The Relationship Between Compliance and Modulus

When an oscillating stress is applied to a material the result is an 

This relationship is the simplest of those describing the connection between stress and strain controlled measurements. Of course it also follows that complex terms must be similarly related  

We can separate out the real and imaginary parts by multiplying by (a — ib), as appropriate. This demonstrates the more sophisticated relationship between the complex compliances and the complex moduli  

These expressions show that, for example, any value of the storage modulus depends upon the values of both the storage and loss compliance. This is true for these dynamic properties, only the ratios interrelate simply  

Deriving this relationship is more than an exercise in mathematics and provides information on the nature of the material. We have argued that 

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