DYNAMICS OF INITIALLY STRESSED HYPERELASTIC SOLIDS

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 Hamilton's 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.

• Corporate Authors:

  State University of New York, Buffalo

  Faculty of Engineering and Applied Sciences
  Buffalo, NY  United States  14214

  Air Force Office of Scientific Research

  Bolling AFB
  Washington, DC  United States  20332
• Authors:
  • Reismann, H
  • Pawlik, P S
• Publication Date: 1976-4

Media Info

• Pagination: 69 p.

Subject/Index Terms

• TRT Terms: Beams; Boundary value problems; Deformation; Dynamic structural analysis; Dynamics; Equations of motion; Hydrostatic pressure; Mechanical elasticity; Motion; Rods; Solids; Stresses; Structural plates; Structural shells; Thermodynamics
• Uncontrolled Terms: Boundary conditions; Increments; Plates
• Old TRIS Terms: Beams (Structural)
• Subject Areas: Bridges and other structures; Highways;

Filing Info

• Accession Number: 00137216
• Record Type: Publication
• Source Agency: National Technical Information Service
• Report/Paper Numbers: 99 Intrm Rpt., AFOSR-TR-76-0592
• Contract Numbers: AF-AFOSR-2943-76
• Files: TRIS
• Created Date: Sep 4 1976 12:00AM