By Samit Roy

''This ebook presents a greater realizing of the theories organization with finite point versions of elastic and viscoelastic reaction of polymers and polymer composites. in keeping with the authors unique paintings within the topic region over the past 3 many years, it covers computational modeling of polymers and polymeric composites. It starts with a evaluate of mathematical preliminaries, equations of anisotropic elasticity,Read more...

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

**Sample text**

Thus, there are only six independent components of the Cauchy and second Piola–Kirchhoff stress tensors. 5 Equations of Motion Consider a given mass of a material body at any instant occupying a volume Ω bounded by a surface Γ. Suppose that the body is acted upon by external surface force T, measured per unit surface area, and body force f , measured per unit mass. For the case of infinitesimal deformation, the Cauchy stress tensor and the second Piola–Kirchhoff stress tensor are essentially the same.

18) to a set of algebraic equations relating ∆s+1 to ∆s . 27) Finite Element Models of Nonlinear Continua Introduction In the linear description of the deformation of solid bodies one assumes that the displacements and strains are infinitesimally small and that the material response is linearly elastic. Therefore, the geometry of the deformed body is assumed to be essentially the same as that of the undeformed body for defining the stress and strain measures and evaluating the integrals appearing in the statement of the principle of virtual displacements.

23) In view of the above simplifications, Eq. 24) is the weak form for the development of two- or three-dimensional finite element models based on the updated Lagrangian formulation. 28) ∆T = {u1 , v1 , u2 , v2 , · · · , un , vn } ¯ T = {¯ ∆ u1 , v¯1 , u ¯2 , v¯2 , · · · , u ¯n , v¯n } Substitution of Eqs. 27) into Eq.