By Yuan-Cheng Fung (auth.)
The aim of this e-book continues to be similar to that said within the first version: to provide a finished point of view of biomechanics from the stand aspect of bioengineering, body structure, and scientific technological know-how, and to enhance mechanics via a chain of difficulties and examples. My three-volume set of Bio mechanics has been accomplished. they're entitled: Biomechanics: Mechanical homes of residing Tissues; Biodynamics: stream; and Biomechanics: movement, stream, rigidity, and progress; and this can be the 1st quantity. The mechanics prerequisite for all 3 volumes continues to be on the point of my publication a primary direction in Continuum Mechanics (3rd version, Prentice-Hall, Inc. , 1993). within the decade of the Eighties the sector of Biomechanics multiplied tremen dously. New advances were made in all fronts. those who have an effect on the fundamental knowing of the mechanical homes of residing tissues are defined intimately during this revision. The references are stated to date.
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Additional resources for Biomechanics: Mechanical Properties of Living Tissues
The velocity of the spring extension is F/J1 if we denote a differentiation with respect to time by a dot. The total velocity is the sum of these two: F F J1 rf u=-+- (Maxwell model). (1) Furthermore, if the force is suddenly applied at the instant of time t = 0, the spring will be suddenly deformed to u(O) = F(O)/J1, but the initial dashpot deflection would be zero, because there is no time to deform. Thus the initial condition for the differential equation (1) is u(O) = F(O). (2) J1 For the Voigt model, the spring and the dashpot have the same displacement.
In the engineering literature, the second Lame constant f1 is practically always written as G and identified as the shear modulus. Writing out Eq. (2) in extenso, and with x, y, z as rectangular cartesian coordinates, we have Hooke's law for an isotropic elastic solid: + eyy + ezz ) + 2Gexx , A(exx + eyy + ezz ) + 2Geyy , (Jxx = A(e xx (Jyy = These equations can be solved for written as eij' (3) But customarily, the inverted form is (4a) or (4b) The constants E, v, and G are related to the Lame constants A and G (or f1).
Tan IX, as the shear strain; the reasons for this will be elucidated later. , the constitutive equation of the material). For example, if we pull on a string, it elongates. The experimental results can be presented as a curve of the tensile stress (J plotted against the stretch ratio 2, or strain e. An empirical formula relating (J to e can be determined. The case of infinitesimal strain is simple because the different strain measures named above all coincide. It was found that for most engineering materials subjected to an infinitesimal strain in uniaxial stretching, a relation like (J = Ee (3) is valid within a certain range of stresses, where E is a constant called Young's modulus.