By Morton E. Gurtin
ISBN-10: 0387986677
ISBN-13: 9780387986678
For the decade, the writer has been operating to increase continuum mechanics to regard relocating obstacles in fabrics focusing, specifically, on difficulties of metallurgy.
This monograph offers a rational therapy of the concept of configurational forces; it's an attempt to advertise a brand new standpoint. integrated is a presentation of configurational forces inside of a classical context and a dialogue in their use in components as various as section transitions and fracture.
The paintings will be of curiosity to fabrics scientists, mechanicians, and mathematicians.
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Additional info for Configurational Forces as Basic Concepts of Continuum Physics: v. 137
Sample text
The phrase transfer of material to ∂P is meant in a general sense that allows for the “transfer of material from ∂P ,” and similarly for the phrase addition of material to ∂P . a. Migrating control volumes P for ∂P (t) and ∂P¯ (t) P (t). Velocity fields Let P P (t) be a (smoothly) migrating control volume with U the (scalar) normal velocity of ∂P in the direction of the outward unit normal n. To describe the working associated with the evolution of P , I introduce a field q interpreted as the velocity with which an external agency adds material to ∂P .
But (assuming that y is smooth) the order of the α and β differentiations is irrelevant, and this yields (1–23b). The result (1–23c) is the consequence of (1–23a) and (1–23b), because these relations imply the identity [(∇F)a]b [∇(F a)]b for all vectors b. ) Let T be a tensor and Λ a 3-tensor; then ΛT, a 3-tensor, and T:Λ, a vector, are defined by (ΛT)a (T:Λ) · a Λ(T a), T · (Λa) for all vectors a. In components, (ΛT)ij k following identities, for T a tensor field and F (T:∇F) · a (1–24a) (1–24b) ij m Tmk , (T:Λ)k ∇y, are useful: Tij ij k .
Here it is useful to consider, within the framework of particle mechanics, a system consisting of, say, a red particle, and a blue particle. B is the counterpart of the set of particle labels, which could be {1, 2}, or {red,blue}, or the initial partial positions {x1 (0), x2 (0)}, and, with respect to these choices, Ematter is the analog of the integers, or the set of primary colors, or three-dimensional Euclidean space. d. Consistency requirement. Objective fields 23 c. Material and spatial observers2 I consider two independent classes of observers: spatial observers that describe Espace and material observers that describe Ematter .
Configurational Forces as Basic Concepts of Continuum Physics: v. 137 by Morton E. Gurtin
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