[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-950813","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\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\u003ED\u00e9tail du volume horaire\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003ECours magistraux :\u003C\/span\u003E\n                                      \u003Cspan\u003E30\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\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\u003E- Continuum mechanics\u003Cbr\u003E\n- Elasticity\u003Cbr\u003E\n- Plasticity\u003Cbr\u003E\n- Visco-plasticity\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\u003EPART I -\u0026nbsp; PROBABILISTIC DESCRIPTION\u003Cbr\u003E\n- Probabilistic description of the degradation and failure of brittle and quasi-brittle materials.\u0026nbsp;\u003Cbr\u003E\n- Analysis of the transition between single and multiple fragmentation.\u0026nbsp;\u003Cbr\u003E\n- Introduction to Poisson point processes. Weibull model.\u0026nbsp;\u003Cbr\u003E\n- Damage models describing multiple cracking.\u003C\/p\u003E\n\u003Cp\u003EPART II - CONTINUOUS DAMAGE \/ DAMAGE MODELS\u003Cbr\u003E\n- Isotropic (scalar) damage, Anisotropic (tensorial) damage\u003Cbr\u003E\n- Principle of strain equivalence, effective stress\u003Cbr\u003E\n- Micro-defect closure effect, partial stiffness recovery\u003Cbr\u003E\n- Isotropic and anisotropic damage evolution laws of ductile materials (Rice \u0026amp; Tracey, Lemaitre, Gurson)\u0026nbsp; and of quasi-brittle materials (Marigo, Le Dantec-Ladev\u00e8ze, Lemaitre-Mazars)\u003Cbr\u003E\n- Elasto-plasticity coupled with isotropic damage (ductile materials)\u003Cbr\u003E\n- Exercises: stress triaxiality makes ductile materials brittle, Low Cycle Fatigue: calculation of W\u00f6hler curve, identification of damage parameters\u003Cbr\u003E\n- Elasticity coupled with isotropic \/ with anisotropic damage (quasi-brittle materials)\u003Cbr\u003E\n- Visco-plasticity coupled with damage (tertiary creep)\u003C\/p\u003E\n\u003Cp\u003EPART III - LOCALIZATION AND INSTABILITIES\u003Cbr\u003E\n- Bifurcation analysis. Perturbation analysis.\u0026nbsp;\u003Cbr\u003E\n- Regularisation and nonlocal\/gradient\/phase field models.\u003C\/p\u003E\n\u003Cp\u003EPART IV - RANDOM\/STOCHASTIC CONTINUOUS DAMAGE MODELS\u003Cbr\u003E\n- Random Continuum Damage Mechanics: Haar measure, random rotations, random fields, Initial damage as a random variable.\u003Cbr\u003E\n- Stochastic Continuum Damage Mechanics: Stochastic elasticity, stochastic damage evolution law.\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\u003EObjectifs d\u0026#039;apprentissage\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EThis course focuses on modeling the materials damage and fracture within probabilistic, continuous, and stochastic frameworks. It begins with a probabilistic description of degradation, including fragmentation processes, Weibull models, and diffuse damage. Continuous isotropic and anisotropic damage models are then presented, along with their coupling to elastoplasticity and viscoplasticity to describe ductile and quasi-brittle materials. The course also covers localization phenomena, instabilities, and non-local or phase-field regularization techniques. Finally, stochastic approaches to continuous damage are introduced to account for the variability and uncertainty of material properties.\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\u003EBibliographie\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003E- J. Lemaitre, A Course on Damage Mechanics, Springer-Verlag, 1992.\u0026nbsp;\u003Cbr\u003E\n- J. Lemaitre, R. Desmorat, Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittles Failures, J Springer, 2005.\u0026nbsp;\u003Cbr\u003E\n- K. Nahshon, J. Hutchinson, J., Modification of the Gurson model for shear failure. European Journal of Mechanics-A\/Solids, 27(1), 1-17, 2008.\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\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}]