AN ELASTIC CONSTITUTIVE EQUATION CONTAINING MOLECULAR PARAMETERS.
Abstract
A constitutive equation is developed which contains microscopic or molecular parameters associated with time-independent elastic solids. Starting with the concept of mathematical stress (tensor component) as defined by Green's potential function method, the tensor stress and strain components are related to the physical stress and strain components (experimentally measurable). Statistical mechanics is then used to bring microscopic or molecular parameters into the physical constitutive equation. It is these parameters which describe the material's resistance to deformation. The tensor constitutive equation is thus transformed into relationships involving physical stress, microscopic parameters, and macroscopic deformations and is not limited to infinitesimal strains. In addition to the microscopic parameters, three functions must be known to evaluate the constitutive equation for the general case of an aeolotropic, nonhomogeneous, elastic material. These functions involve the distribution of molecular sizes and the spatial and directional preferences of the molecules within the solid. The interrelationships between the isothermal elastic tensor coefficients and the microscopic parameters and deformations are derived. These coefficients are then related to the experimental elastic moduli (tensile, bulk, and shear) for the case of a homogeneous, isotropic material. The constitutive equation and the elastic coefficients can be quantitatively determined from the microscopic parameters only by means of numerical techniques. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1967
- Accession Number
- AD0824735
Entities
People
- John N. Majerus