NATO Advanced Research Workshop on Nonlinear Homogenization and Applications to Composites, Polycrystals and Smart Materials; June 23-26, 2003; Kazimierz Dolny, Poland

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Proposal: DMS-0305443PI: Pedro Ponte CastanedaInstitution: University of PennsylvaniaTitle: Group Travel: NATO Advanced Research Workshop on Nonlinear Homogenization and Applications to Composites, Polycrystals and Smart MaterialsABSTRACTThis grant provides complementary support for several US young participants to attend a NATO Advanced Research Workshop on "Nonlinear Homogenization and Applications to Composites, Polycrystals and Smart Materials" to be held in Kazimierz Dolny, Poland, from 23 to 26 June, 2003. Additional funding from the NATO ARW program will cover the travel expenses of the Key Speakers, as well as those of junior participants from NATO Partner countries (mostly Eastern European countries). The aim of the workshop is the evaluation of critical needs in nonlinear homogenization and novel applications in modeling materials systems exhibiting complex microstructures. The behavior of composites, polycrystals and smart materials is often nonlinear. There have been important and significant developments over the last two decades both in terms of nonlinear homogenization methodology (deterministic and stochastic), as well as in terms of novel applications to the above-mentioned classes of materials. Also, phase transformations can be studied by using similar methods. Homogenization methods offer promising new tools for constructing macroscopic models in biomechanics. It is thus highly desirable to gather specialists in nonlinear homogenization, composite materials and micromechanics to promote progress in each of these fields keeping in mind the potential technological applications. The main topics of workshop are: 1) Convex and non-convex homogenization methods and applications to advanced composites, smart materials and structures like plates and shells; 2) Homogenization estimates for polycrystalline aggregates in elasticity, plasticity and shape memory alloys: the effect of texture and its evolution; 3) Multi-scale modeling and discrete-to-continuum passage; 4) Recent developments and new directions in shape optimization; 5) Functionally graded structures for maximum strength and stiffness; 6) Structures of bi-stable inertial elements: waves, averaging, control; and 7) Homogenization methods in modeling bone and soft tissues. The need for research in the field of nonlinear homogenization stems from the ever-increasing role of composites, polycrystals and smart materials in high-tech industries. Materials such as functionally graded materials, piezoelectric composites, magnetic materials and ferroelectrics also belong to this class. It has also become increasingly clear that living tissues exhibit very complex hierarchical microstructures. Among the broader impacts of the proposed workshop are the following. The conference is strongly multi- and inter-disciplinary in character, involving mathematicians, engineers and material scientists with various sub-fields of specialization. In addition, it is expected that the workshop will provide opportunities for the transfer of information between Western and Central/East European countries, between research centers and universities, and among researchers from different scientific areas. The workshop, whose proceedings will be disseminated through a NATO Science Series publication, will seek to identify open problems and future trends in the above-identified areas. Finally, the meeting will include several graduate students, young investigators and faculty from underrepresented groups.