A micromechanical model based on hypersingular integro-differential equations for analyzing micro-crazed interfaces between dissimilar elastic materials

doi:10.1007/s10483-020-2563-8

Applied Mathematics and Mechanics (English Edition) ›› 2020, Vol. 41 ›› Issue (2): 193-206.doi: https://doi.org/10.1007/s10483-020-2563-8

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A micromechanical model based on hypersingular integro-differential equations for analyzing micro-crazed interfaces between dissimilar elastic materials

X. WANG, W. T. ANG, H. FAN

School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore

收稿日期:2019-06-14 修回日期:2019-09-12 出版日期:2020-02-01 发布日期:2020-01-03
通讯作者: W. T. ANG E-mail:mwtang@ntu.edu.sg

A micromechanical model based on hypersingular integro-differential equations for analyzing micro-crazed interfaces between dissimilar elastic materials

X. WANG, W. T. ANG, H. FAN

School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore

Received:2019-06-14 Revised:2019-09-12 Online:2020-02-01 Published:2020-01-03
Contact: W. T. ANG E-mail:mwtang@ntu.edu.sg

摘要/Abstract

摘要： The current work models a weak (soft) interface between two elastic materials as containing a periodic array of micro-crazes. The boundary conditions on the interfacial micro-crazes are formulated in terms of a system of hypersingular integro-differential equations with unknown functions given by the displacement jumps across opposite faces of the micro-crazes. Once the displacement jumps are obtained by approximately solving the integro-differential equations, the effective stiffness of the micro-crazed interface can be readily computed. The effective stiffness is an important quantity needed for expressing the interfacial conditions in the spring-like macro-model of soft interfaces. Specific case studies are conducted to gain physical insights into how the effective stiffness of the interface may be influenced by the details of the interfacial micro-crazes.

关键词: micromechanical modeling, micro-crazed interface, effective stiffness coefficient, hypersingular integro-differential equation

Abstract: The current work models a weak (soft) interface between two elastic materials as containing a periodic array of micro-crazes. The boundary conditions on the interfacial micro-crazes are formulated in terms of a system of hypersingular integro-differential equations with unknown functions given by the displacement jumps across opposite faces of the micro-crazes. Once the displacement jumps are obtained by approximately solving the integro-differential equations, the effective stiffness of the micro-crazed interface can be readily computed. The effective stiffness is an important quantity needed for expressing the interfacial conditions in the spring-like macro-model of soft interfaces. Specific case studies are conducted to gain physical insights into how the effective stiffness of the interface may be influenced by the details of the interfacial micro-crazes.

Key words: micromechanical modeling, micro-crazed interface, effective stiffness coefficient, hypersingular integro-differential equation

中图分类号:

74M25

X. WANG, W. T. ANG, H. FAN. A micromechanical model based on hypersingular integro-differential equations for analyzing micro-crazed interfaces between dissimilar elastic materials[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(2): 193-206.

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A micromechanical model based on hypersingular integro-differential equations for analyzing micro-crazed interfaces between dissimilar elastic materials

A micromechanical model based on hypersingular integro-differential equations for analyzing micro-crazed interfaces between dissimilar elastic materials

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