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A J-Interaction Integral to Compute Force Stress and Couple Stress Intensity Factors for Cracks in Functionally Graded Micropolar Materials

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Advances in Mechanics of Materials and Structural Analysis

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 80))

Abstract

In contrast to classical elasticity, the micropolar continuum theory allows to describe materials with significant microstructural effects, such as particulate, granular and porous composites. Such materials show a size effect and have often a spatially varying distribution of mechanical properties. This contribution focuses on the establishment of the interaction integral (I-integral) for decoupling the force stress intensity factors (FSIFs) and couple stress intensity factors (CSIFs) of a crack in functionally graded micropolar material (FGMM). The I-integral is derived from the J-integral by superimposing an auxiliary field on the actual field. The auxiliary field is examined using three different definitions including the constant-constitutive-tensor (CCT) formulation, the non-equilibrium (NE) formulation and the incompatibility (IC) formulation. The NE and IC formulations are more appropriate than the CCT formulation because the I-integral using the CCT formulation involves strain gradients and curvature gradients, which may cause loss of accuracy in numerical calculations. Furthermore, we introduce the patched extended finite element method (patched-XFEM), which replaces crack-tip enrichment functions from the XFEM by a local refined mesh to improve the numerical precision. The I-integral in combination with the patched-XFEM is employed to examine numerically the influence of material parameters on the FSIFs and CSIFs.

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Acknowledgements

The work was financially supported by the National Natural Science Foundation of China (Grant No. 11772105 and 11472191) and by the Alexander von Humboldt Foundation.

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Authors and Affiliations

  1. Department of Astronautic Science and Mechanics, Harbin Institute of Technology, Harbin, 150001, China

    Hongjun Yu

  2. Technische Universität Bergakademie Freiberg, Institute of Mechanics and Fluid Dynamics, 09596, Freiberg, Germany

    Meinhard Kuna

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  1. Hongjun Yu
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Correspondence to Meinhard Kuna .

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Editors and Affiliations

  1. Institute of Mechanics Faculty of Mechanical Engineering, Otto-von-Guericke-University Magdeburg, Magdeburg, Sachsen-Anhalt, Germany

    Holm Altenbach

  2. Fakultät 5, Abt. 1, Hochschule Bremen, Bremen, Bremen, Germany

    Frank Jablonski

  3. Institut für Mechanik, Technische Universität Berlin, Berlin, Germany

    Wolfgang H. Müller

  4. Institute of Mechanics, Faculty of Mechanical Engineering, Otto-von-Guericke-University Magdeburg, Magdeburg, Sachsen-Anhalt, Germany

    Konstantin Naumenko

  5. Institute for Lightweight Construction and Design (KLuB), Technische Universität Darmstadt, Darmstadt, Germany

    Patrick Schneider

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Yu, H., Kuna, M. (2018). A J-Interaction Integral to Compute Force Stress and Couple Stress Intensity Factors for Cracks in Functionally Graded Micropolar Materials. In: Altenbach, H., Jablonski, F., Müller, W., Naumenko, K., Schneider, P. (eds) Advances in Mechanics of Materials and Structural Analysis. Advanced Structured Materials, vol 80. Springer, Cham. https://doi.org/10.1007/978-3-319-70563-7_19

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  • DOI: https://doi.org/10.1007/978-3-319-70563-7_19

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