GENERALIZATION OF BARENBLATT'S COHESIVE FRACTURE THEORY FOR FRACTAL CRACKS

Fractals ◽  
2002 ◽  
Vol 10 (02) ◽  
pp. 189-198 ◽  
Author(s):  
ARASH YAVARI
Keyword(s):  
Driving Force ◽  
A Priori ◽  
Stress Singularity ◽  
Local Theory ◽  
Fractal Surface ◽  
Cohesive Fracture ◽  
Fracture Theory ◽  
Griffith’S Theory ◽  
Fractal Crack ◽  
Fractal Cracks

In this paper, we generalize Barenblatt's cohesive fracture theory for fractal cracks. We discuss the difficulties of generalizing the concept of traction on a fractal surface. Borodich's modification of Griffith's theory for fractal cracks is reviewed. Irwin's driving force is generalized for fractal cracks and a fractal driving force (Gf) is defined. It is shown that to generalize Barenblatt's theory for fractal cracks it is necessary to introduce a new quantity, D-fractal cohesive pseudo-stress. This new quantity is cohesive force per unit of a fractal measure. Fractal modulus of cohesion is seen to be a function of both the material and the fractal dimension of the crack. Equivalence of fractal Barenblatt's and Griffith's theories is discussed. It is seen that the order of stress singularity at the tip of a fractal crack cannot be obtained using modified Barenblatt's theory because this theory is a local theory and assumes the order of stress singularity a priori.

On Fractal Cracks in Micropolar Elastic Solids

2001 ◽  
Vol 69 (1) ◽  
pp. 45-54 ◽  
Author(s):  
A. Yavari ◽  
S. Sarkani ◽  
E. T. Moyer,
Keyword(s):  
Fracture Mechanics ◽  
Dimensional Analysis ◽  
Asymptotic Method ◽  
Couple Stress ◽  
Stress Singularity ◽  
Stress Singularities ◽  
Elastic Solids ◽  
Fracture Theory ◽  
Fractal Crack ◽  
Fractal Cracks

In this paper we review the fracture mechanics of smooth cracks in micropolar (Cosserat) elastic solids. Griffith’s fracture theory is generalized for cracks in micropolar solids and shown to have two possible forms. The effect of fractality of fracture surfaces on the powers of stress and couple-stress singularity is studied. We obtain the orders of stress and couple-stress singularities at the tip of a fractal crack in a micropolar solid using dimensional analysis and an asymptotic method that we call “method of crack-effect zone.” It is shown that orders of stress and couple-stress singularities are equal to the order of stress singularity at the tip of the same fractal crack in a classical solid.

scholarly journals Albumin protein coronas render nanoparticles surface active: consonant interactions at air–water and at lipid monolayer interfaces

2021 ◽  
Author(s):  
Nasim Ganji ◽  
Geoffrey D. Bothun
Keyword(s):  
Adsorption Kinetics ◽  
Driving Force ◽  
A Priori ◽  
Protein Corona ◽  
Lipid Monolayer ◽  
Surface Active ◽  
Biological Interfaces

Albumin restructuring yields an additional driving force for protein corona-modified nanoparticles to adhere to biological interfaces that can be revealed a priori by modeling adsorption kinetics.

Basic solution of two collinear mode-I cracks in the orthotropic medium by use of the non-local theory

2017 ◽  
Vol 13 (1) ◽  
pp. 100-115 ◽  
Author(s):  
Haitao Liu
Keyword(s):  
Stress Singularity ◽  
Local Theory ◽  
Mode I ◽  
Basic Solution ◽  
Orthotropic Medium ◽  
Dual Integral Equations ◽  
Content Type ◽  
Present Solution ◽  
Crack Tips ◽  
Non Local

Purpose The purpose of this paper is to present the basic solution of two collinear mode-I cracks in the orthotropic medium by the use of the non-local theory. Design/methodology/approach Meanwhile, the generalized Almansi’s theorem and the Schmidt method are used. By the Fourier transform, it is converted to a pair of dual integral equations. Findings Numerical examples are provided to show the effects of the crack length, the distance between the two collinear cracks and the lattice parameter on the stress field near the crack tips in the orthotropic medium. Originality/value The present solution exhibits no stress singularity at the crack tips in the orthotropic medium.

