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Unformatted text preview: EN224: Linear Elasticity Division of Engineering 1.2 Kinetics of Deformable Solids We begin by reviewing general measures of force and balance laws. Internal Forces Define Note To characterize internal forces in a solid, we define the Cauchy Stress tensor T such that: One may define several other measures of stress, for example First Piola-Kirchhoff stress (nominal stress) S: Second Piola-Kirchhoff stress (material stress) : It is straightforward to show that Generated by www.PDFonFly.com at 1/10/2010 9:32:18 PM URL: http://www.engin.brown.edu/courses/en224/Kinetics.html Balance Laws Let v ( x, t ) denote the velocity field Linear momentum balance for an arbitrary volume element requires Angular momentum balance for an arbitrary volume element requires Power Identity Let L = denote the spatial gradient of the velocity field. The rate of work done on a solid by external forces may be computed as Remarks: The components of the Cauchy stress tensor are easily interpreted physically: they are the forces per unit...
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This note was uploaded on 01/10/2010 for the course EN 224 taught by Professor Allenbower during the Spring '05 term at Brown.
- Spring '05