By Samit Roy
''This booklet offers a greater figuring out of the theories organization with finite aspect versions of elastic and viscoelastic reaction of polymers and polymer composites. in keeping with 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 assessment of mathematical preliminaries, equations of anisotropic elasticity, then provides finite point research of viscoelastic fabrics and the diffusion strategy in polymers and polymeric composites. The e-book presents a reference for engineers and scientists and will be used as a textbook in graduate course Read more...
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Extra info for Computational modeling of polymer composites : a study of creep and environmental effects
Application of a constant stress σ0 produces a strain which, in general, contains three components: an instantaneous, a plastic, and a delayed reversible component ε(t) = D∞ + t + ψ(t) σ0 η0 22 EQUATIONS OF SOLID MECHANICS where D∞ σ0 is the instantaneous component of strain, D∞ is the long-term creep compliance, η0 is the Newtonian viscosity coefficient, and ψ(t) the creep function such that ψ(0) = 0. Relaxation test involves determination of stress under constant strain. Application of a constant strain ε0 produces a stress that contains two components σ(t) = [E0 + φ(t)] ε0 where E0 is the static elastic modulus and φ(t) is the relaxation function such that φ(0) = 0.
EQUATIONS OF SOLID MECHANICS By definition, F is a function of both position X and time t; F involves, in general, both stretch and rotation (in reality, stretch and rotation occur simultaneously). Thus, we can write dX = U · dX and dx = R · dX , where U is a stretch tensor and R is an orthogonal rotation tensor, RT · R = I and |R| = 1. 4) where ∇ denotes the gradient operator with respect to the material coordinates X. 5) Note that the Green–Lagrange strain tensor is symmetric, E = ET . 6) which, by definition, is a symmetric second-order tensor.
5) where cij (cji = cij ) are the elasticity (material) constants for an orthotropic medium with the material principal directions (x1 , x2 , x3 ) coinciding with the coordinate axes (x, y, z) used to describe the problem. The cij can be expressed in terms of the engineering constants (E1 , E2 , ν12 , G12 ) for an orthotropic material for plane strain and plane stress problems, as indicated in Eqs. 8), respectively. 2. , the negative of the ratio of the transverse strain in the y-direction to the strain in the x-direction when stress is applied in the x-direction).