1. Simulation of mixed-mode using spring networks Jan Eliáš Institute of Structural Mechanics Faculty of Civil Engineering Brno University of Technology Czech Republic

2. Modes definition according to LEFM

3. Lattice, spring network regular geometry => strong mesh dependency irregular geometry => problems with representation of homogenous material

4. Rigid-body-spring network rigid cells interconnected by normal and shear spring all springs are ideally brittle

5. Aggregates generated according Fuller curve three material phases are distinguished

6. Tensile test simulated by strut lattice discrepancy between experiment and simulation probably caused by incorrect measuring of displacements

7. Mixed-mode simulation correct crack pattern only with rigid-body-spring network simple strut latticerigid-body-spring network

8. Comparison with FEM software Atena crack pattern l-d curve

9. Comparison of stresses notice that comparison is between principal stresses and normal stresses and not at exact same point of l-d curve

10. Elastically uniform lattice  rel,max  rel,min  rel,max  max [rad] Voronoi tesselation 1.0000 1.25e-014 6.54e-018 Centroid tesselation 1.68030.4706 3.46e-0017.47e-005 Voronoi tessellationcentre of gravity tessellation

11. Tessellation of domain 1 input is the set of nodes and virtual specimen borders

12. Tessellation of domain 2 Delaunay triangulation including mirrored nodes

13. Tessellation of domain 3 Voronoi tessellation to ensure elastically uniform lattice = connected centres of escribed circles

14. Tessellation of domain 4 input is the set of circles and virtual specimen borders

15. Tessellation of domain 5 modified Delaunay triangulation – control circle tangents three input circles

16. Tessellation of domain 6 connect centres of control circles

17. 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