Asymptotic expansion homogenization of discrete fine-scale models with rotational degrees of freedom for the simulation of quasi-brittle materials

Rezakhani, Roozbeh; Cusatis, Gianluca

doi:10.1016/j.jmps.2016.01.001

Cited by 67 publications

(64 citation statements)

References 47 publications

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“…Substituting Eqs and into the definition of facet strains, Eq. , and using the macroscopic Taylor expansion of displacement and rotation of node P J around node P I , the following form for the multiple scale definition of facet strains is obtained :

ϵ_{α} = η^{- 1} ϵ_{α}^{- 1} + ϵ_{α}^{0} + η ϵ_{α}^{1}

where ϵ α = facet strains; α = N , M , L with N representing normal components; and M , L representing tangential components. Considering Eq.…”

Section: Multiscale Homogenization Methodsmentioning

confidence: 99%

“…and the facet constitutive equations, it is shown in Ref. that the multiple scale definition of facet tractions is

t_{α} = η^{- 1} t_{α}^{- 1} + t_{α}^{0} + η t_{α}^{1}

, which is assumed to be valid in both elastic and nonlinear regime. Substituting the asymptotic expansion of facet tractions in the particle equilibrium equations (Eqs and ), one can derive separate scale governing equations for both fine‐scale and coarse‐scale problems.…”

Section: Multiscale Homogenization Methodsmentioning

confidence: 99%

See 1 more Smart Citation

A multiscale framework for the simulation of the anisotropic mechanical behavior of shale

Rezakhani

Jin

et al. 2017

Num Anal Meth Geomechanics

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Summary Shale, like many other sedimentary rocks, is typically heterogeneous and anisotropic and is characterized by partial alignment of anisotropic clay minerals and naturally formed bedding planes. In this study, a micromechanical framework based on the lattice discrete particle model is formulated to capture these features. Material anisotropy is introduced through an approximated geometric description of shale internal structure, which includes representation of material property variation with orientation and explicit modeling of parallel lamination. The model is calibrated by carrying out numerical simulations to match various experimental data, including the ones relevant to elastic properties, Brazilian tensile strength, and unconfined compressive strength. Furthermore, parametric study is performed to investigate the relationship between the mesoscale parameters and the macroscopic properties. It is shown that the dependence of the elastic stiffness, strength, and failure mode on loading orientation can be captured successfully. Finally, a homogenization approach based on the asymptotic expansion of field variables is applied to upscale the proposed micromechanical model, and the properties of the homogenized model are analyzed. Copyright © 2017 John Wiley & Sons, Ltd.

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ϵ_{α} = η^{- 1} ϵ_{α}^{- 1} + ϵ_{α}^{0} + η ϵ_{α}^{1}

where ϵ α = facet strains; α = N , M , L with N representing normal components; and M , L representing tangential components. Considering Eq.…”

Section: Multiscale Homogenization Methodsmentioning

confidence: 99%

“…and the facet constitutive equations, it is shown in Ref. that the multiple scale definition of facet tractions is

t_{α} = η^{- 1} t_{α}^{- 1} + t_{α}^{0} + η t_{α}^{1}

Section: Multiscale Homogenization Methodsmentioning

confidence: 99%

A multiscale framework for the simulation of the anisotropic mechanical behavior of shale

Rezakhani

Jin

et al. 2017

Num Anal Meth Geomechanics

Self Cite

View full text Add to dashboard Cite

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“…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]. Various other discrete models, in the form of either lattice or particle models, have been quite successful recently in simulating concrete materials [24,25,26,27,28,29].…”

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

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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.

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“…Furthermore it can be properly formulated to account for fiber reinforcement [17,18] and it was recently extended to simulate the ballistic behavior of ultra-high performance concrete (UHPC) [19]. In addition, LDPM was successfully used in structural element scale analysis using multiscale methods [20][21][22].…”

Section: The Lattice Discrete Particle Modelmentioning

confidence: 99%

Lattice discrete particle modeling (LDPM) of flexural size effect in over reinforced concrete beams

Alnaggar¹,

Pelessone²,

Cusatis³

2016

Proceedings of the 9th International Conference on Fracture Mechanics of Concrete and Concrete Structures

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Abstract. At the macroscopic scale, concrete can be approximated as statistically homogeneous. Nevertheless, its macroscopic behavior shows quasi-brittleness, strain softening, and size effects evidencing a strong influence of material heterogeneity. A model naturally accounting for material heterogeneity is the Lattice Discrete Particle Model (LDPM). LDPM replaces the actual concrete mesostructure by an assemblage of discrete particles interacting through nonlinear and fracturing lattice struts. Each particle represents one coarse aggregate piece. Since the initial development, LDPM has shown superior material modeling capabilities. In this research, LDPM is used to simulate the flexural failure of three groups of over reinforced concrete beams. The groups represent 1D, 2D and 3D geometric similarities. Geometry is generated based on concrete mix design. Then calibration was only guided by the experimentally provided compressive strength. In order to reduce the redundancy of the calibration process, the fracture properties of concrete were estimated using relevant literature. Finally, the rebar assembly was connected to the LDPM mesh using penalty type constraints and the rebars were modeled using 1D beam elements. Numerical results show excellent agreement with experimental data and clear capability of capturing size effects.

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Asymptotic expansion homogenization of discrete fine-scale models with rotational degrees of freedom for the simulation of quasi-brittle materials

Cited by 67 publications

References 47 publications

A multiscale framework for the simulation of the anisotropic mechanical behavior of shale

A multiscale framework for the simulation of the anisotropic mechanical behavior of shale

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

Lattice discrete particle modeling (LDPM) of flexural size effect in over reinforced concrete beams

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