Generalized Strain-Stress Relationships for Ideal Elastic Systems

9 GENERALIZED STRAIN-STRESS RELATIONSHIPS FOR IDEAL ELASTIC SYSTEMS 

When a solid elastic body is under the action of an infinitesimal contact force the strain tensor is related to the stress tensor by the expression 

Let us consider that the only nonzero term of the stress tensor is CTh-According to Eq. (4.118), the relationship between yy and Oy is given by 

This equation in conjunction with Eq. (4.119) permits us to obtain the 

One can see that v - 1 /2 if J 0. Each of the four compliance parameters (/, D, B, and v) can easily be obtained from the values of other two by means of the expressions developed above. The pertinent relationships are 

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Generalized Strain-Stress Relationships for Ideal Elastic Systems 170... 

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