A key matrix N̂ for the stress singularity of the anisotropic elastic composite wedges

Chyanbin Hwu, Masaki Omiya, