Generalized Theoretical Stress-Strain Relationship in Solids with Material Nonlinearity in the Case of Small Deformations

An original theoretical model is presented to formulate a variety of material nonlinearities in ductile, brittle and hyperelastic solids in the case of small deformations. The various stress-strain relationships are described in a generalized but very realistic, clear and compact way. The representation of the analytical formula for hyperbolic tangent by means of exponents allows with only one parameter for the stresses and only a few parameters for the strains to describe the characteristic stress-strain curves for the steels, the different curves in compression and tensile strength for brittle materials such, as a concrete, as well as the specific curves for hyperelastic materials. These parameters are the natural values of the maximum stresses and ultimate strains that occur in solids under static loading.