By Ellis H. Dill
"Most books on continuum mechanics concentrate on elasticity and fluid mechanics. yet even if pupil or practising expert, smooth engineers want a extra thorough remedy to appreciate the habit of the advanced fabrics and structures in use this present day. Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity bargains a whole journey of the topic that comes with not just elasticity and fluid mechanics but additionally covers plasticity, viscoelasticity, and the continuum version for fatigue and fracture mechanics. Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity builds a powerful realizing of the foundations, equations, and finite aspect formulations had to resolve genuine engineering problems."--Jacket. Read more...
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Extra info for Continuum mechanics : elasticity, plasticity, viscoelasticity
2) T(θ *, h*, F*, F*) = Q ⋅ T(θ , h, F, F) ⋅ QT , for all rotation tensors Q(t), where θ* = θ, h* = h, F* = Q ⋅ F, . 3) F* = Q ⋅ F + Q ⋅ F . Because these relations must hold for all Q(t), we can choose Q = RT where F = R ⋅ U as a necessary condition. In that case, F* = R T⋅ F = R T⋅ R ⋅ U = U, F* = R T⋅ R ⋅ U + R T⋅ (R ⋅ U + R ⋅ U ) = U . , Existence of caloric equations of state in thermodynamics, J. Chem. , 40, 1116, 1964. 5) T(θ , h, F, F) = R ⋅ T(θ , h, U, U ) ⋅ R T . This necessary restriction is also seen to be sufficient to satisfy invariance under rigid motions.
23) V0 for every smooth function u(X). If we regard u as a (virtual) displacement then each term has the form of force multiplied by distance, which is work. 23) is called the principle of virtual work. The usual notation is u = δx. An alternative form of the virtual work formula for the deformed configuration is derived as follows. 11) by a function v(x) after absorbing the inertial force into the expression for the body force: ∫ (∇ ⋅ T + ρb) ⋅ v dV = ∫ x V V = ∫ V = ∂Tkj v j dV + ∂x k V ∂(Tkj v j ) dV − ∂x k ∫ nT v dA − ∫ nT v dA − k kj j S = ∫ ρb ⋅ v dV k kj j ∫ V ∫ ρb ⋅ v dV V ∫ ∂v j Tkj dV + ∂x k ∫ ρb ⋅ v dV ∫ ∂v j Tkj dV + ∂x k ∫ ρb ⋅ v dV = 0.
Inside the region V plus the amount of ρ f convected across the surface S bounding the region V by the movement of the material through the surface. Balance laws of mechanics are often postulated in this form, especially for transport processes. This “control volume” approach is an alternative to following a fixed portion of material, as we will do in this book. 8 BALANCE OF MOMENTUM Let the deformed body be divided into two parts by a surface (Fig. 1). At some common point of the surface that divides the two parts, the unit exterior normal vector to the first part is n, and to the other part is −n.
Continuum mechanics : elasticity, plasticity, viscoelasticity by Ellis H. Dill