By Xiaohong Chen
Fracture Mechanics of Electromagnetic Materials presents a complete review of fracture mechanics of conservative and dissipative fabrics, in addition to a common formula of nonlinear box thought of fracture mechanics and a rigorous therapy of dynamic crack difficulties regarding coupled magnetic, electrical, thermal and mechanical box amounts.
Thorough emphasis is put on the actual interpretation of primary ideas, improvement of theoretical types and exploration in their purposes to fracture characterization within the presence of magneto-electro-thermo-mechanical coupling and dissipative results. Mechanical, aeronautical, civil, biomedical, electric and digital engineers attracted to software of the rules of fracture mechanics to layout research and sturdiness review of shrewdpermanent constructions and units will locate this e-book a useful source.
Readership: Graduate scholars, educational researchers and engineering experts in fracture mechanics.
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Additional resources for Fracture Mechanics of Electromagnetic Materials: Nonlinear Field Theory and Applications
115) where T is the absolute temperature and sˆ is the entropy per unit mass. 116) 1 1 1 dhˆ + E ⋅ je − sˆT − . 117) where js is the entropy flux. 118) = + ∇R ⋅ J s ≥ 0 , dt ρ 0 dt where J s = jF −1 ⋅ j s . 119) Elements of Electrodynamics of Continua 43 where E Σ = jF −1 ⋅ E σ ⋅ (F −1 ) T is the second Piola–Kirchhoff stress tensor conjugate to the right Cauchy–Green deformation tensor C, ˆ = jF −1 ⋅ P , is symmetric, Eˆ = E ⋅ F , Π E σ = σ + em σ − F σ = t σ − F σ ˆ = M ⋅ F , Βˆ = jF −1 ⋅ B , J q = jF −1 ⋅ jq , and J = jF −1 ⋅ j .
A convenient selection of the contour Γ. 6 Viscoelastic Fracture Increasing interest in engineering applications of polymeric materials has consequently stimulated the study of viscoelastic fracture mechanics which incorporates a time-dependent response. Willis (1967) first considered anti-plane, steady-state crack propagation in an infinite viscoelastic medium. Later, Atkinson and Popelar (1979) and Popelar and Atkinson (1980) investigated dynamic crack propagation in a viscoelastic strip subjected to mode-I and III loadings.
Hence, the electromagnetic stress tensor can be taken as an extension of the Maxwell stress tensor in classical electrodynamics, which also involves the contribution due to polarization and magnetization defined by Eq. 49). For the special case of electrostatics or magnetostatics, we have the f electric stress or the magnetic stress e σ = D ⊗ E− e u I f σ ( = B ⊗ H + M ⋅ B ) I − u I with the corresponding energy density m m denoted by e u f = ε 0 E⋅ E 2 or m u f = B⋅ B (2µ0 ) . 5 Electromagnetic power The electromagnetic power is the rate of work done by the electromagnetic forces, that is, em w∆v = ∑ δq α ( v + ξα + ξˆ α ) ⋅ e(x + ξα ) .
Fracture Mechanics of Electromagnetic Materials: Nonlinear Field Theory and Applications by Xiaohong Chen