| Summary: | The perfect ability of living tissues to control and adapt their mechanical properties to varying external conditions may be an inspiration for designing engineering materials. An interesting example is the smooth muscle tissue since this "material" is able to change its global mechanical properties considerably by a subtle mechanism within individual muscle cells. Multi-scale continuum models may be useful in designing essentially simpler engineering materials having similar properties. As an illustration we present the model of an incompressible material whose microscopic structure is formed by flexible, soft but incompressible balls connected mutually by linear springs. This simple model, however, shows a nontrivial nonlinear behavior caused by the incompressibility of balls and is very sensitive on some microscopic parameters. It may elucidate the way by which "small" changes in biopolymer networks within individual muscular cells may control the stiffness of the biological tissue, which outlines a way of designing similar engineering materials. The 'balls and springs' material presents also prestress-induced stiffening and allows elucidating a contribution of extracellular fluids into the tissue’s viscous properties.
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