We develop a model of an incompressible material which microscopic structure is formed by flexible but incompressible balls connected mutually by linear springs. The model is motivated by the structure of smooth muscle tissues that exhibit perfect elastic (or visco-elastic) behavior in a large extent of deformations. Moreover, their bulk (macroscopic) stiffness may be very effectively controlled and changed from very low values to essentially higher ones by simply defined structural changes inside individual muscle cells. In the continuum limit, the ''balls and springs'' model gives a nontrivial, highly nonlinear hyperelastic material. The stored strain energy function has generally no analytical expression. However, we find an approximate analytic formula, that is suitable for describing certain mechanical effects coming from the special arrangement of smooth muscle cells.
We construct a simple model of an elastic material whose stiffness can be effectively controlled by an appropriately chosen set of microstructural parameters. The model is based on ideas of the scale-dependent continuum description and might play an important role in modelling of muscle tissues in biomechanics.
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