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Laminated plate theory is widely used for elastic analysis and design of fiber composite structures. Use of the results for prediction of failure and for design of structures to avoid failure (with a margin of safety) is a more complex issue. Use of failure theories in terms of stresses or strains at a point can sometimes yield a very conservative estimate of the failure load. It is recognized that such theories, in conjunction with laminate analysis, yield an estimate of the point of damage onset (often in the matrix), but final failure usually requires progressive fiber breaks and significant load redistribution. Methods have been suggested to perform stress analyses beyond damage initiation, but they are very rarely used in practice (as compared to the use of plasticity theory for metal structures). Many progressive damage models make use of ad hoc assumptions for stiffness knockdowns. The objective of this paper is to demonstrate that damage mechanics (using a single or multiple damage parameters) can yield a set of constitutive laws, which are based on sound physical principles. It is shown that the dissipated energy density in a ply can be used as a damage parameter. Two structural problems are considered for demonstration. Results for the case of a pressure vessel are compared with those from netting analysis, a valid and widely accepted method for such designs. The second case is the problem of the “hole size effect,” which is currently handled in practice by the use of semi-empirical methods and a series of tests.
damage mechanics, stiffness loss, nonlinear constitutive law, multiaxial straining, strain energy dissipation, stress analysis, failure
Staff scientist, Materials Sciences Corporation, Fort Washington, PA