Exact Moduli of Anisotropic Laminates

Abstract

One of the most important aspects of the analysis of the response of composite materials is related to the studies of the overall behavior of laminates composed of anisotropic layers. In this phase of the analysis, we are concerned with the relationship between forces and moments per unit length and the deformations which they produce. These relations may be termed the “effective” laminate constitutive equations since they define the geometric response caused by loads exerted on the laminate, as distinguished from the conventional implication of an elastic constitutive equation, namely the stress-strain relationship of an infinitesimal material element. Once the effective constitutive law is formulated, theories can be developed based upon consideration of the laminate as a unit, rather than resorting to a layer by layer elasticity analysis. Once a particular boundary value problem is solved, however, one can determine the detailed stress distribution throughout the laminate. Another motivation for the study of effective laminate moduli is the popular use of the laminate as a model for the behavior of complex heterogeneous materials, such as composites reinforced with three-dimensional networks of fibers (Halpin and Pagano, 1969; Berkowitz and Cohen, 1970; Halpin et al., 1971). Finally, proper interpretation of data from even the most routine experiments involving composite laminates requires appreciation of an effective constitutive relation.