CESS Seminar : Stability Problems in Mechanics: Multiphysics & Multiscale Aspects (A Mechanician’s Perspective…)
Abstract:
Stability is a fascinating topic in solid mechanics that has its roots in the celebrated Euler column buckling problem, which first appeared in 1744. Over the years advances in technology have led to the study of ever more complicated structures, first in civil and subsequently in mechanical engineering applications. Aerospace applications, most notably failure of solid propellant rockets, led the way in the 1950s. Problems associated with materials and electronics industries came on stage in the 1970s and 1980s, starting with instabilities associated with thin films and phase transformations in shape memory alloys (SMA’s), just to name some of the most preeminent examples. In a parallel path, starting in the late 19th century, mathematicians studying nonlinear differential equations, developed the concept of a bifurcation (term coined by Poincare) and created powerful techniques to study the associated singularities, followed by advances in group-theoretical methods that exploit the problem’s underlying symmetries. Amazing progress has been made since the early days of structural buckling problems and continues to be made in this field, with applications ranging from atomistic to geological scales. With the advent of new materials, the number of applications in this area continues to progress with an ever- increasing pace.
In this talk we present selected applications of stability problems involving phenomena a) across spatial scales and b) driven by multi-physics coupling. In the first class of applications, we visit – by decreasing the size of the underlying scale – the instabilities occurring in fiber reinforced composites, honeycomb, and crystal lattices (shape memory effects). In the second class, we present stability problems in magnetoelastic thin films, liquid crystals, and step-bunching in epitaxial thin film deposition. In all these applications, we use both continuum description of the problem at hand or appropriate micromechanical models and the mathematical tools of bifurcation theory and symmetry groups.
Short bio
Prof. Nicolas Triantafyllidis obtained a Ph.D. in Engineering and an MS in Applied Mathematics from Brown University in 1980. The same year he joined the faculty of the Aerospace Engineering Department at the University of Michigan in Ann Arbor, MI, USA starting as an Assistant Professor and reaching the rank of Full Professor in the Departments of Aerospace Engineering and Mechanical Engineering & Applied Mechanics. He is currently an emeritus Professor of the University of Michigan. In 2009 he moved to France to become CNRS Director of Research in the Solid Mechanics Laboratory (LMS) and a Professor of Mechanics at the Ecole Polytechnique, where he is currently a member of the Haut College.
Prof. Triantafyllidis’ research is in the area of nonlinear continuum mechanics of solids and structures with emphasis on stability, scale effects and Multiphysics aspects. More specifically he has worked on the following topics: Numerical methods (FEM); Finite strain problems in elasticity and plasticity related to metal forming; Failure mechanisms in composites and architected materials; Group theoretical methods in bifurcation and stability; Multi-scale problems and related stability issues in solid mechanics; Phase transformations in SMA’s; Magneto-electro-mechanical coupling problems in solids; Electromagnetic forming and associated stability problems; Stability of solids under high rates of strain; Mechanical effects in semiconductors; Stability of structures under high strain rates; Magneto-rheological and nematic elastomers; Liquid crystals, Epitaxial growth on crystals and associated stability problems; Finite strain chemo-poro-mechanics and subcutaneous injection modeling.
Prof. Triantafyllidis has developed and taught a number of graduate and undergraduate courses in solid mechanics in the topics of stability of solids, micromechanical theories of solids (homogenization techniques), plate and shell theories, numerical techniques (finite elements), shape memory alloys and coupled mechanical-electromagnetic field theories. He has supervised the Doctoral Theses of several graduate students in the US and France. In addition, Prof. Triantafyllidis has collaborated extensively with researchers on both sides of the Atlantic and has served, through different functions, the international solid mechanics community.
Sandwiches offered after the seminar.
Stability is a fascinating topic in solid mechanics that has its roots in the celebrated Euler column buckling problem, which first appeared in 1744. Over the years advances in technology have led to the study of ever more complicated structures, first in civil and subsequently in mechanical engineering applications. Aerospace applications, most notably failure of solid propellant rockets, led the way in the 1950s. Problems associated with materials and electronics industries came on stage in the 1970s and 1980s, starting with instabilities associated with thin films and phase transformations in shape memory alloys (SMA’s), just to name some of the most preeminent examples. In a parallel path, starting in the late 19th century, mathematicians studying nonlinear differential equations, developed the concept of a bifurcation (term coined by Poincare) and created powerful techniques to study the associated singularities, followed by advances in group-theoretical methods that exploit the problem’s underlying symmetries. Amazing progress has been made since the early days of structural buckling problems and continues to be made in this field, with applications ranging from atomistic to geological scales. With the advent of new materials, the number of applications in this area continues to progress with an ever- increasing pace.
In this talk we present selected applications of stability problems involving phenomena a) across spatial scales and b) driven by multi-physics coupling. In the first class of applications, we visit – by decreasing the size of the underlying scale – the instabilities occurring in fiber reinforced composites, honeycomb, and crystal lattices (shape memory effects). In the second class, we present stability problems in magnetoelastic thin films, liquid crystals, and step-bunching in epitaxial thin film deposition. In all these applications, we use both continuum description of the problem at hand or appropriate micromechanical models and the mathematical tools of bifurcation theory and symmetry groups.
Short bio
Prof. Nicolas Triantafyllidis obtained a Ph.D. in Engineering and an MS in Applied Mathematics from Brown University in 1980. The same year he joined the faculty of the Aerospace Engineering Department at the University of Michigan in Ann Arbor, MI, USA starting as an Assistant Professor and reaching the rank of Full Professor in the Departments of Aerospace Engineering and Mechanical Engineering & Applied Mechanics. He is currently an emeritus Professor of the University of Michigan. In 2009 he moved to France to become CNRS Director of Research in the Solid Mechanics Laboratory (LMS) and a Professor of Mechanics at the Ecole Polytechnique, where he is currently a member of the Haut College.
Prof. Triantafyllidis’ research is in the area of nonlinear continuum mechanics of solids and structures with emphasis on stability, scale effects and Multiphysics aspects. More specifically he has worked on the following topics: Numerical methods (FEM); Finite strain problems in elasticity and plasticity related to metal forming; Failure mechanisms in composites and architected materials; Group theoretical methods in bifurcation and stability; Multi-scale problems and related stability issues in solid mechanics; Phase transformations in SMA’s; Magneto-electro-mechanical coupling problems in solids; Electromagnetic forming and associated stability problems; Stability of solids under high rates of strain; Mechanical effects in semiconductors; Stability of structures under high strain rates; Magneto-rheological and nematic elastomers; Liquid crystals, Epitaxial growth on crystals and associated stability problems; Finite strain chemo-poro-mechanics and subcutaneous injection modeling.
Prof. Triantafyllidis has developed and taught a number of graduate and undergraduate courses in solid mechanics in the topics of stability of solids, micromechanical theories of solids (homogenization techniques), plate and shell theories, numerical techniques (finite elements), shape memory alloys and coupled mechanical-electromagnetic field theories. He has supervised the Doctoral Theses of several graduate students in the US and France. In addition, Prof. Triantafyllidis has collaborated extensively with researchers on both sides of the Atlantic and has served, through different functions, the international solid mechanics community.
Sandwiches offered after the seminar.
Practical information
- Informed public
- Free
Organizer
- Prof. Olga Fink (IMOS), Prof. Alexandre Alahi (VITA), Prof. Dusan Licina (HOBEL), Prof. Alain Nussbaumer (RESSLab)
Contact
- Prof. Jean-François Molinari