  Collagen is the main structural and load-bearing element of various
connective tissues, where it forms the extracellular matrix that supports
cells. It has long been known that collagenous tissues exhibit a highly
nonlinear stress-strain relationship (Fung YC, Am J Physiol 213(6),1967;
Humphrey JD, Proc R Soc Lond A: Math Phys Eng Sci 459(2029),2003), although the
origins of this nonlinearity remain unknown (McMahon TA, Lec Math Life Sci
13,1980). Here, we show that the nonlinear stiffening of reconstituted type I
collagen networks is controlled by the applied stress, and that the network
stiffness becomes surprisingly insensitive to network concentration. We
demonstrate how a simple model for networks of elastic fibers can
quantitatively account for the mechanics of reconstituted collagen networks.
Our model points to the important role of normal stresses in determining the
nonlinear shear elastic response, which can explain the approximate exponential
relationship between stress and strain reported for collagenous tissues (Fung
YC, Am J Physiol 213(6),1967). This further suggests new principles for the
design of synthetic fiber networks with collagen-like properties, as well as a
mechanism for the control of the mechanics of such networks.
