By Samit Roy
''This e-book presents a greater figuring out of the theories organization with finite aspect versions of elastic and viscoelastic reaction of polymers and polymer composites. in accordance with the authors unique paintings within the topic zone over the last 3 a long time, it covers computational modeling of polymers and polymeric composites. It starts with a overview of mathematical preliminaries, equations of anisotropic elasticity, then offers finite point research of viscoelastic fabrics and the diffusion technique in polymers and polymeric composites. The e-book offers a reference for engineers and scientists and will be used as a textbook in graduate course Read more...
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Extra resources 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.
It is this configuration that satisfies Newton’s second law of motion of the system. The configurations that satisfy the geometric constraints, but not necessarily Newton’s second law, are called admissible configurations. These configurations are restricted to a neighborhood of the true configuration so that they are obtained from infinitesimal variations of the true configuration. During such variations, the geometric constraints of the system are not violated and all the forces are fixed at their actual values.
Since F is the gradient of x with respect to X, we require that FiJ,K = FiK,J or ∂ 2 xi ∂ 2 xi = ∂XJ ∂XK ∂XK ∂XJ It should be noted that the strain compatibility equations are satisfied automatically when the strains are computed from a given displacement field. 4 Stress Vector and Stress Tensor Stress at a point is a measure of force per unit area. The force per unit area acting on an elemental area ds of the deformed body is called the stress vector acting on the element. The concept also applies to the surface created by slicing the deformed body with a plane.