Dynamic cohesive fracture: Models and analysis

2014 ◽  
Vol 24 (09) ◽  
pp. 1857-1875 ◽  
Author(s):  
Christopher J. Larsen ◽  
Valeriy Slastikov
Keyword(s):  
Energy Density ◽  
Existence Of Solutions ◽  
A Priori ◽  
Regular Case ◽  
Mathematical Study ◽  
Cohesive Fracture ◽  
One Dimensional ◽  
Cohesive Energy Density ◽  
Fracture Models ◽  
The One

Our goal in this paper is to initiate a mathematical study of dynamic cohesive fracture. Mathematical models of static cohesive fracture are quite well understood, and existence of solutions is known to rest on properties of the cohesive energy density ψ, which is a function of the jump in displacement. In particular, a relaxation is required (and a relaxation formula is known) if ψ′(0+) ≠ ∞. However, formulating a model for dynamic fracture when ψ′(0+) = ∞ is not straightforward, compared to when ψ′(0+) is finite, and especially compared to when ψ is smooth. We therefore formulate a model that is suitable when ψ′(0+) = ∞ and also agrees with established models in the more regular case. We then analyze the one-dimensional case and show existence when a finite number of potential fracture points are specified a priori, independent of the regularity of ψ. We also show that if ψ′(0+) < ∞, then relaxation is necessary without this constraint, at least for some initial data.

Non-Local Stress and Stain Analysis at Crack Tip Based on Different Types of Weighted Functions

2010 ◽  
Vol 146-147 ◽  
pp. 198-201
Author(s):  
Zhong Chang Wang
Keyword(s):  
Stress Singularity ◽  
Crack Tip ◽  
Local Stress ◽  
Local Strain ◽  
Local Theory ◽  
Weighted Functions ◽  
Different Types ◽  
Non Local ◽  
Distribution Of Stress ◽  
Stain Analysis

The characteristics of different types of the weighted functions are discussed, and the dependency of the influence domain on the intrinsic length scale is examined. Distribution of stress field of I-II mixed mode crack is analyzed by non-local theory with different types of weighted functions. The effects of the stress intensity factor KI and KII on the all components of strains at the crack tip are analyzed by the non-local theories based on different types of weighted functions. The non-local strain will be considerably reduced. The size of non-local strain field with the bell-shaped weighted functions is larger than that obtained by either Green’s or Gaussian weighted functions. The non-local theory is instructive to avoid the trouble resulting from stress singularity at crack tip.

Crack-Tip Stress Fields in FGMs under Anti-Plane Shear Impact Loading Using the Non-Local Theory

2007 ◽  
Vol 348-349 ◽  
pp. 821-824
Author(s):  
Xian Shun Bi ◽  
Xue Feng Cai ◽  
Jian Xun Zhang
Keyword(s):  
Integral Equations ◽  
Impact Loading ◽  
Infinite Plate ◽  
Stress Singularity ◽  
Crack Tip ◽  
Functionally Graded ◽  
Local Theory ◽  
Dual Integral Equations ◽  
Plane Shear ◽  
Non Local

A crack in an infinite plate of functionally graded materials (FGMs) under anti-plane shear impact loading is analyzed by making use of non-local theory. The shear modulus and mass density of FGMs are assumed to be of exponential form and the Poisson’s ratio is assumed to be constant. The mixed boundary value problem is reduced to a pair dual integral equations through the use of Laplace and Fourier integral transform method. In solving the dual integral equations, the crack surface displacement is expanded in a series using Jacobi’s polynomials and Schmidt’s method is used. The numerical results show that no stress singularity is present at the crack tip. The stress near the crack tip tends to increase with time at first and then decreases in amplitude and the peak values of stress decreases with increasing the graded parameters.

EXAMPLES OF FRACTALS IN SOIL MECHANICS

Fractals ◽  
1993 ◽  
Vol 01 (04) ◽  
pp. 795-805 ◽  
Author(s):  
HANS J. HERRMANN ◽  
MUHAMMAD SAHIMI ◽  
FRANK TZSCHICHHOLZ
Keyword(s):  
Soil Mechanics ◽  
Square Lattice ◽  
Beam Model ◽  
Invasion Percolation ◽  
Fractal Structures ◽  
Self Organized ◽  
Fractal Patterns ◽  
The One ◽  
Fractal Crack ◽  
Fractal Cracks

Models will be presented for fractal structures appearing naturally in soils. On the one hand, we discuss the opening of brittle media via hydraulic fracturing at constant pressure using a square lattice beam model with disorder. We consider the case in which only beams under tension can break, and discuss under which conditions the resulting cracks may develop fractal patterns. The stress field of the fractal cracks is visualized by photoelastic fringes. Then we present a modelization for a fluid penetrating under a pressure gradient into a fractal crack which it is itself opening. To do this, we investigate invasion percolation fingers in a quenched medium in which the randomness has a gradient corresponding to the density of microcracks that arise in a self-organized way around a large crack.

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