Comparison between predicted and observed elastic properties

4 Comparison between predicted and observed elastic properties 

The prediction of the elastic constants of an oriented polymer provides a further, more stringent, test for the deformation models because these properties depend in a more complex way on the details of the distribution 

It is shown in the appendix that the state of stress within a homogeneously stressed material can be represented by a symmetric second-rank tensor [cr,y] with six independent components. For a cube with faces perpendicular to OT1T2T3 the component cr represents the outwardly directed force per unit area applied in the direction parallel to Ox,- on the face perpendicular to Ox,. It thus represents a normal stress. The component a,y for i j represents the force per unit area applied in the Ox, direction to the face perpendicular to Ox,-, so that it represents a shear stress. It is also shown in the appendix that the state of strain in the material can be 

Deduce the relationship between Young s modulus Ei measured in the OY, direction and the appropriate compliance. 

Equation (11.14b) shows that if the only non-zero stress is ov, = a, as it is when determining Young s modulus in the OY,- direction, then Sa = Sma, so that Ei = a I Bn = Xlsun. 

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