Constitutive Relations of Materials under Impact Loadings: Experiments, Theoretical and Numerical Aspects
July 16, 2012 — July 20, 2012
- Tomasz Lodygowski (Poznan University of Technology, Poland)
- Alexis Rusinek (National Engineering School of Metz, France)
Fundamentally important is the better understanding of complex behavior of materials under unusual – extreme – loadings.
By impact loadings we mean rigid hitting and crash, blasts and similar events which result in extensive, often localized, deformations, as well as high strain rates and strong wave effects.
Describing the constitutive properties of modern materials, which are employed under these demanding conditions, is not trivial and involves combining knowledge coming from laboratory tests, theoretical material modeling (based on the physical mechanisms responsible for plastic flow and fracture) and numerical computations.
The course will focus on non-linear effects in recently developed constitutive relations, with applications to computing. The course focuses the attention on experimental tests, their interpretation, theoretical modeling and numerical aspects, related also to the solution of inverse problems.
It is obvious, that using numerical methods for the analysis of any problem requires a proper constitutive relation. Polymers may behave as highly non-linear materials. The non-linear behavior of polymers must be introduced via precise mathematical formulation of all nonlinear effects in modeling. Time and temperature factors as well as large deformations are the most important considerations in polymer mechanics. Those materials and the related problems are the subject of a part of the course.
The application of composites in different branches of industry, including automotive and aviation industries, requires very specific constitutive relations.
The problem of homogenization is of paramount importance for the application of constitutive relations to computer codes. Some techniques of homogenization and the resulting algorithms are thus the subject of another part of the course. In this context, numerical problems encountered in modelling several composites are also discussed. Another important aspect of composite mechanics is damage, especially the rate-dependent propagation of localization. Experimental setup that allows defining dynamic behavior of materials at high strain rates will be presented.
The commercial computer codes for engineering applications are very frequently limited to oversimplified constitutive relations. The most recent software versions permit the solution of some engineering problems with an adequate accuracy. The gap between the material science approach and the phenomenology, and the limits of the latter, will also be fulfilled. The fracture and failure criteria will be introduced to the
All the topics included in the lectures are strongly connected with industrial needs and many results obtained by the lecturers were generated by practical engineering requirements.
The course is addressed to PhD students, researchers and industrial engineers, involved in the fields of structural engineering and technology, interested in recent developments in laboratory experiments, phenomenological modeling of materials and computational solid mechanics.
KEYWORDS: Impact Loadings, Experimental Stress Analysis, Homogenization Methodologies, Fracture Criteria, Failure Cricteria.