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Download Computational modeling of polymer composites : a study of by Samit Roy PDF

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By Samit Roy

''This publication offers a greater realizing of the theories organization with finite point types of elastic and viscoelastic reaction of polymers and polymer composites. in response to the authors unique paintings within the topic zone over the past 3 many years, it covers computational modeling of polymers and polymeric composites. It starts with a overview of mathematical preliminaries, equations of anisotropic elasticity, Read more...

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Extra info for Computational modeling of polymer composites : a study of creep and environmental effects

Sample text

15) are known as the natural boundary conditions. 3 The Principle of Minimum Total Potential Energy A special case of the principle of virtual displacements is known as the principle of minimum total potential energy. 16) represents the constitutive equation of a hyperelastic material. The strain energy density U0 is a single-valued function of strains at a point, and is assumed to be positive-definite. 17) can be identified as −δWE . 22) The sum U + V = Π is called the total potential energy of the elastic body.

55) Additional discussion of the viscoelastic constitutive models, including thermal and moisture effects, is presented in Chapter 3. 1 Energy Principles of Solid Mechanics Introduction and Concept of Work Done As already stated in the introduction, this book deals with computational models of the response of polymers. The computational models used here are based on the finite element method, which is reviewed in Chapter 2. The conventional finite element models of solid mechanics, especially those found in commercial codes, are based on the principle of virtual displacements.

9) must be expressed in terms of quantities referred to the reference configuration. 13) V0 tci δui dSc = Sc t0i δui dS0 S0 where fic and tci are the body force and boundary traction components referred to in the configuration C0 . 14) 0p where δEij = 0 because it is not a function of the unknown displacements. Substituting Eqs. 7) into Eq. 15) 0 is expressed in terms of the incremental strain components using the The term Sij generalized Hooke’s law 0 0 Sij ≈ Cijk e0k , ε0ij ≈ δe0ij Then Eq. 3.

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