A constitutive model for protein-based materials

Protein-based materials are critical to the construction of tissue substitutes that exhibit precisely defined mechanical properties. Under physiologically relevant conditions, materials derived from natural or synthetic structural proteins are characterized by nonlinear elastic responses at medium and large deformations, time-dependent or viscoelastic behavior, and display the effects of strain-induced structural changes. Although a constitutive model that accurately describes mechanical behavior is essential for the rational design of tissue constructs, few models account for all of these characteristics. In this report, we present a new constitutive model for protein based materials, in which nonlinear elasticity is captured by the Arruda–Boyce eight-chain model, time dependant viscoelasticity is described by a generalized Maxwell model, and the effect of strain-induced structural change is incorporated using a network alteration theory originally proposed by Tobolsky. The model was applied to a number of protein-based materials and cell containing constructs, including recombinant elastin-mimetic protein polymers and fibroblast populated collagen gel matrices. Significantly, numerical implementation of this model is straightforward and mechanical behavior accurately described under a variety of loading conditions. Moreover, when calibrated using stress relaxation data alone, the model accurately predicted cyclic loading responses. Although limitations exist, this model provides a convenient tool to correlate viscoelastic data obtained by different testing modes and may assist in reducing the number of experimental tests required to fully capture the range of viscoelastic responses of protein-based materials.