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High Quality Content by WIKIPEDIA articles! In continuum mechanics, an equation of state suitable for modeling solids is naturally rather different from the ideal gas law. A solid has a certain equilibrium volume V0, and the energy increases quadratically as volume is increased or decreased a small amount from that value.Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuum. The French mathematician Augustin Louis Cauchy was the first to formulate such models in the 19th century, but research in the area continues today.