Branched Cracks in Anisotropic Elastic Solids

1989 ◽  
Vol 56 (4) ◽  
pp. 858-864 ◽  
Author(s):  
Makoto Obata ◽  
Siavouche Nemat-Nasser ◽  
Yoshiaki Goto
Keyword(s):  
Hilbert Problem ◽  
Anisotropic Body ◽  
Singular Integral Equations ◽  
Isotropic Case ◽  
Density Functions ◽  
Intensity Factors ◽  
Elastic Solids ◽  
Variable Approach ◽  
Crack Problems ◽  
Anisotropic Elastic

Branched crack problems are analyzed in two-dimensional, anisotropically elastic homogeneous solids. The method of analysis is based on the complex variable approach of Savin and Lekhnitskii. The Hilbert problem in an anisotropic body is defined, and a pair of singular integral equations are derived for dislocation density functions associated with a branched crack. For both symmetric and nonsymmetric geometries, and under symmetric and antisymmetric loads, the stress intensity factors and the energy release rate are computed numerically by extrapolation for infinitesimally small lengths of branched cracks. The results are compared with those of the isotropic case given in the literature and the effects of anisotropy are discussed.

Analysis of Branched Interface Cracks Between Dissimilar Anisotropic Media

1989 ◽  
Vol 56 (4) ◽  
pp. 844-849 ◽  
Author(s):  
G. R. Miller ◽  
W. L. Stock
Keyword(s):  
Stress Intensity ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Crack Branching ◽  
Intensity Factors ◽  
Function Solution ◽  
Special Cases ◽  
Branch Crack

A solution is presented for the problem of a crack branching off the interface between two dissimilar anisotropic materials. A Green’s function solution is developed using the complex potentials of Lekhnitskii (1981) allowing the branched crack problem to be expressed in terms of coupled singular integral equations. Numerical results for the stress intensity factors at the branch crack tip are presented for some special cases, including the no-interface case which is compared to the isotropic no-interface results of Lo (1978).

Mixed Mode Stress Singularities in Anisotropic Composites

1999 ◽  
Author(s):  
Wan-Lee Yin
Keyword(s):  
Stress Intensity ◽  
Asymptotic Solution ◽  
Stress Intensity Factors ◽  
Stress Singularity ◽  
Free Edge ◽  
Complex Conjugate ◽  
Circular Path ◽  
Intensity Factors ◽  
Element Analysis ◽  
Anisotropic Elastic

Abstract Multi-material wedges composed of fully anisotropic elastic sectors generally show intrinsic coupling of the anti-plane and in-plane modes of deformation. Each anisotropic sector has three complex conjugate pairs of material eigensolutions whose form of expression depends on five distinct types of anisotropic materials. Continuity of the displacements and the tractions across the sector interfaces and the traction-free conditions on two exterior boundary edges determine an infinite sequence of eigenvalues and eigensolutions of the multi-material wedge. These eigensolutions are linearly combined to match the traction-boundary data (generated by global finite element analysis of the structure) on a circular path encircling the singularity. The analysis method is applied to a bimaterial wedge near the free edge of a four-layer angle-ply laminate, and to a trimaterial wedge surrounding the tip of an embedded oblique crack in a three-layer composite. Under a uniform temperature load, the elasticity solution based on the eigenseries yields interfacial stresses that are significantly different from the asymptotic solution (given by the first term of the eigenseries), even as the distance from the singularity decreases to subatomic scales. Similar observations have been found previously for isotropic and orthotropic multi-material wedges. This raises serious questions with regard to characterizing the criticality of stress singularity exclusively in terms of the asymptotic solution and the associated stress intensity factors or generalized stress intensity factors.

scholarly journals Volumetric Constraint Models for Anisotropic Elastic Solids

2004 ◽  
Vol 71 (5) ◽  
pp. 731-734 ◽  
Author(s):  
Carlos A. Felippa ◽  
Eugenio On˜ate
Keyword(s):  
Hydrostatic Stress ◽  
Stress Pattern ◽  
Stress System ◽  
Anisotropic Behavior ◽  
Elastic Solids ◽  
Physical Behavior ◽  
Special Cases ◽  
Anisotropic Elastic ◽  
Arbitrary Anisotropy ◽  
Physical Materials

We study three “incompressibility flavors” of linearly elastic anisotropic solids that exhibit volumetric constraints: isochoric, hydroisochoric, and rigidtropic. An isochoric material deforms without volume change under any stress system. An hydroisochoric material does so under hydrostatic stress. A rigidtropic material undergoes zero deformations under a certain stress pattern. Whereas the three models coalesce for isotropic materials, important differences appear for anisotropic behavior. We find that isochoric and hydroisochoric models under certain conditions may be hampered by unstable physical behavior. Rigidtropic models can represent semistable physical materials of arbitrary anisotropy while including isochoric and hydroisochoric behavior as special cases.

Finite strains in an anisotropic elastic continuum

1950 ◽  
Vol 202 (1070) ◽  
pp. 345-358 ◽  
Keyword(s):  
Equations Of State ◽  
Elastic Solid ◽  
Finite Strains ◽  
Free Energy Function ◽  
Elastic Solids ◽  
Elastic Continuum ◽  
Invariance Properties ◽  
Anisotropic Elastic ◽  
Necessary And Sufficient ◽  
Thermodynamic Restrictions

The discussion in a previous paper (Oldroyd 1950), on the invariance properties required of the equations of state of a homogeneous continuum, is extended by taking into account thermodynamic restrictions on the form of the equations, in the case of an elastic solid deformed from an unstressed equilibrium configuration. The general form of the finite strainstress-temperature relations, expressed in terms of a free-energy function, is deduced without assuming that the material is isotropic. The results of other authors based on the assumption of isotropy are shown to follow as particular cases. The equations of state are derived by considering quasi-static changes in an elastic solid continuum; the results then apply to non-ideally elastic solids in equilibrium, or subjected to quasi-static changes only, and to ideally elastic solids in general motion. A necessary and sufficient compatibility condition for the finite strains at different points of a continuum is also derived. As a simple illustration of the derivation and use of equations of state involving anisotropic physical constants, the torsion of an anisotropic cylinder is discussed briefly.

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