 |
 |
 |
 |
|
|
|
|
 |
Steven L. Crouch Computational Modeling of Composite and Functionally Graded Materials This presentation discusses the development of a computational basis for modeling micro- and macroscopic behavior of composite and functionally graded materials. A significant aspect of the work is the capability of directly simulating the microstructure of porous, composite, and functionally graded materials by numerous non-overlapping inclusions (particles) and holes (pores) of arbitrary size; detailed interactions of all of the structural features in the model are explicitly taken into account in the computations. For functionally graded materials, the volume fraction of particles in the matrix can be gradually varied in the direction of gradation to provide a smooth and continuous change in the material properties. Current work assumes either circular (two dimensions) or spherical inclusions and holes, but elliptical or spheroidal features could theoretically also be considered. Nonlinear effects due to localized slip and/or separation of the interfaces between the particles and the material matrix or cracking inside the particles or the matrix can be included in the model. Also, time-dependent effects due to transient heat conduction and thermal stresses or to viscoelastic behavior of the material can be treated. Computational realization of the model includes the use of fast methods (based on fast multipole acceleration) that make it possible to examine detailed interactions among tens of thousands (or more) particles and pores. The method allows for accurate calculation of the displacement, stress, and temperature fields anywhere within the material, including the inclusions and the interphases between the inclusions and the matrix. The overall properties of a composite material can be found from the properties of the microstructure using the concept of a representative volume element. For a functionally graded material, where a representative volume element cannot be uniquely defined, the numerical method allows for direct simulation of the grading without reference to such elements. Ideas for future development of the numerical method are presented, including multi-scale simulations based on strain-gradient continuum theories of the type developed by Mindlin (Micro-structure in linear elasticity, Arch. Rat. Mech. Anal . 16 , 51–78, 1964) and Toupin (Elastic materials with couple stresses, Arch. Rat. Mech. Anal . 11 , 385–414, 1962). The use of such non-local theories will allow us to overcome limitations of classical elasticity theory in dealing with geometrical size effects and accounting for the effects of large deformation gradients. Additionally, the use of strain gradient theories will allow us to examine the effects of boundary layers on the overall properties of composite materials. The general method discussed in the presentation can be used as a tool for comparing various continuum, discrete, and micromechanical approaches for the modeling of composite and functionally graded materials.
|
