Module 3 Constitutive Equations
Concept Question 3.1.1. Derivation of Hooke’s law. Derive the Hooke’s law from quadratic strain energy function Starting from the quadratic strain energy function and the de nition for the stress components given in the notes, 1.derive the Generalized Hooke’s law ˙ ij = C ijkl kl. Solution: We start by computing: @ ij @ kl = ik jl
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www.mit.eduFor our Hooke’s law example earlier, the slope is the spring constant2. 2Since the spring constant k is de ned as F= kx (where is the force and x is the stretch), the slope in Figure3.1ais actually the inverse of the spring constant. 2. Statistics for Research Projects Chapter 3