Dynamic fracture mechanics Sample Clauses

Dynamic fracture mechanics. The analysis of the models of these mechanical problems leads to deep mathematical questions originated by two common features: the energies are not convex and the solutions exhibit discontinuities both with respect to space and time. In addition, plasticity problems often lead to concentration of the strains, whose mathe- matical description requires singular measures. Most of these problems have a variational structure and are governed by partial differential equations. Therefore, the construction of consistent models and their analysis need advanced mathematical tools from the calculus of variations, from measure theory and geometric measure theory, and also from the theory of nonlinear elliptic and parabolic partial differential equations. The mod- els of dynamic crack growth considered in the project also need results from the theory of linear hyperbolic equations. Our goal is to develop new mathematical tools in these areas for the study of the selected problems. a. State of the art and objectives
Sample 1
Dynamic fracture mechanics. The analysis of the models of these mechanical problems leads to deep mathematical questions originated by two common features: the energies are not convex and the solutions exhibit discontinuities both with respect to space and time. In addition, plasticity problems often lead to concentration of the strains, whose mathe- matical description requires singular measures. Most of these problems have a variational structure and are governed by partial differential equations. Therefore, the construction of consistent models and their analysis need advanced mathematical tools from the calculus of variations, from measure theory and geometric measure theory, and also from the theory of nonlinear elliptic and parabolic partial differential equations. The mod- els of dynamic crack growth considered in the project also need results from the theory of linear hyperbolic equations. Our goal is to develop new mathematical tools in these areas for the study of the selected problems. Qua- sistatic evolution problems in plasticity with hardening and softening will be studied through a vanishing viscos- ity approach, that has been successfully used by the P.I. in the study of the Cam-Clay model in soil mechanics. Quasistatic models of crack growth will be developed under different assumptions on the elastic response of the material and on the mechanisms of crack formation. For the problem of crack growth in the dynamic regime our aim is to develop a model that predicts the crack path as well as the time evolution of the crack along its path, taking into account all inertial effects. Section 1: The Principal Investigator 3 a. Scientific Leadership Profile 3 Content and impact of major scientific contributions 3 International recognition 3 Efforts and ability to inspire younger researchers 3 b. Curriculum Vitae 4 Professional Preparation, Appointments, and Scientific Councils 4 International Prizes, Ph.D. Theses, and Jury member abroad 4 Visiting Professor 5 Funding ID 5 c. 10-Year-Track-Record 6 10 publications 6 Chapters in collective volumes 7 Invited presentations to international conferences and to international advanced schools 7 Organization of international conferences 7 International Prizes and Membership to Editorial Boards of International Journals 7 Section 2: The Research Project 8 a. State of the art and objectives 8 a1. Plasticity with hardening and softening 9 a2. Quasistatic crack growth 10 a3. Dynamic fracture mechanics 12 References 13 b. Methodology 17 b1...
Sample 1

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