Stress concentration in porous materials is one of the most crucial culprits of mechanical failure. This paper focuses on planar porous materials with porosity less than 5%. We present a stress-prediction model of an arbitrarily rotated elliptical hole in a rhombus shaped representative volume element (RVE) that can represent a class of generic planar tessellations, including rectangular, triangular, hexagonal, Kagome, and other patterns. The theoretical model allows the determination of peak stress and distribution of stress generated near the edge of elliptical holes for any arbitrary tiling under displacement loading and periodic boundary conditions. The results show that the alignment of the void with the principal directions minimizes stress concentration. Numerical simulations support the theoretical findings and suggest the observations remain valid for porosity as large as 5%. This work provides a fundamental understanding of stress concentration in low-porosity planar materials with insight that not only complements classical theories on the subject but also provides a practical reference for material design in mechanical, aerospace, and other industry.
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October 2018
Research-Article
Stress Concentration in Low-Porosity Periodic Tessellations With Generic Patterns of Elliptical Holes Under Biaxial Strain
Jiazhen Leng,
Jiazhen Leng
Mem. ASME
Department of Mechanical Engineering,
McGill University,
817 Sherbrooke Street West,
Montreal, QC H3A 0C3, Canada
e-mail: jiazhen.leng@mcgill.ca
Department of Mechanical Engineering,
McGill University,
817 Sherbrooke Street West,
Montreal, QC H3A 0C3, Canada
e-mail: jiazhen.leng@mcgill.ca
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Gerard Reynolds,
Gerard Reynolds
Department of Mechanical Engineering,
McGill University,
Montreal, QC H3A 0C3, Canada
e-mail: gerard.reynolds@mail.mcgill.ca
McGill University,
817 Sherbrooke Street West
,Montreal, QC H3A 0C3, Canada
e-mail: gerard.reynolds@mail.mcgill.ca
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Megan Schaenzer,
Megan Schaenzer
Siemens Power and Gas,
Dorval, QC H9P 1A5, Canada
e-mail: megan.schaenzer@siemens.com
9545 Côte-de-Liesse
,Dorval, QC H9P 1A5, Canada
e-mail: megan.schaenzer@siemens.com
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Minh Quan Pham,
Minh Quan Pham
Siemens Power and Gas,
Dorval, QC H9P 1A5, Canada
e-mail: minhquan.pham@siemens.com
9545 Côte-de-Liesse
,Dorval, QC H9P 1A5, Canada
e-mail: minhquan.pham@siemens.com
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Genevieve Bourgeois,
Genevieve Bourgeois
Siemens Power and Gas,
Dorval, QC H9P 1A5, Canada
e-mail: genevieve.bourgeois@siemens.com
9545 Côte-de-Liesse
,Dorval, QC H9P 1A5, Canada
e-mail: genevieve.bourgeois@siemens.com
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Damiano Pasini
Damiano Pasini
Mem. ASME
Department of Mechanical Engineering,
McGill University,
Montreal, QC H3A 0C3, Canada
e-mail: damiano.pasini@mcgill.ca
Department of Mechanical Engineering,
McGill University,
817 Sherbrooke Street West
,Montreal, QC H3A 0C3, Canada
e-mail: damiano.pasini@mcgill.ca
Search for other works by this author on:
Jiazhen Leng
Mem. ASME
Department of Mechanical Engineering,
McGill University,
817 Sherbrooke Street West,
Montreal, QC H3A 0C3, Canada
e-mail: jiazhen.leng@mcgill.ca
Department of Mechanical Engineering,
McGill University,
817 Sherbrooke Street West,
Montreal, QC H3A 0C3, Canada
e-mail: jiazhen.leng@mcgill.ca
Gerard Reynolds
Department of Mechanical Engineering,
McGill University,
Montreal, QC H3A 0C3, Canada
e-mail: gerard.reynolds@mail.mcgill.ca
McGill University,
817 Sherbrooke Street West
,Montreal, QC H3A 0C3, Canada
e-mail: gerard.reynolds@mail.mcgill.ca
Megan Schaenzer
Siemens Power and Gas,
Dorval, QC H9P 1A5, Canada
e-mail: megan.schaenzer@siemens.com
9545 Côte-de-Liesse
,Dorval, QC H9P 1A5, Canada
e-mail: megan.schaenzer@siemens.com
Minh Quan Pham
Siemens Power and Gas,
Dorval, QC H9P 1A5, Canada
e-mail: minhquan.pham@siemens.com
9545 Côte-de-Liesse
,Dorval, QC H9P 1A5, Canada
e-mail: minhquan.pham@siemens.com
Genevieve Bourgeois
Siemens Power and Gas,
Dorval, QC H9P 1A5, Canada
e-mail: genevieve.bourgeois@siemens.com
9545 Côte-de-Liesse
,Dorval, QC H9P 1A5, Canada
e-mail: genevieve.bourgeois@siemens.com
Ali Shanian
Damiano Pasini
Mem. ASME
Department of Mechanical Engineering,
McGill University,
Montreal, QC H3A 0C3, Canada
e-mail: damiano.pasini@mcgill.ca
Department of Mechanical Engineering,
McGill University,
817 Sherbrooke Street West
,Montreal, QC H3A 0C3, Canada
e-mail: damiano.pasini@mcgill.ca
1Corresponding author.
Manuscript received March 24, 2018; final manuscript received May 28, 2018; published online July 6, 2018. Assoc. Editor: Shaoxing Qu.
J. Appl. Mech. Oct 2018, 85(10): 101010 (13 pages)
Published Online: July 6, 2018
Article history
Received:
March 24, 2018
Revised:
May 28, 2018
Citation
Leng, J., Reynolds, G., Schaenzer, M., Pham, M. Q., Bourgeois, G., Shanian, A., and Pasini, D. (July 6, 2018). "Stress Concentration in Low-Porosity Periodic Tessellations With Generic Patterns of Elliptical Holes Under Biaxial Strain." ASME. J. Appl. Mech. October 2018; 85(10): 101010. https://doi.org/10.1115/1.4040539
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