3.1: Prologue to Development of Constitutive Equations for Continuum, Beams and Plates

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This chapter deals with the determination of relations between stresses and strains, called the constitutive equations. For an elastic material the term elasticity law or the Hooke’s law are often used. In one dimension we would write

\[\sigma = E\epsilon \label{3.1.1}\]

where \(E\) is the Young’s (elasticity) modulus. All types of steels, independent on the yield stress have approximately the same Young modulus \(E = 2.\) GPa. The corresponding value for aluminum alloys is \(E = 0.80\) GPa. What actually is \(\sigma\) and \(\epsilon\) in the above equation? We are saying the “uni-axial” state but such a state does not exist simultaneously for stresses and strains. One dimensional stress state produces three-dimensional strain state and vice versa.