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A non-intrusive stochastic phase field method for crack propagation in functionally graded materials

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Abstract

This work presents a framework to study the quasi-static brittle fracture in functionally graded materials with random material properties using a non-intrusive phase field method. The model accounts for variation in the material and fracture properties. Further, the effective Young’s modulus, the gradient index and the fracture properties of the constituent materials are considered as random input variables. The output randomness is represented by polynomial chaos expansion. Two-dimensional benchmark numerical examples are presented to demonstrate the benefits of the non-intrusive approach to study fracture characteristics. The influence of the randomness in the material properties on the peak load carrying capacity is considered as a primary quantity of interest in this study. A systematic parametric study is carried out to bring out the sensitivity of the input randomness on the stochastic output response using Sobol indices.

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Acknowledgements

Shaima M Dsouza and Hirshikesh thank Ministry of Human Resource Development (MHRD), Government of India for the financial support.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu, 600036, India

    Shaima M. Dsouza,  Hirshikesh, Tittu V. Mathew & Sundararajan Natarajan

  2. Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, 247667, India

    Indra Vir Singh

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  1. Shaima M. Dsouza
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Dsouza, S.M., Hirshikesh, Mathew, T.V. et al. A non-intrusive stochastic phase field method for crack propagation in functionally graded materials. Acta Mech 232, 2555–2574 (2021). https://doi.org/10.1007/s00707-021-02956-z

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