Fractal fragmentation theory for size effects of quasi-brittle materials in compression

Carpinteri, Alberto; Pugno, Nicola

doi:10.1680/macr.2005.57.6.309

Cited by 11 publications

(3 citation statements)

References 17 publications

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“…As an RCP Voronoi mesh is refined to smaller scales the question of self-consistency between the explicit macroscopic representation of cracks and the implicit homogenized representation comes into question. This notion of self-consistency and scale dependence is a central theme in fractal geometry descriptions of materials [14,15,26,48], and is important for understanding the size effect in quasi-brittle materials such as concrete [3,4].…”

Section: Examplementioning

confidence: 99%

Simulating the pervasive fracture of materials and structures using randomly close packed Voronoi tessellations

Bishop

2009

Comput Mech

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Under extreme loading conditions most often the extent of material and structural fracture is pervasive in the sense that a multitude of cracks are nucleating, propagating in arbitrary directions, coalescing, and branching. Pervasive fracture is a highly nonlinear process involving complex material constitutive behavior, material softening, localization, surface generation, and ubiquitous contact. A pure Lagrangian computational method based on randomly close packed Voronoi tessellations is proposed as a rational and robust approach for simulating the pervasive fracture of materials and structures. Each Voronoi cell is formulated as a finite element using the Reproducing Kernel Method. Fracture surfaces are allowed to nucleate only at the intercell faces, and cohesive tractions are dynamically inserted. The randomly seeded Voronoi cells provide a regularized random network for representing fracture surfaces. Example problems are used to demonstrate the proposed numerical method. The primary numerical challenge for this class of problems is the demonstration of model objectivity and, in particular, the identification and demonstration of a measure of convergence for engineering quantities of interest.

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Section: Examplementioning

confidence: 99%

Simulating the pervasive fracture of materials and structures using randomly close packed Voronoi tessellations

Bishop

2009

Comput Mech

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“…Recently, the fragmentation theory has been investigated on quasi brittle materials under compressive loads [15]. In this paper, emphasis is given to show material (ferrite) behaviors under fatigue loading conditions.…”

Section: Introductionmentioning

confidence: 99%

Fatigue crack analysis of ferrite material by acoustic emission technique

Khan¹,

Rashid²,

Hidaka³

et al. 2019

JMES

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Recently in various fields, numerous researches are going on for the assessment of material damage on the basis of crack initiation and propagation. Various methods are available in NDT for this purpose, among which analysis using released acoustic emission (AE) waves due to crack propagation is very effective due to its dynamic monitoring features. Various approaches are proposed for long time to make it an ideal method for accurate monitoring of crack behaviors in materials. In fragmentation theory there are some proportionality among the relations of AE event, AE energy, area and volume of cracks etc., which are calculated from the released AE waves from any dynamic crack. It has been found that the necessity of calculating the fractal dimension is important in verifying these relationships. This parameter is emphasized for determining the geometry of the irregularity in crack surface and crack volume. In this paper a novel approach based on image processing is proposed to find out the fractal dimension for analyzing the crack propagation characteristics. Finally, the proportionality relationships of AE parameters with crack propagation behavior in ferrite cast iron under fatigue loading are demonstrated experimentally.

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“…It is pointed out that rock deformation and failure is a comprehensive result of energy dissipation and energy release. Carpinteri and Pugno [ 12 ] theoretically and experimentally studied the effect of particle size on the energy density and intensity of brittle materials dissipated during compression, and derived the dissipated energy density of structural components under compression.Hu et al [ 13 ] applied the energy dissipation law and brittle dynamic fracture criterion in rock under impact load, and applied the fatigue damage iterative relationship under stress wave to the post-destruction stage of rock, and obtained the relationship between impact energy, rock damage, and block distribution.…”

Section: Introductionmentioning

confidence: 99%

Research on the Impact Loading and Energy Dissipation of Concrete after Elevated Temperature under Different Heating Gradients and Cooling Methods

Zhai

et al. 2018

Materials

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To provide theoretical basis for fire rescue, post-disaster safety evaluation, and reinforcement of concrete structures, C35 concrete materials are treated with high-temperature heating (200 °C, 400 °C, 600 °C, 800 °C) under two different heating gradients. After natural cooling and water cooling to normal temperature, an impact compression test was carried out at different loading rates using a Split Hopkinson Pressure Bar (SHPB) system with a diameter of 100 mm, and finally the crushed specimens were subjected to a sieving test. The effects of elevated temperatures, cooling methods, heating gradients, and loading rates on the fragment size distribution, fractal characteristics, and energy dissipation of impact-compressed concrete specimens were studied. The results show that with the increase of the loading rate and the rise of the heating temperature, the crushing degree of concrete specimens gradually increases, the average fragment size decreases, and the mass distribution of the fragments move from the coarse end to the fine end. The fragment size distribution of the specimen has obvious fractal characteristics. In addition, its fractal dimension increases with the increase of loading rate and heating temperature, the average size of the specimen fragments decreases correspondingly, and the fracture of the specimen becomes more serious. When the different heating gradients were compared, it was found that the fractal dimension of the specimens subjected to rapid heating treatment was larger than that of the slow heating treatment specimens, and the crushing degree of the specimens with different cooling methods was discrete. By analyzing the energy dissipation of the specimen under different conditions, it is shown that both the fractal dimension and the peak stress increase with the increase of the fragmentation energy dissipation density. It shows that there is a close correlation between the change of fractal dimension and its macroscopic dynamic mechanical properties.

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Fractal fragmentation theory for size effects of quasi-brittle materials in compression

Cited by 11 publications

References 17 publications

Simulating the pervasive fracture of materials and structures using randomly close packed Voronoi tessellations

Simulating the pervasive fracture of materials and structures using randomly close packed Voronoi tessellations

Fatigue crack analysis of ferrite material by acoustic emission technique

Research on the Impact Loading and Energy Dissipation of Concrete after Elevated Temperature under Different Heating Gradients and Cooling Methods

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