By Marcelo Epstein
An attractive and interesting creation to Continuum Mechanics in Biosciences
This ebook provides the weather of Continuum Mechanics to humans drawn to functions to organic platforms. it truly is divided into elements, the 1st of which introduces the fundamental thoughts inside of a strictly one-dimensional spatial context. This coverage has been followed to be able to permit the newcomer to Continuum Mechanics to understand how the idea should be utilized to big concerns in Biomechanics from the very starting. those comprise mechanical and thermodynamical stability, fabrics with fading reminiscence and chemically reacting mixtures.
In the second one a part of the ebook, the absolutely fledged 3-dimensional concept is gifted and utilized to hyperelasticity of sentimental tissue, and to theories of reworking, getting older and progress. The publication closes with a bankruptcy dedicated to Finite aspect research. those and different issues are illustrated with case experiences influenced through biomedical purposes, equivalent to vibration of air within the air canal, hyperthermia therapy of tumours, striated muscle reminiscence, biphasic version of cartilage and adaptive elasticity of bone. The publication deals a tough and beautiful advent to Continuum Mechanics for college kids and researchers of biomechanics, and different engineering and medical disciplines.
Explains continuum mechanics utilizing examples from biomechanics for a uniquely available creation to the topic
Moves from starting place subject matters, reminiscent of kinematics and stability legislation, to extra complex parts equivalent to theories of progress and the finite aspect method..
Transition from a one-dimensional method of the overall concept offers the ebook vast insurance, supplying a transparent advent for rookies new to the subject, in addition to a great beginning for these contemplating relocating to extra complex software
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Extra info for The Elements of Continuum Biomechanics
48) can also be written as ∂ρ ∂(ρv ) + = 0. 49) This equation is known as the continuity equation. We have already used it in the example of trafﬁc ﬂow. 2 Balance of (Linear) Momentum Although originally formulated for a single material particle and then extended to discrete systems, Newton’s second law of motion is postulated to be applicable also to continuous systems. The quantity to be balanced is the total linear9 momentum, whose Lagrangian density is ρ0 v (per unit length in the reference conﬁguration).
29), express the temperature as a Lagrangian ﬁeld over the reference conﬁguration. 29) by ﬁrst obtaining the Lagrangian ﬁeld and then explicitly inverting the equation of motion as X = X (x , t). 10 The Material Derivative A similar treatment of derivatives with respect to the time variable gives rise to the important notion of the material derivative or, more precisely, material time derivative. 37) where v (X , t) is the referential version of the velocity ﬁeld. 37) can also be written as ˆ , t) ∂ψ(X , t) ∂ ψ(x = + (grad ψ) v (X , t).
49), we obtain ∂ ρˆ ∂(ρv ˆ ) ∂ ln sˆ (x ) + + ρv ˆ = 0. 57) If the cross section is constant the last term cancels out. Similarly, the internal force n(x , t), in the case of a gas, is obtained by multiplying the pressure p(x , t) times the cross-sectional area sˆ (x ), namely, n(x , t) = −p(x , t) sˆ (x ). 58) The negative sign is placed for consistency, since a positive pressure corresponds to compression. 53)) yields ρˆ ∂v (x , t) ∂v (x , t) ∂p ∂ ln sˆ (x ) + ρˆ v (x , t) = − − p(x , t) . 59) Once again, if the cross section is constant (which we will henceforth assume) the last term cancels out.
The Elements of Continuum Biomechanics by Marcelo Epstein