Stress flow analysis of bio-structures using the finite element method and the flow network approach

Patel, Reena; Riveros, Guillermo A.; Thompson, David S.; Perkins, Edward J.; Hoover, Jan Jeffrey; Peters, John F.; Tordesillas, Antoinette

doi:10.1016/j.finel.2018.09.003

Cited by 6 publications

(12 citation statements)

References 25 publications

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“…This problem arises in many settings: traffic on a road network, fluid in a pipeline network, data on the Internet, electricity on a power grid, etc. (DueÃas-Osorio and Vemuru, 2009;West and Scafetta, 2010;Estrada et al, 2012;Patel et al, 2018;van der Linden et al, 2019). In general, this process involves an evolution on and of the network; that is, the flow that takes place on the network can change the structure of the network, and vice versa (Ahuja et al, 1993;van der Linden et al, 2019).…”

Section: Related Past Workmentioning

confidence: 99%

“…We have tested the potential of a network flow approach in the characterization and modeling of force transmission from data in various 2D and 3D granular systems (Tordesillas et al, 2013(Tordesillas et al, , 2015aLin and Tordesillas, 2014;Kahagalage et al, 2017) and, more recently, in a biostructure like the paddlefish rostrum (Patel et al, 2018). Data came from high performance computational mechanics models which were supported by physical experiments with respect to the model calibration and micro/meso-structural information.…”

Section: Related Past Workmentioning

confidence: 99%

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Coupled Evolution of Preferential Paths for Force and Damage in the Pre-failure Regime in Disordered and Heterogeneous, Quasi-Brittle Granular Materials

et al. 2020

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A disordered and heterogeneous, quasi-brittle granular material can withstand certain levels of internal damage before global failure. This robustness depends not just on the bond strengths but also on the topology and redundancy of the bonded contact network, through which forces and damage propagate. Despite extensive studies on quasi-brittle failure, there still lacks a unified framework that can quantitatively characterize and model the interdependent evolution of damage and force transmission. Here we develop a framework to do so. It is data-driven, multiscale and relies solely on the contact strengths and topology of the contact network for material properties. The discrete element method (DEM) was used to directly simulate quasi-brittle materials like concrete under uniaxial tension. Concrete was modeled as a random heterogeneous 2-phase and 3-phase material composed of aggregate particles, cement matrix and interfacial transitional zones with experimental-based meso-structure from X-ray micro-CT-images of real concrete. We uncover evidence of an optimized force transmission, characterized by two novel transmission patterns that predict and explain the coupled evolution of force and damage pathways from the microstructural to the macroscopic level. The first comprises the shortest possible percolating paths that can transmit the global force transmission capacity. These paths reliably predict tensile force chains. The second pattern is the flow bottleneck, a path in the optimized route that is prone to congestion and is where the macrocrack emerges. The cooperative evolution of preferential pathways for damage and force casts light on why sites of highest concentrations of stress and damage in the nascent stages of pre-failure regime do not provide a reliable indicator of the ultimate location of the macrocrack.

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Section: Related Past Workmentioning

confidence: 99%

Section: Related Past Workmentioning

confidence: 99%

Coupled Evolution of Preferential Paths for Force and Damage in the Pre-failure Regime in Disordered and Heterogeneous, Quasi-Brittle Granular Materials

et al. 2020

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“…In other previous works, Patel et al [19] studied stress flow patterns on the rosta of Paddlefish using a finite element and flow network approach to create a flow network graph. This approach was validated in their work [19][20][21] using classical approaches. Recently, Riveros et al [22] developed finite-element models (FEM) to evaluate the mechanical behavior of the rostrum.…”

Section: Introductionmentioning

confidence: 99%

Instrumenting Polyodon spathula (Paddlefish) Rostra in Flowing Water with Strain Gages and Accelerometers

et al. 2020

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The prominent rostrum of the North American Paddlefish, supported by a lattice-like endoskeleton, is highly durable, making it an important candidate for bio-inspiration studies. Energy dissipation and load-bearing capacity of the structure from extreme physical force has been demonstrated superior to that of man-made systems, but response to continuous hydraulic forces is unknown and requires special instrumentation for in vivo testing on a live fish. A single supply strain gage amplifier circuit has been combined with a digital three-axis accelerometer, implemented in a printed circuit board (PCB), and integrated with the commercial-off-the-shelf Adafruit Feather M0 datalogger with a microSD card. The device is battery powered and enclosed in silicon before attachment around the rostrum with a silicon strap "watch band." As proof-of-concept, we tested the instrumentation on an amputated Paddlefish rostrum in a water-filled swim tunnel and successfully obtained interpretable data. Results indicate that this design could work on live swimming fish in future in vivo experiments.

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“…Patel et al developed the methodology of using network theory with finite element analysis in their previous work [39], which used a single source and sink combination to analyze the stress flow pattern on the rostrum. They also presented the procedure of preparing the data in an appropriate format from finite element binary database files to an abstract mathematical domain in their recent publication [40]. Patel et al have also developed bioinspired structural systems to analyze the relationship of structural resiliency and geometrical complexity [39].…”

Section: Introductionmentioning

confidence: 99%

“…In Stage 4, the flow network graph was provided as input to the mathematical algorithm that computes the minimum cut of the flow network graph. The details of the procedure involved in the four stages mentioned above is described in the previous work of Patel et al [40].…”

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confidence: 99%

A Transdisciplinary Approach for Analyzing Stress Flow Patterns in Biostructures

Patel

Riveros

Thompson

et al. 2019

MCA

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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.

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Stress flow analysis of bio-structures using the finite element method and the flow network approach

Cited by 6 publications

References 25 publications

Coupled Evolution of Preferential Paths for Force and Damage in the Pre-failure Regime in Disordered and Heterogeneous, Quasi-Brittle Granular Materials

Coupled Evolution of Preferential Paths for Force and Damage in the Pre-failure Regime in Disordered and Heterogeneous, Quasi-Brittle Granular Materials

Instrumenting Polyodon spathula (Paddlefish) Rostra in Flowing Water with Strain Gages and Accelerometers

A Transdisciplinary Approach for Analyzing Stress Flow Patterns in Biostructures

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