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The production of mechanical stresses in living organisms largely relies onlocalized, force-generating active units embedded in filamentous matrices.Numerical simulations of discrete fiber networks with fixed boundaries haveshown that buckling in the matrix dramatically amplifies the resulting activestresses. Here we extend this result to a bucklable continuum elastic mediumsubjected to an arbitrary external stress, and derive analytical expressionsfor the active, nonlinear constitutive relations characterizing the full activemedium. Inserting these relations into popular "active gel" descriptions ofliving tissues and the cytoskeleton will enable investigations into nonlinearregimes previously inaccessible due to the phenomenological nature of thesetheories.

Stress-dependent amplification of active forces in nonlinear elastic media