On stress and strain descriptions of continuum mechanics
Date Issued
2011
Date
2011
Author(s)
Li, Ching-Yao
Abstract
We propose a parametric description and use the theory of differential forms to study the mechanical behavior of continuum with memory. We define mass scalar-valued differential 3-forms (mass form) and traction vector-valued differential 2-forms (traction form), and re-derive the conservation laws of mass, linear momentum, and angular momentum. According to the principle of virtual work, the stretch vector-valued differential 1-form (stretch form) are obtained as the work-conjugate variable of the traction form. The elastic constitutive law in term of the traction and stretch forms and the objectivities of the forms and the law are established. The shortcomings of other descriptions are also pointed out. In order to verify the accessibility and the simplicity of the parametric description three examples, simple shear deformation, pure torsion of solid cylinder, and simultaneous extension, inflation, and torsion of solid cylinder, are demonstrated.
Subjects
continuum with memory
large deformation
parametric description
stress
strain
Type
thesis
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