In?. .I. Engng Sci. Vol. 27, No. 11, pp. 1397-1405, 1989 OO20-7225/89 $3.00+ 0.00 Printed in Great Britain. All rights reserved Copyright @I 1989 Pergamon Press plc STRESS FIELDS IN A COMPOSITE MATERIAL BY MEANS OF A NON-CLASSICAL APPROACH EMIN SELCUK ARDIC, MICHAEL H. SANTARE and TSU-WE1 CHOU Department of Mechanical Engineering, University of Delaware, Newark, zyxwvutsrqponmlkjihgfedcbaZY DE 19716, U.S.A. Abstract-For a two dimensional, bimaterial composite body under elastic deformation, a method is developed to determine separate stress field expressions for each material in the body. Far-field strain components, measured or calculated by classical methods, are considered as known inputs. By considering the long-range effects, caused by the inhomogeneity on a micro-structural scale, the interactions between the point of consideration and the other material regions are expressed. Combining the local stresses and the stresses caused by the long-range interactions, separate expressions for the stresses in the different materials of the body are obtained. Two solutions for a plane strain, bimaterial, laminated composite are obtained through the methods of classical elasticity for the purposes of comparison with the present method. 1. INTRODUCTION Several studies which analyze the stress field equations for a composite structure that consists of two or more different materials, have been published. Generally, these studies use an anisotropic elasticity solution or classical elasticity approach for a unit composite. Because of the complex interactions between fiber and matrix, it is difficult to determine precisely the internal stress distribution for a whole body. An extension of the unit composite solutions to several material regions is necessary to understand the mechanical properties of in- homogeneous materials in general and fiber-reinforced composites in particular. Some of the former studies analyze the stresses in composites as a whole, the main assumption in these studies is that the material is homogeneous and anisotropic. Since these studies ignore the inhomogeneity, the stresses in each material region cannot be determined by them. The classical methods, ignoring the inhomogeneity, generally approach the composite analysis by using the laminated plate or shell theories following the assumption of linear variations of the in-plane displacement components through the thickness (Ashton and Whitney [l]). For relatively thick laminates the assumption of linear displacement is very poor, this can easily be seen in the work of Pagan0 and Hatfield [2]. Pagan0 [3,4] investigated the limitations of classical laminated plate theory, and found exact solutions for laminated composites by expressing the displacements and the stresses with Fourier series. He showed that the conventional plate theory leads to a very poor description of laminate response at low span-to-depth ratios, but converges to the exact solution as this ratio increases. The derivations and applications of the classical composite solutions using the effective elastic constants, found by the rule-of-mixtures, have been demonstrated, for example, by Vinson and Chou [5], Vinson and Sierakowski [6], and Tsai and Hahn [7]. Some other studies consider a unit composite approach, for example Amirbayat and Hearle [8,9]. These kind of studies can be used to determine the separate stresses in the different materials of the composite body, but these solutions ignore the interactions occurring on a larger scale. For an inhomogeneous material a nonlocal continuum mechanics theory can be used to determine the field equations. Eringen [lo, 111 summarized the theories of nonlocal continuum mechanics, applied them to a number of problems, and demonstrated the effectiveness of these theories by predicting various physical phenomena ranging from the global to the atomic scales. In the study presented in this paper, a method similar to the nonlocal theory and a simple elasticity analysis are used in a combined manner. Eringen [lo] states that an inner characteristic length should be associated with a given body and this length can be, for instance, the average spacing distance between fibers in a composite. In this study, the average distance between the center lines of two adjacent material regions is considered to be the inner characteristic length. The nonlocal constitutive equations, which were presented e.g. by Krijner [12] and Eringen [lo, 11, 13, 141, are used as the basis of the formulation for the long-range 1397