Multi-scale Analysis of Heterogeneous Media
Abstract
The project develops new mathematical tools for the description of multi-scale stress transfer inside composite materials. The first research activity provides new mathematical methods to characterize the extreme local stress excursions inside linear elastic composite materials. Research in this area has lead to new asymptotic formulations for the local stress excursions across lamina interfaces inside fiber reinforced laminates. New fast computational methods for calculating bounds on the extreme local stress excursions inside prestressed composites are developed using the asymptotic expansions. The second research track examines the effects of elasto-plasticity on the extreme local stress excursions inside composite media. New upper bounds on the strength domain of the composite are found that incorporate multi-scale information on the norms of solutions to nonlinear elasticity and conductivity problems. The third research activity develops a novel and systematic computational design method for the design of composite structures that hedge against structural failure. The fourth research thrust characterizes the influence of the boundary data on the local stress fluctuations inside microstructured media. New rigorous lower bounds on the boundary layer decay of stress fluctuations with respect to the length scale of oscillation in the boundary data have been obtained.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 15, 2008
- Accession Number
- ADA483948
Entities
People
- Robert Lipton
Organizations
- Louisiana State University