The materials science of collagen.

Collagen is the principal biopolymer in the extracellular matrix of both vertebrates and invertebrates. It is produced in specialized cells (fibroblasts) and extracted into the body by a series of intra and extracellular steps. It is prevalent in connective tissues, and the arrangement of collagen determines the mechanical response. In biomineralized materials, its fraction and spatial distribution provide the necessary toughness and anisotropy. We review the structure of collagen, with emphasis on its hierarchical arrangement, and present constitutive equations that describe its mechanical response, classified into three groups: hyperelastic macroscopic models based on strain energy in which strain energy functions are developed; macroscopic mathematical fits with a nonlinear constitutive response; structurally and physically based models where a constitutive equation of a linear elastic material is modified by geometric characteristics. Viscoelasticity is incorporated into the existing constitutive models and the effect of hydration is discussed. We illustrate the importance of collagen with descriptions of its organization and properties in skin, fish scales, and bone, focusing on the findings of our group.