216 Mechanics of Composite Materials,Second Edition Longitudinal Young's modulus,E Transverse Young's modulus,E2 Major Poisson's ratio,V12 In-plane shear modulus,G12 Three approaches for determining the four elastic moduli are discussed next. 3.3.1 Strength of Materials Approach From a unidirectional lamina,take a representative volume element*that consists of the fiber surrounded by the matrix(Figure 3.3).This representa- tive volume element(RVE)can be further represented as rectangular blocks. The fiber,matrix,and the composite are assumed to be of the same width, h,but of thicknesses frfm,and f,respectively.The area of the fiber is given by Ar=tih. (3.27a) The area of the matrix is given by Am =tmh (3.27b) and the area of the composite is given by A=th. (3.27c) The two areas are chosen in the proportion of their volume fractions so that the fiber volume fraction is defined as V= A A (3.28a) and the matrix fiber volume fraction V is A representative volume element(RVE)of a material is the smallest part of the material that represents the material as a whole.It could be otherwise intractable to account for the distribu- tion of the constituents of the material. 2006 by Taylor Francis Group,LLC216 Mechanics of Composite Materials, Second Edition • Longitudinal Young’s modulus, E1 • Transverse Young’s modulus, E2 • Major Poisson’s ratio, ν12 • In-plane shear modulus, G12 Three approaches for determining the four elastic moduli are discussed next. 3.3.1 Strength of Materials Approach From a unidirectional lamina, take a representative volume element* that consists of the fiber surrounded by the matrix (Figure 3.3). This representa￾tive volume element (RVE) can be further represented as rectangular blocks. The fiber, matrix, and the composite are assumed to be of the same width, h, but of thicknesses tf, tm, and tc, respectively. The area of the fiber is given by . (3.27a) The area of the matrix is given by (3.27b) and the area of the composite is given by (3.27c) The two areas are chosen in the proportion of their volume fractions so that the fiber volume fraction is defined as (3.28a) and the matrix fiber volume fraction Vm is * A representative volume element (RVE) of a material is the smallest part of the material that represents the material as a whole. It could be otherwise intractable to account for the distribu￾tion of the constituents of the material. A th f f = A th m m = , A th c c = . V A A t t f f c f c = = , 1343_book.fm Page 216 Tuesday, September 27, 2005 11:53 AM © 2006 by Taylor & Francis Group, LLC