By Alan Freed
This textbook offers the actual ideas pertinent to the mathematical modeling of soppy fabrics utilized in engineering perform, together with either man-made fabrics and organic tissues. it truly is meant for seniors and masters-level graduate scholars in engineering, physics or utilized arithmetic. it is going to even be a important source for researchers operating in mechanics, biomechanics and different fields the place the mechanical reaction of sentimental solids is relevant.
Soft Solids: A Primer to the Theoretical Mechanics of Materials is split into components. half I introduces the fundamental innovations had to provide either Eulerian and Lagrangian descriptions of the mechanical reaction of sentimental solids. half II provides distinctive theories of elasticity and their linked theories of viscoelasticity. Seven boundary-value difficulties are studied over the process the booklet, each one concerning an scan used to signify fabrics. those difficulties are mentioned on the finish of every bankruptcy, giving scholars the chance to use what they discovered within the present bankruptcy and to construct upon the fabric in past chapters.
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Additional resources for Soft Solids: A Primer to the Theoretical Mechanics of Materials
2. Simple extension, equi-biaxial extension, pure shear, and biaxial extension are each shear-free motions, whereas simple shear, homogeneous planar membranes, and extension followed by simple shear are each shearing motions. 1 Uniaxial Extension Without a doubt, uniaxial extension is the single most important experiment done on materials for the purpose of their characterization. 11) where (t) = `(t)/`0 is the stretch, `0 = `(t0 ) is the gage length, and `(t) is the current length of extension; therefore, stretch is normalized so that (t0 ) = 1.
The focus of this text is on viscoelasticity as a material model, rather than viscoelasticity as a mechanical system. , the textbooks by Lakes (1998), Mainardi (2010), and Wineman and Rajagopal (2000) if you are interested in more of a solid-mechanics/mechanical-engineering approach to viscoelasticity. Viscoelasticity is one of the simpler constitutive theories for describing dissipating materials. Other theories include, for fluids, Newtonian and non-Newtonian fluid mechanics and, for crystalline solids, creep, plasticity, and viscoplasticity.
They arise when transforming our theories into forms that are more readily implemented into software. Notational exceptions are kept to a minimum and typically arise for historical reasons. Two frames of reference are commonly used in mechanics: material and spatial. Both reside within the infinite ambient space that we call our world or universe. The material frame is often referred to as the reference, initial, or undeformed frame, while the spatial frame also goes by the name of the current or deformed frame.