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![Page 1: Simulation of mixed-mode using spring networks Jan Eliáš Institute of Structural Mechanics Faculty of Civil Engineering Brno University of Technology Czech.](https://reader036.fdocuments.us/reader036/viewer/2022062805/5697bfb61a28abf838c9e0ea/html5/thumbnails/1.jpg)
Simulation of mixed-mode using spring networks
Jan Eliáš
Institute of Structural Mechanics Faculty of Civil Engineering Brno University of Technology Czech Republic
![Page 2: Simulation of mixed-mode using spring networks Jan Eliáš Institute of Structural Mechanics Faculty of Civil Engineering Brno University of Technology Czech.](https://reader036.fdocuments.us/reader036/viewer/2022062805/5697bfb61a28abf838c9e0ea/html5/thumbnails/2.jpg)
Modes definition• according to LEFM
![Page 3: Simulation of mixed-mode using spring networks Jan Eliáš Institute of Structural Mechanics Faculty of Civil Engineering Brno University of Technology Czech.](https://reader036.fdocuments.us/reader036/viewer/2022062805/5697bfb61a28abf838c9e0ea/html5/thumbnails/3.jpg)
Lattice, spring network• regular geometry => strong mesh
dependency• irregular geometry => problems with
representation of homogenous material
![Page 4: Simulation of mixed-mode using spring networks Jan Eliáš Institute of Structural Mechanics Faculty of Civil Engineering Brno University of Technology Czech.](https://reader036.fdocuments.us/reader036/viewer/2022062805/5697bfb61a28abf838c9e0ea/html5/thumbnails/4.jpg)
Rigid-body-spring network• rigid cells interconnected by normal and shear
spring• all springs are ideally brittle
![Page 5: Simulation of mixed-mode using spring networks Jan Eliáš Institute of Structural Mechanics Faculty of Civil Engineering Brno University of Technology Czech.](https://reader036.fdocuments.us/reader036/viewer/2022062805/5697bfb61a28abf838c9e0ea/html5/thumbnails/5.jpg)
Aggregates• generated according Fuller curve• three material phases are distinguished
![Page 6: Simulation of mixed-mode using spring networks Jan Eliáš Institute of Structural Mechanics Faculty of Civil Engineering Brno University of Technology Czech.](https://reader036.fdocuments.us/reader036/viewer/2022062805/5697bfb61a28abf838c9e0ea/html5/thumbnails/6.jpg)
Tensile test simulated by strut lattice
• discrepancy between experiment and simulation probably caused by incorrect measuring of displacements
![Page 7: Simulation of mixed-mode using spring networks Jan Eliáš Institute of Structural Mechanics Faculty of Civil Engineering Brno University of Technology Czech.](https://reader036.fdocuments.us/reader036/viewer/2022062805/5697bfb61a28abf838c9e0ea/html5/thumbnails/7.jpg)
Mixed-mode simulation
• correct crack pattern only with rigid-body-spring network
simple strut lattice
rigid-body-spring network
![Page 8: Simulation of mixed-mode using spring networks Jan Eliáš Institute of Structural Mechanics Faculty of Civil Engineering Brno University of Technology Czech.](https://reader036.fdocuments.us/reader036/viewer/2022062805/5697bfb61a28abf838c9e0ea/html5/thumbnails/8.jpg)
Comparison with FEM software Atena
• crack pattern
• l-d curve
![Page 9: Simulation of mixed-mode using spring networks Jan Eliáš Institute of Structural Mechanics Faculty of Civil Engineering Brno University of Technology Czech.](https://reader036.fdocuments.us/reader036/viewer/2022062805/5697bfb61a28abf838c9e0ea/html5/thumbnails/9.jpg)
Comparison of stresses
• notice that comparison is between principal stresses and normal stresses and not at exact same point of l-d curve
![Page 10: Simulation of mixed-mode using spring networks Jan Eliáš Institute of Structural Mechanics Faculty of Civil Engineering Brno University of Technology Czech.](https://reader036.fdocuments.us/reader036/viewer/2022062805/5697bfb61a28abf838c9e0ea/html5/thumbnails/10.jpg)
Elastically uniform lattice
rel,max rel,min rel,max max [rad]
Voronoi tesselation 1.0000 1.0000 1.25e-014 6.54e-018Centroid
tesselation 1.6803 0.4706 3.46e-001 7.47e-005
Voronoi tessellation centre of gravity tessellation
![Page 11: Simulation of mixed-mode using spring networks Jan Eliáš Institute of Structural Mechanics Faculty of Civil Engineering Brno University of Technology Czech.](https://reader036.fdocuments.us/reader036/viewer/2022062805/5697bfb61a28abf838c9e0ea/html5/thumbnails/11.jpg)
Tessellation of domain 1
• input is the set of nodes and virtual specimen borders
![Page 12: Simulation of mixed-mode using spring networks Jan Eliáš Institute of Structural Mechanics Faculty of Civil Engineering Brno University of Technology Czech.](https://reader036.fdocuments.us/reader036/viewer/2022062805/5697bfb61a28abf838c9e0ea/html5/thumbnails/12.jpg)
Tessellation of domain 2
• Delaunay triangulation including mirrored nodes
![Page 13: Simulation of mixed-mode using spring networks Jan Eliáš Institute of Structural Mechanics Faculty of Civil Engineering Brno University of Technology Czech.](https://reader036.fdocuments.us/reader036/viewer/2022062805/5697bfb61a28abf838c9e0ea/html5/thumbnails/13.jpg)
Tessellation of domain 3
• Voronoi tessellation to ensure elastically uniform lattice = connected centres of escribed circles
![Page 14: Simulation of mixed-mode using spring networks Jan Eliáš Institute of Structural Mechanics Faculty of Civil Engineering Brno University of Technology Czech.](https://reader036.fdocuments.us/reader036/viewer/2022062805/5697bfb61a28abf838c9e0ea/html5/thumbnails/14.jpg)
Tessellation of domain 4
• input is the set of circles and virtual specimen borders
![Page 15: Simulation of mixed-mode using spring networks Jan Eliáš Institute of Structural Mechanics Faculty of Civil Engineering Brno University of Technology Czech.](https://reader036.fdocuments.us/reader036/viewer/2022062805/5697bfb61a28abf838c9e0ea/html5/thumbnails/15.jpg)
Tessellation of domain 5
• modified Delaunay triangulation – control circle tangents three input circles
![Page 16: Simulation of mixed-mode using spring networks Jan Eliáš Institute of Structural Mechanics Faculty of Civil Engineering Brno University of Technology Czech.](https://reader036.fdocuments.us/reader036/viewer/2022062805/5697bfb61a28abf838c9e0ea/html5/thumbnails/16.jpg)
Tessellation of domain 6
• connect centres of control circles
![Page 17: Simulation of mixed-mode using spring networks Jan Eliáš Institute of Structural Mechanics Faculty of Civil Engineering Brno University of Technology Czech.](https://reader036.fdocuments.us/reader036/viewer/2022062805/5697bfb61a28abf838c9e0ea/html5/thumbnails/17.jpg)
Conclusions • lattice models are able to simulate a fracture
process • relationship between overall properties and
beam properties is not clear• modified Voronoi tessellation of domain has
been suggested