The investigator develops new mathematical and computational tools for the quantitative description of multi-scale phenomena seen in composite structures. The effort focuses on properties related to failure initiation. Failure is often precipitated by extreme excursions of the local fields at the level of the microgometry. Three projects are carried out that seek to make new connections between the excursions of local deformation, strain, and stress fields as functions of applied boundary loads and initial conditions. The first project examines load transfer between length scales for hierarchical structures when the substructure is known only in a statistical sense. The goal is to provide new variational tools for teasing out relationships that connect the local field response to the applied long wavelength loads. The objective is to use these relationships to discover explicit criteria on the applied loads that are necessary for failure initiation inside composite media. The second project seeks to understand how field fluctuations inside heterogeneous media depend on the boundary data in the presence of residual stress. The goals of this project are to: i) quantify the roles of boundary data, microgeometry and residual stress on the penetration of high stress zones inside statistically defined media and ii) understand the effect of residual stress on the decay of high frequency boundary data inside the composite domain. Understanding these phenomena facilitates the design of tough composite structures for use in aviation and infrastructure. The third project investigates the dynamics of heterogeneous media using nonlocal models for elastic interactions. The goal is to develop a multi-scale peridynamic formulation for modeling deformation fields inside fiber reinforced laminates. This formulation provides the mathematical framework and associated numerical methods necessary to capture the dynamic interactions between small and large length scales. It is anticipated that the basic mathematical work and subsequent numerical investigations can resolve new dynamic phenomena that contribute to the delamination and failure of fiber reinforced laminates.
The investigator develops new mathematical and computational tools for the quantitative description of multi-scale phenomena seen in composite structures. Composite materials are rapidly becoming the materials of choice for structural applications. This is due to their light weight and superior stiffness properties. In order to accelerate their deployment an improved understanding of their strength properties based upon their microstructural geometry is required. This proposal focuses on properties related to failure initiation. Failure is often precipitated by extreme excursions of the local fields at the level of the microgometry. The proposal consists of three projects that make new connections between the excursions of local deformation, strain, and stress fields as functions of applied boundary loads and initial conditions. The projects are chosen to address issues of practical interest that if solved can accelerate the use of light weight composite materials for applications in aviation and infrastructure.
