Predicting the Flexural Modulus of Variable Pitch Angle, Porous Bouligand Structured 3D Printed Polymer
Our study considered porous Bouligand structured polymer, comprising polymer fibres with porous spaces between them. These are more complicated structures than the non-porous Bouligand, since the addition of porosity into the material creates a secondary variable besides fibre pitch. There is curren...
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2025-01-01
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| author | Praveenkumar S. Patil Edward D. McCarthy Parvez Alam |
| author_facet | Praveenkumar S. Patil Edward D. McCarthy Parvez Alam |
| author_sort | Praveenkumar S. Patil |
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| description | Our study considered porous Bouligand structured polymer, comprising polymer fibres with porous spaces between them. These are more complicated structures than the non-porous Bouligand, since the addition of porosity into the material creates a secondary variable besides fibre pitch. There is currently no analytical model available to predict the modulus of such materials. Our paper explores the correlation between porosity, polymer fibre pitch angle, and flexural modulus in porous Bouligand structured polymers. Our structures were digitally manufactured using stereolithography (SLA) additive manufacturing methods, after which they were subjected to three-point bending tests. Our aim was to simply and parametrically develop an analytical model that would capture the influences of both porosity and polymer fibre pitch angle on the flexural modulus of the material. Our model is expressed as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>E</mi><mi>f</mi></msub><mo>=</mo><msub><mi>E</mi><mrow><mi>p</mi><mi>o</mi><mi>r</mi><mi>o</mi></mrow></msub><mrow><mo>(</mo><mi>a</mi><msubsup><mi>θ</mi><mi>f</mi><mn>3</mn></msubsup><mo>+</mo><mi>b</mi><msubsup><mi>θ</mi><mi>f</mi><mn>2</mn></msubsup><mo>+</mo><mi>c</mi><msub><mi>θ</mi><mi>f</mi></msub><mo>+</mo><mi>d</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, and we derive this by applying non-linear regression to our experimental data. This model predicts the flexural modulus, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>E</mi><mi>f</mi></msub></semantics></math></inline-formula>, of porous Bouligand structured polymer as a function of both porosity and pitch angle. Here, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>E</mi><mrow><mi>p</mi><mi>o</mi><mi>r</mi><mi>o</mi></mrow></msub></semantics></math></inline-formula> is defined as the solid material modulus, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>E</mi><mrow><mi>s</mi><mi>o</mi><mi>l</mi><mi>i</mi><mi>d</mi></mrow></msub></semantics></math></inline-formula>, multiplied by porosity, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula> and is a linear reduction in the modulus as a function of increasing porosity, while <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mi>f</mi></msub></semantics></math></inline-formula> signifies the polymer fibre pitch angle. This relationship is relatively accurate within the range of 10° ≤ <i>θ<sub>f</sub></i> ≤ 50°, and for porosity values ranging from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.277</mn><mo>≤</mo><mn>0.356</mn></mrow></semantics></math></inline-formula>, as supported by our evidence to date. |
| format | Article |
| id | doaj-art-746d42b3a8a947aa90dafd568bdc11d4 |
| institution | Kabale University |
| issn | 2673-4605 |
| language | English |
| publishDate | 2025-01-01 |
