[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-958012","data":"\u003Cdiv class=\u0022container content-rte\u0022\u003E\n  \u003Cdiv class=\u0022row\u0022\u003E\n    \u003Cdiv class=\u0022box col-md-6 bg-primary text-white\u0022\u003E\n      \u003Ch2 class=\u0022h1 text-left\u0022\u003E  Continuum Damage Mechanics for Quasi-brittle Materials\n\u003C\/h2\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EECTS :\n          3\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ESemestre calendaire :\n          Semester 1\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n                    \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ELangue d\u0026#039;enseignement\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EAnglais\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EEnseignement \u00e0 distance\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003Enon\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n    \u003Cdiv class=\u0022box col-md-6\u0022\u003E\n            \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EPr\u00e9requis\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EContinuum Mechanics, elasto-plasticity, thermodynamics of irreversible processes\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EProgramme \/ plan \/ contenus\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EThree-dimensional isotropic (scalar) damage models are first described, such as those proposed by Marigo and Mazars. These models will be criticized from the points of view both of thermodynamics soundness and of representativity of multiaxial responses of cementitious materials.\u003C\/p\u003E\n\u003Cp\u003EThe question of the tensorial nature of damage is then addressed. Effective stresses are defined, and the principle of strain equivalence is used to couple both elasticity and (visco-)plasticity with damage. A sound thermodynamics formulation of the loading-induced damage anisotropy of quasi-brittle materials is then provided.\u0026nbsp;\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003ESought properties of a damage variable\u003C\/li\u003E\n\u003Cli\u003EEffective stress concept (1D, 3D, isotropic damage, anisotropic damage).\u003C\/li\u003E\n\u003Cli\u003EFirst damage models (Marigo 1981, Lemaitre-Mazars 1980, Mazars 1984).\u003C\/li\u003E\n\u003Cli\u003EThermodynamics of damage, on the difficulties of ensuring the positivity of the intrinsic dissipation in Continuum Damage Mechanics.\u003C\/li\u003E\n\u003Cli\u003ELoading-induced anisotropic damage of quasi-brittle materials such as concrete.\u003C\/li\u003E\n\u003Cli\u003EPermanent strains due to damage, coupling or not coupling with (visco-)plasticity\u003C\/li\u003E\n\u003Cli\u003EElements of modeling of cyclic mechanical responses of quasi-brittle materials.\u003C\/li\u003E\n\u003Cli\u003EVisco-damage.\u003C\/li\u003E\n\u003Cli\u003EQuasi-implicit numerical schemes for anisotropic damage models.\u003C\/li\u003E\n\u003Cli\u003ENonlocal, Eikonal Nonlocal, Gradient damage models, Phase field regularization.\u003C\/li\u003E\n\u003C\/ul\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EObjectifs d\u0026#039;apprentissage\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cul\u003E\n\u003Cli\u003EThe main objective is to derive, in the thermodynamics framework of Continuum Damage Mechanics, three-dimensional\u0026nbsp;constitutive equations for quasi-brittle materials such as concrete.\u003C\/li\u003E\n\u003Cli\u003EThe student will become fluent in Continuum Damage Mechanics. They will acquire the necessary insight to propose relevant tests and procedures for identifying the material parameters.\u003C\/li\u003E\n\u003C\/ul\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n                                \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EBibliographie\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cul\u003E\n\u003Cli\u003E\u003Cem\u003EJ. Lemaitre, A course on damage mechanics, Springer Verlag, 1992.\u003C\/em\u003E\u003C\/li\u003E\n\u003Cli\u003E\u003Cem\u003EJ. Lemaitre, R. Desmorat, Engineering damage mechanics: ductile, creep, fatigue and brittle failures, Springer, 2005.\u003C\/em\u003E\u003C\/li\u003E\n\u003Cli\u003E\u003Cem\u003EJ. Lemaitre, J.-L. Chaboche, R. Desmorat, A. Benallal, M\u00e9canique des mat\u00e9riaux solides, 3e \u00e9d. 2020.\u003C\/em\u003E\u003C\/li\u003E\n\u003C\/ul\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ENature de l\u0026#039;\u00e9valuation\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EEvaluation Terminale\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n  \u003C\/div\u003E\n\u003C\/div\u003E\n","settings":null}]