3D lattice type fracture model for concrete

Lilliu, G; Mier, J.G.M. van

doi:10.1016/s0013-7944(02)00158-3

Cited by 380 publications

(257 citation statements)

References 9 publications

Supporting

Mentioning

253

Contrasting

Unclassified

Order By: Relevance

“…Likewise, for investigating the mechanical responses of other materials, e.g. concrete and polymers, lattice models and discrete networks are often applied (Lilliu and Van Mier, 2003;Cusatis et al, 2003;Ostoja-Starzewski and Wang, 2006;Rinaldi et al, 2008;Kim and Buttlar, 2009;Zhao, 2012). The advantage of discrete models is that they naturally incorporate discrete phenomena occurring in meso-and microstructures of many materials.…”

Section: Introductionmentioning

confidence: 99%

A multiscale quasicontinuum method for dissipative lattice models and discrete networks

Beex¹,

Peerlings²,

Geers³

2014

Journal of the Mechanics and Physics of Solids

View full text Add to dashboard Cite

Lattice models and discrete networks naturally describe mechanical phenomena at the mesoscale of fibrous materials. A disadvantage of lattice models is their computational cost. The quasicontinuum (QC) method is a suitable multiscale approach that reduces the computational cost of lattice models and allows the incorporation of local lattice defects in large-scale problems. So far, all QC methods are formulated for conservative (mostly atomistic) lattice models. Lattice models of fibrous materials however, often require non-conservative interactions. In this article, a QC formulation is derived based on the virtual-power of a non-conservative lattice model. By using the virtual-power statement instead of force-equilibrium, errors in the governing equations of the force-based QC formulations are avoided. Nevertheless, the non-conservative interaction forces can still be directly inserted in the virtualpower QC framework. The summation rules for energy-based QC methods can still be used in the proposed framework as shown by two multiscale examples.

show abstract

Section: Introductionmentioning

confidence: 99%

A multiscale quasicontinuum method for dissipative lattice models and discrete networks

Beex¹,

Peerlings²,

Geers³

2014

Journal of the Mechanics and Physics of Solids

View full text Add to dashboard Cite

show abstract

“…These models were first developed to describe the behavior of particulate materials [13] and to solve elastic problems in the pre-computers era [14]. Later, they have been adapted to simulate fracture and failure of quasi-brittle materials in both two [15] and three dimensional problems [16,17,18,19]. In this class of models, it is worth mentioning the rigid-body-spring model developed by Bolander and collaborators, which dicretizes the material domain using Voronoi diagrams with random geometry, interconnected by zero-size springs, to simulate cohesive fracture in two and three dimensional problems [20,21,22,23].…”

Section: Introductionmentioning

confidence: 99%

Discontinuous Cell Method (DCM) for the simulation of cohesive fracture and fragmentation of continuous media

Cusatis

Rezakhani

Schauffert³

2017

Engineering Fracture Mechanics

View full text Add to dashboard Cite

In this paper, the Discontinuous Cell Method (DCM) is formulated with the objective of simulating cohesive fracture propagation and fragmentation in homogeneous solids without issues relevant to excessive mesh deformation typical of available Finite Element formulations. DCM discretizes solids by using the Delaunay triangulation and its associated Voronoi tessellation giving rise to a system of discrete cells interacting through shared facets. For each Voronoi cell, the displacement field is approximated on the basis of rigid body kinematics, which is used to compute a strain vector at the centroid of the Voronoi facets. Such strain vector is demonstrated to be the projection of the strain tensor at that location. At the same point stress tractions are computed through vectorial constitutive equations derived on the basis of classical continuum tensorial theories. Results of analysis of a cantilever beam are used to perform convergence studies and comparison with classical finite element formulations in the elastic regime. Furthermore, cohesive fracture and fragmentation of homogeneous solids are studied under quasi-static and dynamic loading conditions. The mesh dependency problem, typically encountered upon adopting softening constitutive equations, is tackled through the crack band approach. This study demonstrates the capabilities of DCM by solving multiple benchmark problems relevant to cohesive crack propagation. The simulations show that DCM can handle effectively a wide range of problems from the simulation of a single propagating fracture to crack branching and fragmentation.

show abstract

“…Schneider et al [11] highlighted that beam models provide a good compromise between computational time and accuracy. The use of beam elements to represent cementitious materials may also be found in regular [15,16] or random [17] lattice models. However, particle based models, unlike lattice models, permit frictional contacts to exist between particles after beam failure has occurred.…”

Section: Introductionmentioning

confidence: 99%

A bond model for DEM simulation of cementitious materials and deformable structures

2014

View full text Add to dashboard Cite

There is an increasing use of the discrete element method (DEM) to study cemented (e.g. concrete and rocks) and sintered particulate materials. The chief advantage of the DEM over continuum based techniques is that it does not make assumptions about how cracking and fragmentation initiate and propagate, since the DEM system is naturally discontinuous. The ability for the DEM to produce a realistic representation of a cemented granular material depends largely on the implementation of an inter-particle bonded contact model. This paper presents a new bonded contact model based on the Timoshenko beam theory which considers axial, shear and bending behaviour of the bond. The bond model was first verified by simulating both the bending and dynamic response of a simply supported beam. The loading response of a concrete cylinder was then investigated and compared with the Eurocode equation prediction. The results show significant potential for the new model to produce satisfactory predictions for cementitious materials. A unique feature of this model is that it can also be used to accurately represent many deformable structures such as frames and shells, so that both particles and structures or deformable boundaries can be described in the same DEM framework.

show abstract

3D lattice type fracture model for concrete

Cited by 380 publications

References 9 publications

A multiscale quasicontinuum method for dissipative lattice models and discrete networks

A multiscale quasicontinuum method for dissipative lattice models and discrete networks

Discontinuous Cell Method (DCM) for the simulation of cohesive fracture and fragmentation of continuous media

A bond model for DEM simulation of cementitious materials and deformable structures

Contact Info

Product

Resources

About