Dynamics of Initially Stressed Hyperelastic Solids.
STATE UNIV OF NEW YORK AT BUFFALO FACULTY OF ENGINEERING AND APPLIED SCIENCES
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This report presents a linear, three-dimensional theory for the incremental motion of initially stressed, hyperelastic solids. The magnitude of the initial deformation and the form of the strain energy density function are both arbitrary except for the usual restrictions placed on them by the principles of mechanics and thermodynamics. A variational approach, using Hamiltons Principle, is used to derive the equations of motion and the proper natural boundary conditions for the incremental motion. This approach yields a variational principle which, because of its scalar form, can be used to derive the appropriate equations in any particular coordinate system. This variational principle also provides a framework for the systematic development of special, approximate theories, for the incremental motion of rods, beams, plates, shells, etc. In addition to the general theory, the report presents a resolution of the forced, incremental motion problem of hyperelastic solids of bounded extent. The investigation concludes with two applications a The solid subjected to initial hydrostatic pressure, and b the theory of the initially stressed beam.
- Solid State Physics