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| spelling | doaj-art-746d42b3a8a947aa90dafd568bdc11d42025-08-20T03:27:33ZengMDPI AGMaterials Proceedings2673-46052025-01-01201110.3390/materproc2025020001Predicting the Flexural Modulus of Variable Pitch Angle, Porous Bouligand Structured 3D Printed PolymerPraveenkumar S. Patil0Edward D. McCarthy1Parvez Alam2School of Engineering, The University of Edinburgh, Sanderson Building, Robert Stevenson Road, The King’s Buildings, Edinburgh EH9 3FB, UKSchool of Engineering, The University of Edinburgh, Sanderson Building, Robert Stevenson Road, The King’s Buildings, Edinburgh EH9 3FB, UKSchool of Engineering, The University of Edinburgh, Sanderson Building, Robert Stevenson Road, The King’s Buildings, Edinburgh EH9 3FB, UKOur study considered porous Bouligand structured polymer, comprising polymer fibres with porous spaces between them. These are more complicated structures than the non-porous Bouligand, since the addition of porosity into the material creates a secondary variable besides fibre pitch. There is currently no analytical model available to predict the modulus of such materials. Our paper explores the correlation between porosity, polymer fibre pitch angle, and flexural modulus in porous Bouligand structured polymers. Our structures were digitally manufactured using stereolithography (SLA) additive manufacturing methods, after which they were subjected to three-point bending tests. Our aim was to simply and parametrically develop an analytical model that would capture the influences of both porosity and polymer fibre pitch angle on the flexural modulus of the material. Our model is expressed as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>E</mi><mi>f</mi></msub><mo>=</mo><msub><mi>E</mi><mrow><mi>p</mi><mi>o</mi><mi>r</mi><mi>o</mi></mrow></msub><mrow><mo>(</mo><mi>a</mi><msubsup><mi>θ</mi><mi>f</mi><mn>3</mn></msubsup><mo>+</mo><mi>b</mi><msubsup><mi>θ</mi><mi>f</mi><mn>2</mn></msubsup><mo>+</mo><mi>c</mi><msub><mi>θ</mi><mi>f</mi></msub><mo>+</mo><mi>d</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, and we derive this by applying non-linear regression to our experimental data. This model predicts the flexural modulus, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>E</mi><mi>f</mi></msub></semantics></math></inline-formula>, of porous Bouligand structured polymer as a function of both porosity and pitch angle. Here, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>E</mi><mrow><mi>p</mi><mi>o</mi><mi>r</mi><mi>o</mi></mrow></msub></semantics></math></inline-formula> is defined as the solid material modulus, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>E</mi><mrow><mi>s</mi><mi>o</mi><mi>l</mi><mi>i</mi><mi>d</mi></mrow></msub></semantics></math></inline-formula>, multiplied by porosity, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula> and is a linear reduction in the modulus as a function of increasing porosity, while <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mi>f</mi></msub></semantics></math></inline-formula> signifies the polymer fibre pitch angle. This relationship is relatively accurate within the range of 10° ≤ <i>θ<sub>f</sub></i> ≤ 50°, and for porosity values ranging from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.277</mn><mo>≤</mo><mn>0.356</mn></mrow></semantics></math></inline-formula>, as supported by our evidence to date.https://www.mdpi.com/2673-4605/20/1/1biomimicrySLA 3D printingporous Bouligand structuresnapping shrimpthree-point bendingelastic modulus |
| spellingShingle | Praveenkumar S. Patil Edward D. McCarthy Parvez Alam Predicting the Flexural Modulus of Variable Pitch Angle, Porous Bouligand Structured 3D Printed Polymer Materials Proceedings biomimicry SLA 3D printing porous Bouligand structure snapping shrimp three-point bending elastic modulus |
| title | Predicting the Flexural Modulus of Variable Pitch Angle, Porous Bouligand Structured 3D Printed Polymer |
| title_full | Predicting the Flexural Modulus of Variable Pitch Angle, Porous Bouligand Structured 3D Printed Polymer |
| title_fullStr | Predicting the Flexural Modulus of Variable Pitch Angle, Porous Bouligand Structured 3D Printed Polymer |
| title_full_unstemmed | Predicting the Flexural Modulus of Variable Pitch Angle, Porous Bouligand Structured 3D Printed Polymer |
| title_short | Predicting the Flexural Modulus of Variable Pitch Angle, Porous Bouligand Structured 3D Printed Polymer |
| title_sort | predicting the flexural modulus of variable pitch angle porous bouligand structured 3d printed polymer |
| topic | biomimicry SLA 3D printing porous Bouligand structure snapping shrimp three-point bending elastic modulus |
| url | https://www.mdpi.com/2673-4605/20/1/1 |
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