The Non-Linear Field Theories of Mechanics

Abstract

The book is based on class notes used by the author ill teaching engineering design at the University of Pennsylvania. It aims to show how analytical met.hods can be practically useful and how applied mechanics can be applied.

On the stress in an internally constrained elastic material

“…The usual approach (cf. Truesdell and Noll [2]) is to define Con globally as the zero-set of some real-valued functions on Inv. Since we will be working in a neighborhood of L this definition is not necessary.…”

“…Truesdell and Noll [2] hypothesized that the stress in an internally constrained elastic material is determined by the deformation gradient only to within all additive stress which has zero stress-power in any admissible motion. The indeterminate stress is called the reaction stress.…”

“…The indeterminate stress is called the reaction stress. Using the hypothesis of Truesdell and Noll [2], one may obtain a representation for the reaction stress. The portion of the stress determined by the deformation gradient, the determinate stress, is herein assumed to be given by a mapping defined on the constraint manifold.…”

“…Truesdell and Noll [2]), the constraint manifold has been defined globally as the zero-set of real-valued functions. The work in Section 3.2 follows this approach at the local level.…”

Boundary layers in finite thermoelasticity

“…While significant strides have been made during the past few decades in understanding the thermomechanics of elastic materials in general, and the physics of rubber-like materials in particular (cf. Truesdell and Noll [1], Chadwick and Sect [-2], Flory [3], Treloar [,4], Bianchi and Price I-5], Besseling and Voetman [6], Chadwick [7], Blatz [,8], Dillon [9], Herrman [10], Martin and Carlson [11]), few boundary value problems have been solved within the context of a full thermomechanical theory. For that matter, until recently there have not been that many inhomogeneous deformations that had been studied within the purview of a purely mechanical theory.…”