ABSTRACT
WHEN A COMPOSITE is uniformly fabricated, in a statistical sense at a larger length scale,the composite can be treated as a statistically homogeneous material, and the stress and strain at a material point can be evaluated by the averages of stress and strain on an RVE. Here an RVE in a continuum body is a material volume that statistically represents the neighborhood of a material point. The microstructure can be periodic, random, or even functionally graded materials. From the relation between averaged stress and strain, we can derive an effective mechanical constitutive law of the RVE. Whether an RVE can provide an accurate prediction of effective material behavior has been an interesting problem. Drugan [34] used ensemble average to obtain the effective elastic properties and found a maximumerror of 5%when theminimumGreen’s function can be obtained in lower dimensions too. An RVE size is no less than the twice of the particle size for any volume fraction. Their formulation has been derived using the Green’s function in the infinite domain, which has been used by Eshelby [5]. However, because there commonly exist particles close to the boundary of a composite, Eshelby’s assumption for one particle embedded in an infinite matrix cannot be exactly satisfied, and thus the boundary effect has not been included in the modeling [3]. The recent development of advanced materials commonly requires fabrication of materials in thin layers or films. Moreover, the characterization of materials can be conducted at micron or nanometer levels. The miniaturization of material testing and fabrication attracts significant attention about the boundary effect on particulate composites. This chapter will first introduce fundamental solutions for a concentrated force in a semi-infinite domain and then use it in the equivalent inclusion method for investigation of boundary effects on a semi-infinite domain containing one, two or many particles. Then, an algorithm for virtual experiments of a composite sample is introduced.
