Strain localization—short to long correlation length transition

Krajčinović, Dušan; Vujosevic, Milena

doi:10.1016/s0020-9683(97)00307-7

Cited by 42 publications

(12 citation statements)

References 39 publications

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“…13, splitting in Case 5 is characterized by macrocracks aligned in the direction of the applied compression, whereas shear bands are macrocracks at an angle in Cases 4 and 9. These failure modes are observed in compressive experiments on concrete, for instance in Gerstle et al (1980), but also in lattice models from Krajcinovic and Vujosevic (1998). The existence of two failure modes when switching the compression axis between Cases 4 and 5 is intimately connected to the microstructural topology and is due to the different role of the Poisson effect in the two cases.…”

Section: Application: Lattice Models and Multiaxial Damagementioning

confidence: 79%

“…Hansen et al (1989), Sahimi (2000), Krajcinovic and Basista (1991), Krajcinovic and Vujosevic (1998), Mastilovic and Krajcinovic (1999), , , Delaplace et al (1996), He and Thorpe (1985) and others have shown that statistical lattice models offer a convenient framework for the study of the damage process associated to microcracks formation and growth. The usage of the statistics to account for the disorder of the microstructure is one distinctive feature of such statistical models.…”

Section: Introductionmentioning

confidence: 99%

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Lattice models of polycrystalline microstructures: A quantitative approach

Rinaldi

Krajčinović

Peralta

et al. 2008

Mechanics of Materials

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This paper addresses the issue of creating a lattice model suitable for design purposes and capable of quantitative estimates of the mechanical properties of a disordered microstructure. The lack of resemblance between idealized lattice models and real materials has limited these models to the realm of qualitative analysis. Two procedures based on the same methodology are presented in the two-dimensional case to achieve the rigorous mapping of the geometrical and the elastic properties of a disordered polycrystalline microstructure into a spring lattice. The theory is validated against finite elements models and literature data of NiAl. The statistical analysis of 900 models provided the effective Young's modulus and Poisson ratio as function of the lattice size. The lattice models that were created have in average the same Young's modulus of the real microstructure. However, the Poisson's ratio could not be matched in the two-dimensional case. The spring constants of the lattices from this technique follow a Gaussian distribution, which intrinsically reflects the mechanical and geometrical disorder of the microscale. The detailed knowledge of the microstructure and the Voronoi tessellation necessary to implement this technique are supplied by modern laboratory equipments and software. As an illustrative example of lattice application, damage simulations of several biaxial loading schemes are briefly reported to show the effectiveness of discrete models towards elastic anisotropy induced by damage and damage localization.

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Section: Application: Lattice Models and Multiaxial Damagementioning

confidence: 79%

Section: Introductionmentioning

confidence: 99%

Lattice models of polycrystalline microstructures: A quantitative approach

Rinaldi

Krajčinović

Peralta

et al. 2008

Mechanics of Materials

Self Cite

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“…This is always debatable, and accoustic techniques may be helpful at this point. The renowed experiments by Lockner and Byerlee (1992) were compared to molecular dynamics simulations by Krajcinovic and Vujosevic (1998), which showed that localization manifests itself in the steep part of the softening curve just beyond peak. The agreement between the acoustic experiments of Lockner and Byerlee, which gave a truly 3D view on the distribution of AE-events over the specimens volume loaded in confined compression, and the 2D-simulations of Krajcinovic and Vujosevic was quite good, where one could add, however, a question mark.…”

Section: What Happens Before Localization?mentioning

confidence: 99%

Some Notes on Microcracking, Softening, Localization, and Size Effects

Mier

Man

2008

International Journal of Damage Mechanics

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Fracture of concrete and other brittle disordered materials is a complex process involving microcracks (that can be arrested by the heterogeneous material structure) and macrocracks (that lead to failure of the structure/specimen). The process is basically the same for any type of loading as long as global failure is not ductile (for these materials: usually at high confinement). The focus in the article is on mode I cracking, showing similarities of the fracture process for other loading cases, in particular (multiaxial) compression. The fracture process in tension can be sub-divided in four stages: elastic, microcracking, macrocrack growth (localization), and bridging. Improvements in simulations over two decades are shown. The various fracture stages can be simulated using models that allow for local brittle mode I fracture and where the material structure has been included. At present simulations in 3D, with great amount of detail such as realistic particle distributions and particle shapes can be carried out routinely. One example is shown, focusing on size effects of fracture strength in 3-point bending. The results reveal that the microcrack population at peak-load is the fracture pattern to consider, and not the localized macrocrack at the end of the softening branch. The consequence is that size-effect must be expressed in terms of log(nominal stress) versus log(volume) diagrams, which makes the formulation more general.

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“…L ATTICE MODELS ARE generally divided into two categories: those simulating directly atomic lattices or materials whose internal structures are naturally lattice-like McKown et al, 2008;Queheillalt et al, 2008) and the ones used to model continuum systems in an equivalent manner (Bolander and Saito, 1998;Gao and Klein, 1998;Hansen and Roux, 2000;Krajcinovic and Vujosevic, 1998;van Mier et al, 2002;Liu et al, 2007). The latter have been successfully used to solve classical elastic problems (Hrennikoff, 1941).…”

Section: Introductionmentioning

confidence: 99%

“…Then, such models have been employed for simulating the progressive failure in heterogeneous media, especially by theoretical physicists (Hansen and Roux, 2000;Herrmann and Roux, 1992). It has been shown that statistical lattice models offer a convenient framework to explore the evolution of damage associated with microcracks formation and growth (Delaplace et al, 1996;Hansen and Roux, 2000;Krajcinovic and Rinaldi, 2005;Krajcinovic and Vujosevic, 1998;Mastilovic and Krajcinovic, 1999;Rinaldi and Lai, 2007;Sahimi, 2000). Dynamic behaviors are also simulated (McKown et al, 2008) but they are not discussed in this study.…”

Section: Introductionmentioning

confidence: 99%

On the Load–Unload (L–U) and Force–Release (F–R) Algorithms for Simulating Brittle Fracture Processes via Lattice Models

Liu

Sayed

2011

International Journal of Damage Mechanics

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General summaries on the loadunload and forcerelease methods indicate that the two methods are efficient for different-charactered quasi-static failures; therefore, it is important to choose the right one for different applications. Then we take, as an example, the case where the release of the ruptured element's internal force is infinitely slower than the relaxation of the lattice system and analyze why the forcerelease method works better than the loadunload method in this particular case. Different trial deformation fields are used by them to track the next equilibrium state. Forcerelease method ensures that the deformation throughout the whole failure process coincides exactly with the controlled-displacement boundary conditions and we utilize the 'left modulus' concept to prove that this method satisfies the energetic evolution in the forcedisplacement diagram; both of which are not satisfied by the loadunload method. To illustrate that the forcerelease method is not just another form of the loadunload method, a tensile test on a specifically designed system is analyzed to further compare the above two methods, showing that their predicted sequences of elemental failures can be different. In closing, we simulate the uniaxial tensile test on a beam lattice system by the loadunload and forcerelease methods and exploit the details of the resulting fracture processes.

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Strain localization—short to long correlation length transition

Cited by 42 publications

References 39 publications

Lattice models of polycrystalline microstructures: A quantitative approach

Lattice models of polycrystalline microstructures: A quantitative approach

Some Notes on Microcracking, Softening, Localization, and Size Effects

On the Load–Unload (L–U) and Force–Release (F–R) Algorithms for Simulating Brittle Fracture Processes via Lattice Models

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