yield criterion of a porous material satisfying Gurson criterion conditions is studied here. We use the twofold limit analysis approach applied to a representative volume element of the porous media and recent optimization codes. Both upper and lower bounds are very close, and they give quasi-exact solutions. As a result, the Gurson approach is slightly improved and, for the first time, validated by a rigorous, full 3D static approach.
The yield criterion of a porous material satisfying Gurson criterion conditions is studied here. ... more The yield criterion of a porous material satisfying Gurson criterion conditions is studied here. We use the twofold limit analysis approach applied to a representative volume element of the porous media and recent optimization codes. Both upper and lower bounds are very close, and they give quasi-exact solutions. As a result, the Gurson approach is slightly improved and, for the first time, validated by a rigorous, full 3D static approach.
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