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**Three-dimensional numerical modelling by XFEM of spring-layer imperfect curved interfaces with applications to linearly elastic composite materials.**
*(English)*
Zbl 1242.74181

Summary: The spring-layer interface model is widely used in describing some imperfect interfaces frequently involved in materials and structures. Typically, it is appropriate for modelling a thin soft interphase layer between two relatively stiff bulk media. According to the spring-layer interface model, the displacement vector suffers a jump across an interface whereas the traction vector is continuous across the same interface and is, in the linear case, proportional to the displacement vector jump. In the present work, an efficient three-dimensional numerical approach based on the extended finite element method is first proposed to model linear spring-layer curved imperfect interfaces and then applied to predict the effective elastic moduli of composites in which such imperfect interfaces intervene. In particular, a rigorous derivation of the linear spring-layer interface model is provided to clarify its domain of validity. The accuracy and convergence rate of the elaborated numerical approach are assessed via benchmark tests for which exact analytical solutions are available. The computated effective elastic moduli of composites are compared with the relevant analytical lower and upper bounds.

### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74E30 | Composite and mixture properties |

74B05 | Classical linear elasticity |

### Keywords:

imperfect interface; spring-layer interface model; extended finite element method (XFEM); composite; inclusion; micromechanics
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\textit{Q. Z. Zhu} et al., Int. J. Numer. Methods Eng. 88, No. 4, 307--328 (2011; Zbl 1242.74181)

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