Accession Number : AD0728717

Title :   Research in Non-Linear Continuum Mechanics.

Descriptive Note : Final scientific rept.,

Corporate Author : CARNEGIE-MELLON UNIV PITTSBURGH PA MELLON INST OF SCIENCE

Personal Author(s) : Coleman,Bernard D.

Report Date : AUG 1971

Pagination or Media Count : 8

Abstract : The research supported by this grant was concentrated in two areas: (I) the theory of functional-differential equations, and (II) continuum physics, with emphasis on the mechanics, thermodynamics, and optical behavior of nonlinear media with memory. For many dynamical problems involving non-linear viscoelastic materials, thermodynamical considerations supply Lyapunov functionals which can be used to investigate the stability of equilibrium points. The work done here on functional-differential equations was directed toward such dynamical problems. The research in continuum physics led to the development of a mathematical framework for the description of induced birefringence in materials with long-range memory. It was shown that for certain broad classes of motions in general isotropic materials, material symmetry and the principle of frame-indifference can be employed to simplify the relation between the history strain and dielectric properties, without invoking special hypotheses of smoothness. It was shown that for all motions of plane strain and for some motions of plane stress, general reduced formulae can be derived for quantities accessible to measurement with a plan polariscope, such as the birefringence and the inclination of the axes of refraction. A study was made of thermodynamical restrictions on electromagnetic constitutive equations. (Author)

Descriptors :   (*CONTINUUM MECHANICS, NONLINEAR SYSTEMS), (*VISCOELASTICITY, MATHEMATICAL MODELS), (*DIFFERENTIAL EQUATIONS, INTEGRATION), THERMODYNAMICS, BIREFRINGENCE, STRAIN(MECHANICS), STRESSES, DIELECTRIC PROPERTIES

Subject Categories : Numerical Mathematics
      Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE