Transcription of Module 3 Constitutive Equations
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Module 3 Constitutive Equations
Module 3 Constitutive EquationsLearning Objectives Understand basic stress-strain response of engineering materials. Quantify the linear elastic stress-strain response in terms of tensorial quantities and inparticular the fourth-order elasticity or stiffness tensor describing Hooke s Law. Understand the relation between internal material symmetries and macroscopic anisotropy,as well as the implications on the structure of the stiffness tensor. Quantify the response of anisotropic materials to loadings aligned as well as rotatedwith respect to the material principal axes with emphasis on orthotropic and transversely-isotropic materials.
46 MODULE 3. CONSTITUTIVE EQUATIONS 1 E 1^ = 2 E 2 Figure 3.1: Stress-strain curve for a linear elastic material subject to uni-axial stress ˙(Note that this is not uni-axial strain due to Poisson e ect) In this expression, Eis Young’s modulus. Strain Energy Density For a given value of the strain , the strain energy density (per unit volume ...
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