Erratum to: Interaction integrals for fracture analysis of functionally graded magnetoelectroelastic materials

M. Kuna TU Bergakademie Freiberg, Institut fur Mechanik und Fluiddynamik, Lampadiusstrase 4, 09596 Freiberg, Germany esi j,1, hsi j,1, κis,1, βis,1 and γis,1 are O (r) with α ≥ 0, the second integral in Eqs. 56, 60 and 64 exists as the limit r → 0. In the limit r → 0, Ci jks (r, θ) = C∗ i jks, esi j (r, θ) = e∗ si j , hsi j (r, θ) = h∗si j , κis (r, θ) = κ∗ is, βis (r, θ) = β∗ is and γis (r, θ) = γ ∗ is in Eq. 7. Hence in the limit r → 0, in constant constitutive tensor formulation σ (1) i j e (2) i j,1 = σ (2) i j,1e i j , σ (1) i j,1e i j = σ (2) i j e i j,1, D j E (2) j,1 = D j,1E (1) j , D j,1E (2) j = D j E (1) j,1, B j H (2) j,1 = B j,1H (1) j , and B j,1H (2) j = B j H (1) j,1 , and in incompatibility formulation u i, j1 = e i j,1,φ , j1 = −E (2) j,1, and φ(2) , j1 = −H (2) j,1 . Therefore, the integrand of the second integral in Eq. 56 and the incompatibility terms in the integrand of the second integral in Eq. 60 naturally vanish. Note that in incompatibility formulation the auxiliary fields are compatible very near the crack tip (asymptotically).