Simulation of mixed-mode using spring networks

Jan Eliáš

Institute of Structural Mechanics Faculty of Civil Engineering Brno University of Technology Czech Republic

Modes definition• according to LEFM

Lattice, spring network• regular geometry => strong mesh

dependency• irregular geometry => problems with

representation of homogenous material

Rigid-body-spring network• rigid cells interconnected by normal and shear

spring• all springs are ideally brittle

Aggregates• generated according Fuller curve• three material phases are distinguished

Tensile test simulated by strut lattice

• discrepancy between experiment and simulation probably caused by incorrect measuring of displacements

Mixed-mode simulation

• correct crack pattern only with rigid-body-spring network

simple strut lattice

rigid-body-spring network

Comparison with FEM software Atena

• crack pattern

• l-d curve

Comparison of stresses

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

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

Tessellation of domain 1

• input is the set of nodes and virtual specimen borders

Tessellation of domain 2

• Delaunay triangulation including mirrored nodes

Tessellation of domain 3

• Voronoi tessellation to ensure elastically uniform lattice = connected centres of escribed circles

Tessellation of domain 4

• input is the set of circles and virtual specimen borders

Tessellation of domain 5

• modified Delaunay triangulation – control circle tangents three input circles

Tessellation of domain 6

• connect centres of control circles

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