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Fourth-order phase-field modeling for brittle fracture in piezoelectric materials

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Abstract

Failure analyses of piezoelectric structures and devices are of engineering and scientific significance. In this paper, a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilton principle. Three typical electric boundary conditions are involved in the present model to characterize the fracture behaviors in various physical situations. A staggered algorithm is used to simulate the crack propagation. The polynomial splines over hierarchical T-meshes (PHT-splines) are adopted as the basis function, which owns the C1 continuity. Systematic numerical simulations are performed to study the influence of the electric boundary conditions and the applied electric field on the fracture behaviors of piezoelectric materials. The electric boundary conditions may influence crack paths and fracture loads significantly. The present research may be helpful for the reliability evaluation of the piezoelectric structure in the future applications.

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Author notes

  1. These authors contributed equally to this work

Authors and Affiliations

  1. State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu, 610059, China

    Yu Tan

  2. College of Science, Chang’an University, Xi’an, 710064, China

    Fan Peng

  3. Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu, 610031, China

    Chang Liu, Daiming Peng & Xiangyu Li

Authors
  1. Yu Tan
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  2. Fan Peng
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  3. Chang Liu
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  4. Daiming Peng
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  5. Xiangyu Li
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Correspondence to Xiangyu Li.

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Conflict of interest The authors declare no conflict of interest.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 12072297 and 12202370) and the Natural Science Foundation of Sichuan Province of China (No. 24NSFSC4777)

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Tan, Y., Peng, F., Liu, C. et al. Fourth-order phase-field modeling for brittle fracture in piezoelectric materials. Appl. Math. Mech.-Engl. Ed. 45, 837–856 (2024). https://doi.org/10.1007/s10483-024-3118-9

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  • DOI: https://doi.org/10.1007/s10483-024-3118-9

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