Elastic Behavior of Multidirectional Laminates

The behavior of a multidirectional laminate will depend on the properties and stacking sequence of the individual layers. 

The classical lamination theory will predict the behavior of a thin laminate, provided it is not a hybrid and the following assumptions are met when the laminate is extended or bent  

Normals remain straight and do not bend remain unstretched and keep the same length remain normal and always make a right angle to the neutral plane. 

The material will have a given strength expressed as stress or strain, beyond which it fails. In order to postulate the failure, it is necessary to have a failure criterion with an associate theory to be able to effect a satisfactory design. Such theories include maximum stress, maximum strain, Tsai-Hill (based on deviatoric strain energy theory) and Tsai-Wu (based on interactive polynomial theory). The Tsai-Wu theory is the most commonly used. 

Since the laminate comprises a number of laminae oriented in different directions with respect to each other, having the same stress-strain relations, the stress-strain equation of the /cth layer of the laminate is as given by Hull [4] as  

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