ABSTRACT
For some applications of viscoelastic materials, it is sufficient to understand creep and relaxation properties. In other applications the response to an arbitrary load or strain history is required. To predict this response, constitutive equations which incorporate all possible responses are of use. This chapter develops the constitutive equation for linear materials, the Boltzmann superposition principle, which states that the effect of a compound cause is the sum of the effects of the individual causes. It considers the strain associated with a relaxation and recovery experiment, with the intention to use the idea of linearity as embodied in the Boltzmann superposition principle to predict the resulting stress history. Constitutive equations have been developed for the adaptive elasticity of bone. The concept of linearity as embodied in the Boltzmann superposition principle was used to obtain an integral equation, the Boltzmann superposition integral, as the constitutive equation for linear viscoelasticity.
