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2014 | Buch

Kinematics Kapitel lesen Erstes Kapitel lesen

Soft Solids

A Primer to the Theoretical Mechanics of Materials

verfasst von: Alan D. Freed

Verlag: Springer International Publishing

Buchreihe : Modeling and Simulation in Science, Engineering and Technology

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This textbook presents the physical principles pertinent to the mathematical modeling of soft materials used in engineering practice, including both man-made materials and biological tissues. It is intended for seniors and masters-level graduate students in engineering, physics or applied mathematics. It will also be a valuable resource for researchers working in mechanics, biomechanics and other fields where the mechanical response of soft solids is relevant.

Soft Solids: A Primer to the Theoretical Mechanics of Materials is divided into two parts. Part I introduces the basic concepts needed to give both Eulerian and Lagrangian descriptions of the mechanical response of soft solids. Part II presents two distinct theories of elasticity and their associated theories of viscoelasticity. Seven boundary-value problems are studied over the course of the book, each pertaining to an experiment used to characterize materials. These problems are discussed at the end of each chapter, giving students the opportunity to apply what they learned in the current chapter and to build upon the material in prior chapters.

Inhaltsverzeichnis

Frontmatter

Continuum Fields

Frontmatter
Chapter 1. Kinematics
Abstract
Kinematics is the study of motion. This text addresses the kinematics of an idealized material called a continuum, also referred to as a body.
Alan D. Freed
Chapter 2. Deformation
Abstract
The velocity and acceleration vectors derived in the preceding chapter are important kinematic fields, but, in and of themselves, they are not capable of describing how a body \(\mathcal{B}\) deforms; they only describe how any particle \(\mathcal{P}\) within \(\mathcal{B}\) moves through ambient space \({\mathbb{R}}^{3}\). In order to study deformation, one needs to quantify the change in shape of a body \(\mathcal{B}\) as it is transformed from some initial configuration \(\Omega _{0}\) into its final configuration \(\Omega\) over some interval [t 0, t] in time, which is the topic of this chapter.
Alan D. Freed
Chapter 3. Strain
Abstract
Strain has been defined and quantified a number of different ways over the past two centuries. Essentially, strain is a measure of the change in shape of a localized region in a body \(\mathcal{B}\) that has been deformed from its reference configuration Ω0 (where strain is typically normalized to be zero) into its current configuration Ω. Strain is a two-state property; it depends upon Ω0 and Ω.
Alan D. Freed
Chapter 4. Stress
Abstract
The concept of stress traces back nearly two centuries to the published works of Cauchy (1827). Cauchy generalized Euler’s concept of pressure and the hydrodynamic laws that Euler derived some 70 years earlier. Cauchy made the notion of stress precise. He surmised that a body responds to externally applied loads by transmitting forces internally throughout the body via a matrix valued field that now bears his name: Cauchy stress. Not only did Cauchy develop the concept of stress, but he also derived the physical conservation laws that apply to stress. In doing so, he generalized Euler’s theory for an inviscid fluid.
Alan D. Freed

Constitutive Equations

Frontmatter
Chapter 5. Explicit Elasticity
Abstract
The theory of constitutive equations is steeped in physics and mathematics and is an important discipline within the topic of the mechanics of continuous media. Physical laws have already been introduced. The conservation of mass was addressed in the discussion on deformation, which led to a constraint equation for isochoric deformations. Newton’s laws of motion entered into discussion in the previous chapter on stress via the conservation of momenta, with the conservation of angular momentum requiring a symmetric stress tensor. Constitutive equations have their association with physical laws through the conservation of energy.
Alan D. Freed
Chapter 6. Implicit Elasticity
Abstract
Explicit elastic solids establish stress through a potential function in strain. This potential has its origin in the thermodynamics of reversible processes. The theory produces material models in which the value of stress only depends upon the current state of strain. The final state of stress has no dependence upon the path that strain has traversed in order to reach the current state of stress (Holzapfel 2000; Marsden and Hughes 1983; Ogden 1984; Treloar 1975).
Alan D. Freed
Chapter 7. Viscoelasticity
Abstract
Viscoelastic materials exhibit both elastic and viscous behaviors through their simultaneous storage and dissipation of mechanical energies. Boltzmann (1874) formulated his visco-elastic theory in terms of a convolution integral with a hereditary kernel, what we now refer to as a Volterra (1930) integral equation of the second kind. Coleman and Noll (1961) have summarized the mathematical and physical considerations necessary to construct a linear theory of visco-elasticity in their review paper of some 50 years ago.
Alan D. Freed
Backmatter
Metadaten
Titel
Soft Solids
verfasst von
Alan D. Freed
Copyright-Jahr
2014
Electronic ISBN
978-3-319-03551-2
Print ISBN
978-3-319-03550-5
DOI
https://doi.org/10.1007/978-3-319-03551-2

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