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A Transdisciplinary Approach for Analyzing Stress Flow Patterns in Biostructures

1
US Army Engineer Research and Development Center, Vicksburg, MS 39180, USA
2
Department of Aerospace Engineering, Mississippi State University, Starkville, MS 39762, USA
3
Center for Advanced Vehicular Systems (CAVS), Mississippi State University, Starkville, MS 39762, USA
4
School of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010, Australia
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2019, 24(2), 47; https://doi.org/10.3390/mca24020047
Received: 27 March 2019 / Revised: 22 April 2019 / Accepted: 24 April 2019 / Published: 26 April 2019
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Abstract

This work presents a transdisciplinary, integrated approach that uses computational mechanics experiments with a flow network strategy to gain fundamental insights into the stress flow of high-performance, lightweight, structured composites by investigating the rostrum of paddlefish. Although computational mechanics experiments give an overall distribution of stress in the structural systems, stress flow patterns formed at nascent stages of loading a biostructure are hard to determine. Computational mechanics experiments on a complex model will involve a high degree of freedom thereby making the extraction of finer details computationally expensive. To address this challenge, the evolution of the stress in the rostrum is formulated as a network flow problem generated by extracting the node and connectivity information from the numerical model of the rostrum. The flow network is weighted based on the parameter of interest, which is stress in the current research. The changing kinematics of the system is provided as input to the mathematical algorithm that computes the minimum cut of the flow network. The flow network approach is verified using two simple classical problems. When applied to the model of the rostrum, the flow network approach identifies strain localization in tensile regions, and buckling/crushing in compressive regions. View Full-Text
Keywords: biostructure; rostrum; paddlefish; Polyodon spathula; maximum-flow/minimum-cut; stress patterns biostructure; rostrum; paddlefish; Polyodon spathula; maximum-flow/minimum-cut; stress patterns
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Patel, R.; Riveros, G.; Thompson, D.; Perkins, E.; Hoover, J.J.; Peters, J.; Tordesillas, A. A Transdisciplinary Approach for Analyzing Stress Flow Patterns in Biostructures. Math. Comput. Appl. 2019, 24, 47.

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