Integral representation of linear

This idea can be used to formulate an integral representation of linear viscoelasticity. The strategy is to perform a thought experiment in which a step function in strain is applied, e t) = Cq H t), where H t) is the Heaviside step function, and the stress response a t) is measured. Then a stress relaxation modulus can be defined by E t) = <7(t)/ o Note that does not have to be infinitesimal due to the assumed superposition principle. To develop a model capable of predicting the stress response from an arbitrary strain history, start by decomposing the strain history into a sum of infinitesimal strain increments ... 

This idea can be used to formulate an integral representation of linear viscoelasticity. The strategy is to perform a thought experiment in which a step fimction in strain is applied, e(f)= b- H(f), where H(f) is the Heaviside step... 

The Boltzmann superposition principle is one starting point for a theory of linear viscoelastic behaviour, and is sometimes called the integral representation of linear viscoelasticity , because it defines an integral equation. An equally valid starting point is to relate the stress to the strain by a linear differential equation, which leads to a differential representation of linear viscoelasticity. In its most general form, the equation is expressed as... 

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