(Drs. Iwona Jasiuk and Martin Ostoja-Starzewski, co-advisors)
"Scale and Boundary Conditions Effects in Random Fiber-Reinforced Composites"
Prediction of effective properties of composite materials has been a subject of considerable research for several decades. Traditionally, a representative volume element (RVE) is assumed, and the effective properties of such an RVE, theoretically infinite in size relative to inclusions, are obtained by various analytical methods. This approach, however, does not address the convergence of apparent properties (defined over finite domains) to the effective ones as the domain size increases. A systematic study of this issue is the primary motivation of the present research. One important application lies in the finite element analysis (FEA) of heterogeneous materials, where some 'smoothing' needs to be done to construct an element's constitutive matrix when the element is smaller than the RVE.
This research focuses on apparent properties of fiber-reinforced composites, including the scale of and boundary conditions applied to a meso-scale domain, also called a window. A hierarchy structure of upper and lower bounds - corresponding to uniform displacement and traction boundary conditions, respectively - on effective property of nonlinear composites is obtained by means of variational principles. To grasp more information about the scale and boundary conditions effects, extensive simulations of elastic as well as elastoplastic behaviors are done using the finite element method and the spring network program. For random composites, in order to investigate the effect of random fiber arrangement, a number of samples are analyzed to obtain the statistics. In the elastic problem, first and second order statistics and distribution information of apparent properties are obtained. In the elastoplastic problem, both the local plastic strain fields and the global effective stress-strain curves are investigated for different window sizes and boundary conditions.
Summarizing, the scale and boundary conditions effects investigation
carried out here offers new insights on the size of the RVE - an important
issue in micromechanics of heterogeneous materials. Even though the present
research is in the solid mechanics area, it should also be very helpful
to the investigation of apparent properties of heterogeneous materials
in other areas: thermal conductivity problem, electrical conduction problem,
magnetic permittivity, etc.