Nonlinear Theory of Elasticity: Applications in Biomechanics by Larry A Taber

By Larry A Taber

Smooth organic tissues frequently endure huge elastic (or approximately elastic) deformations that may be analyzed utilizing the nonlinear conception of elasticity. a result of different techniques to nonlinear elasticity within the literature, a few elements of the topic should be tricky to understand. This e-book makes an attempt to explain and unify these remedies, illustrating the benefits and downsides of every via a number of examples within the mechanics of sentimental tissues. functions contain muscle, arteries, the guts, embryonic tissues, and organic membranes.

Show description

Read Online or Download Nonlinear Theory of Elasticity: Applications in Biomechanics PDF

Similar mechanics books

Unilateral contact problems: variational methods and existence theorems

-------------------Description-------------------- The mathematical research of touch difficulties, without or with friction, is a space the place development relies seriously at the integration of natural and utilized arithmetic. This publication offers the cutting-edge within the mathematical research of unilateral touch issues of friction, besides an incredible a part of the research of dynamic touch difficulties with no friction.

Foundations of Mechanics: 2nd Edition

Ebook by way of Ralph Abraham, Jerrold E. Marsden, Tudor Ratiu, Richard Cushman

DIANA Computational Mechanics ‘94: Proceedings of the First International Diana Conference on Computational Mechanics

Advances in computational mechanics can simply be accomplished at the foundation of fruitful dialogue among researchers and training engineers. This has been accomplished within the current book, which includes all of the papers offered on the first overseas DIANA convention on Computational Mechanics.

Operator Algebras and Quantum Statistical Mechanics: Equilibrium States. Models in Quantum Statistical Mechanics

For nearly 20 years this has been the classical textbook on functions of operator algebra thought to quantum statistical physics. It describes the final constitution of equilibrium states, the KMS-condition and balance, quantum spin platforms and non-stop platforms. significant adjustments within the re-creation relate to Bose--Einstein condensation, the dynamics of the X-Y version and questions about section transitions.

Additional info for Nonlinear Theory of Elasticity: Applications in Biomechanics

Sample text

For instance, using Eq. 44)i, we can transform g2 = gy to g2 = Se by gs = A'gy — A*e y ~ —rsin# r cos# 0 cos( smt 0 —r sin 9 0 r cos 9 0 0 1 = - r sin 6 ex + r cos 9 ey which agrees with gg in Eq. 10). Components of the Coordinate Transformation Tensors In practice, the components of the transformation tensors usually are computed from the equations that relate the unbarred and barred curvilinear coordinates. For a unique mapping of one system to the other, we can write xl = xl(xj), xl = xl(xj).

In fact, comparing Eqs. 115) shows that this rotation can be considered a coordinate transformation from the unbarred to the barred base vectors. In matrix form, inserting Eqs. 117) = e^e^ + eyey + ezez = I can be verified easily. Physical Components In general curvilinear coordinates, the components of vectors and tensors do not always have a direct physical meaning. If the base vectors have different dimensions, for example, then the components have different dimensions, since their combination must be consistent with the dimensions of the vector or tensor.

132) =^ij9ki- Similarly, dotting both sides of Eq. 133) Hence, although Tijk and Tk, are not tensor components, the components of the metric tensor can be used to raise or lower the third index. A useful formula for computing the Christoffel symbols in a given coordinate system can be found by differentiating the expression 9ij — Si'gj with respect to xk to obtain 9ijik giik ' g j ~r -L ikj i J- jki gi'gjik 46 Vectors, Dyadics, and Tensors where Eq. 128)i has been used. Permuting the subscripts and using Eqs.

Download PDF sample

Nonlinear Theory of Elasticity: Applications in Biomechanics by Larry A Taber
Rated 4.35 of 5 – based on 15 votes