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kinematics

kinematics - EN224 Linear Elasticity Division of...

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EN224: Linear Elasticity Division of Engineering 1. Review of the Field Equations of Linear Elasticity Objective: derive field equations governing the behavior of linear elastic solids from the perspective of finite deformations of general solids. Review constitutive models for elastic solids 1.1 Kinematics of Deformable Solids We describe the deformation and motion of a solid by a mapping . Suppose a material is at position X in the undeformed solid, and moves to a position x when the solid is loaded. A mapping would describe the motion. We assume that χ is twice jointly differentiable wrt time and position, and satisfies The displacement of a material point is Homogeneous deformations Homogeneous deformations are of particular interest to us, because the constitutive response of a solid is usually determined by measuring the forces required to induce a homogeneous deformation within a solid specimen. A homogeneous deformation has the form Generated by www.PDFonFly.com at 1/10/2010 9:30:28 PM URL: http://www.engin.brown.edu/courses/en224/Kinematics.html
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Where A is a constant two tensor such that det( A)> 0, and
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