By Meinhard Kuna

Fracture mechanics has tested itself as an enormous self-discipline of becoming curiosity to these operating to evaluate the protection, reliability and repair lifetime of engineering buildings and fabrics. so as to calculate the loading state of affairs at cracks and defects, these days numerical strategies like finite point approach (FEM) became fundamental instruments for a extensive variety of purposes. the current monograph offers an creation to the fundamental techniques of fracture mechanics, its major objective being to obtain the detailed thoughts for FEM research of crack difficulties, that have so far in simple terms been mastered by way of specialists. every kind of static, dynamic and fatigue fracture difficulties are handled in - and third-dimensional elastic and plastic structural parts. the use of some of the answer concepts is verified via pattern difficulties chosen from sensible engineering case reports. the first goal workforce contains graduate scholars, researchers in academia and engineers in practice.

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**Extra resources for Finite Elements in Fracture Mechanics: Theory - Numerics - Applications (Solid Mechanics and Its Applications)**

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Technical university of Denmark. , 1979 • Kanninen, M. F. and Popelar, C. : Advanced Fracture Mechanics. : Fracture and Size Effects in Concrete and other Quasibrittle Materials. : Fracture Mechanics of Cementitious Materials. : Fracture of Brittle Solids. : Fracture at High Temperature. : Fracture Mechanics. : Fatigue of Materials. Cambridge University Press, Cambridge, 1998 • Ravichandran, K. , Ritchie, R. O. : Small fatigue cracks. mechanics, mechanisms and applications. : Fatigue of Structures and Materials.

Only the result for the crack tip near field will be given here. 22) K II = τ πa , z2 − a2 − z , χ (z) = iτ z + i ⎧ θ θ 3θ ⎪ ⎪ − sin 2 + cos cos ⎪ ⎧ ⎫ ⎪ ⎪ 2 2 2 ⎪ ⎪ ⎪ ⎨ σ11 ⎪ ⎬ K II ⎨ θ 3θ θ σ22 = √ sin cos cos ⎪ ⎪ 2 2 2 2πr ⎪ ⎪ ⎩ ⎭ ⎪ τ12 ⎪ ⎪ θ θ 3θ ⎪ ⎪ 1 − sin sin ⎩ cos 2 2 2 τ 2 ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎧ II ⎫ f11 (θ)⎪ ⎪ ⎨ ⎬ K II II =√ (θ) . 23) and in cylindrical coordinates ⎧ θ ⎧ ⎫ ⎪ ⎪ −5 sin 2 + 3 sin ⎨ σrr ⎬ K II ⎨ σθθ = √ −3 sin 2θ − 3 sin ⎩ ⎭ 4 2πr ⎪ ⎪ τrθ ⎩ cos θ + 3 cos 3θ 2 2 3θ 2 3θ 2 ⎫ ⎪ ⎪ ⎬ ⎪ ⎪ ⎭ .

50) sin(2λπ) = 0 ⇒ λ = 2 This reveals the same eigenvalues as in mode I and mode II. The entire solution can now be composed by combining all eigenfunctions with the coefficient Cn . 49), which means the coefficients are alternating either purely real or imaginary: ∞ Ω(z) = n Cn z 2 , Cn = −in cn . 32) is √ exactly reproduced, whereby the relation K III = c1 π/2 applies. The eigenfunction for n = 2 corresponds to a constant shear stress τ13 = T13 = c2 . 2 Linear-Elastic Fracture Mechanics 35 The derived eigenfunctions apply to all plane elastic crack problems.