Results and discussion The formulation using singular integral equations to determine the stress intensity factors of cracked functionally graded magneto electro elastic materials was established. For validation, the results for the case of a sufficiently thick layer, were compared to those of infinite medium (Rekik et al 2012) and a good agreement was obtained (Fig. 2). Then, a number of simulations, for different magneto electro mechanical load cases, were performed by varying the nonhomogeneity parameter, crack position, crack length and permeability parameters. The considered material is a bimorph composed of the Barium Titanium Oxide, BaTiO3 and the Cobalt Iron Oxide, CoFe2O4. Fig. 3 illustrates the effect of varying the nonhomogeneity parameter a on the fields’ intensity factors for normal tractions, tangential tractions, magnetic and electric loadings in case of a central crack as large as the layer thickness and electromagnetic permeability of 25%. For each loading case, the corresponding field’’s intensity factors showss lower sensibility to material’s nonhomogeneity while remaining fields’ intensity factors increase monotonouslymonotonically. Fig. 4 illustrates the effect of varying the crack position on the fields’ intensity factors for the same loading cases in the case of a crack as large as the layer thickness and electromagnetic permeability of 25%. In case of normal traction, electric or magnetic loadings, k1, kB and kD show parabolic variation with crack position while k2 varies oddly. Similarly, in case of tangential traction loading, k2 varies parbolicallyparabolically while the k1, kB and kD vary oddly. Fig. 5 illustrates the effect of varying magneto electric permeabilities parameter in case of a central crack as large as the layer thickness. Fields’ intensity factors vary linearly with increasing impermeability.
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