Elastic solids with many cracks: A simple method of analysis

Kachanov, Mark

doi:10.1016/0020-7683(87)90030-8

Cited by 460 publications

(235 citation statements)

References 13 publications

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“…One type of such a matrix interaction relation, due to Kachanov (1985Kachanov ( , 1987, has led to the following field equation This is a Fredholm integral equation in which V = volume of the structure; A ( z , < ) = crack influence function, characterizing in a statistically smeared manner the normal stress across a frozen crack at coordinate z caused by a unit pressure applied at the faces of a crack at e; (..) is a spatial averaging operator; AS(') or AS(1' = increment (in the current loading step) of the principal stress labeled by (1) before or after the effect of crack interactions. The integral in this equation is not an averaging integral because its kernel has spatial average 0.…”

Section: Fracturing Truss Model For Shear Failure Of Reinforced Concretementioning

confidence: 99%

Scaling of structural failure

Bažant

Chen

1997

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Section: Fracturing Truss Model For Shear Failure Of Reinforced Concretementioning

confidence: 99%

Scaling of structural failure

Bažant

Chen

1997

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“…1, we consider a stress state which is suddenly imposed at time t = 0 and kept constant thereafter (t > 0), see the uniform stress boundary conditions (10). Since time-dependent behavior of the composite is related to in-plane dislocations of the interfaces, see the viscous interface law (4), and given the structure of state equation (7) together with the non-zero components according to (123-128), the time-dependent macroscopic stresses obey the form of pure shear,…”

Section: Review Of Creep Functionsmentioning

confidence: 99%

“…When it comes to the special case of inclusions in form of flat interfaces, i.e., to that of matrix-interface composites, interaction among interfaces would be clearly expected as well; however, the two-dimensional nature of interfaces is responsible for particularly surprising interaction properties [8,9], reminiscent of the situation encountered with micro-cracked materials [10,11]. The present contribution tackles the question of how interaction among microscopic viscous interfaces, believed to be at the origin of creep of hydrated biomaterials and geomaterials [12][13][14], affects the overall macroscopic creep and relaxation functions of matrix-interface composites.…”

Section: Introductionmentioning

confidence: 99%

How interface size, density, and viscosity affect creep and relaxation functions of matrix-interface composites: a micromechanical study

2015

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Matrix-inclusion composites are known to exhibit interaction among the inclusions. When it comes to the special case of inclusions in form of flat interfaces, interaction among interfaces would be clearly expected, but the two-dimensional nature of interfaces implies quite surprising interaction properties. This is the motivation to analyze how interaction among two different classes of microscopic interfaces manifests itself in macroscopic creep and relaxation functions of matrix-interface composites. To this end, we analyze composites made of a linear elastic solid matrix hosting parallel interfaces, and we consider that creep and relaxation of such composites result from micro-sliding within adsorbed fluid layers filling the interfaces. The latter idea was recently elaborated in the framework of continuum micromechanics, exploiting eigenstress homogenization schemes, see Shahidi et al. (Eur J Mech A Solids 45:41-58, 2014). After a rather simple mathematical exercise, it becomes obvious that creep functions do not reflect any interface interaction. Mathematical derivation of relaxation functions, however, turns out to be much more challenging because of pronounced interface interaction. Based on a careful selection of solution methods, including Laplace transforms and the method of non-dimensionalization, we analytically derive a closed-form expression of the relaxation functions, which provides the sought insight into interface interaction. The seeming paradox that no interface interaction can be identified from creep functions, while interface interaction manifests itself very clearly in the relaxation functions of matrix-interface materials, is finally resolved based on stress and strain average rules for interfaced composites. They clarify that uniform stress boundary conditions lead to a direct external control of average stress and strain states in the solid matrix, and this prevents interaction among interfaces. Under uniform strain boundary conditions, in turn, interfacial dislocations do influence the average stress and strain states in the solid matrix, and this results in pronounced interface interaction.

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“…The solutions for these configurations imply the usage of various numerical methods [2][3][4][5][6][7], like extended element method (XFEM), which is nowadays becoming more prevalent since it suppresses the need to mesh and remesh the crack surfaces and is used for modelling different discontinuities in 1D, 2D and 3D domains [8] . All those methods are time-consuming and computationally intense [9,10].…”

Section: Introductionmentioning

confidence: 99%