Advances in Constitutive Relations Applied in Computer Codes
July 23, 2007 — July 27, 2007
Coordinator:
- Janusz R. Klepaczko (Universitè de Metz, Metz Cedex, France)
Numerical analyses of engineering problems in different branches of mechanical design and technology are nowadays powerful tools for use in everyday practice. Not only practical engineering problems can be analyzed by numerical methods, but also many research projects can be effectively supported by use of specially designed computer codes. Advances both in software and hardware permit the numerical analysis of a variety of problems in quasi-static loading as well as in short-time loadings with impact. Of course, a variety of traditional structural materials are subject to analysis, as are more recently developed materials, such as new automotive alloy steels, aluminum and magnesium alloys, composites and polymers. Using numerical methods every analysis problem requires a proper constitutive relation. Therefore a correct and accurate constitutive relation is a key factor in application to computer codes. Since linear elasticity has been well established in different numerical schemes, including vibrations and wave propagation, the course will focus on non-linear effects in constitutive relations, with applications to computing.
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 problems are the subject of one part of the course.
Application of composites in different branches of industry, including automotive and aviation industries, requires not only advanced computer techniques but also very specific constitutive relations. The problem of homogenization is one of the fundamental problems in application of constitutive relations to computer codes. Some techniques of homogenization and resulting algorithms are the subject of the course. Examples of numerical problems for several composites are one of the tasks of the course. Another aspect of composite mechanics is damage, especially the rate-dependent propagation of damage.
Metals and alloys are still the principal structural materials. In recent decades, however, many new alloys have been introduced in a variety of manufacturing industries, including automotive and aerospace. The new materials include high-strength steels, which can absorb much energy during accidents, novel aluminum alloys applied in the aviation industry, and new armor alloys with a high resistance to penetration. Another important area of interest is the metalworking of those new alloys. The first step in understanding behavior of such materials under different loading conditions is a fundamental knowledge of physical processes underlying plastic deformation. The material science approach to establish the basis for a correct formulation of constitutive relations for metals and alloys will be addressed during the course as well.
At present, the commercial computer codes are limited in engineering applications to very frequently oversimplified constitutive relations. Among many of those relations, the most used ones will be the subject of discussion and analyses. The most recent software versions permit the solution of some engineering problems with an adequate accuracy. The gap between the materials science approach and the phenomenology and limits of the latter will also be addressed. A further important issue in constitutive modeling is development and use of fracture and failure criteria. The most important ones applied in numerical simulations are the subjects of analyses. In all cases, strain rate and temperature dependent effects will be introduced in the modeling.
Finally, the use of computer codes needs some knowledge on optimization of the solution concerning not only the characteristics and performance of a code but also its range of applications. Through examples and case studies, it will be demonstrated how a solution can be optimized with respect to these needs.
The course is addressed to PhD students, researches and industrial engineers, involved in the fields of structural engineering and technology, interested in recent developments in computational solid mechanics.