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**An edge dislocation near a nanosized circular inhomogeneity with interface slip and diffusion.**
*(English)*
Zbl 1406.74062

Summary: We study the transient elastic field induced by an edge dislocation near a nanosized circular elastic inhomogeneity in which the effects of interface slip and diffusion are incorporated into the model of deformation. Separate Gurtin-Murdoch surface elasticities are specified on the surface of the inhomogeneity and on the adjoining surface of the surrounding matrix. In addition, rate-dependent interface slip and diffusion are assumed to occur concurrently on the inhomogeneity-matrix interface. The ensuing interaction problem is solved using a simple yet effective method based on analytic continuation and a convenient decomposition of the proposed solution. In particular, our method allows us to circumvent the second-order tangential derivative taken with respect to the interfacial normal stress, typically a source of additional complication and often an obstacle to the solution of such problems. The original problem is reduced to two coupled linear algebraic equations and a number of mutually independent sets of state-space equations, the general solutions of which can be obtained by solving the associated generalized eigenvalue problem. The image force acting on the edge dislocation is derived using the Peach-Koehler formula. Corresponding stress and displacement fields as well as the image force are found to be dependent on four size-dependent dimensionless parameters (arising from the surface elasticities) and on two size-dependent parameters (having the dimension of time) arising from the incorporation of interface slip and diffusion and they evolve with an infinite number of size-dependent relaxation times.

### MSC:

74A50 | Structured surfaces and interfaces, coexistent phases |

74E30 | Composite and mixture properties |

### Keywords:

inhomogeneity; edge dislocation; surface elasticity; rate-dependent slip; diffusion; relaxation time; image force; analytical continuation; state-space equation
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\textit{X. Wang} et al., Eur. J. Mech., A, Solids 61, 122--133 (2017; Zbl 1406.74062)

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### References:

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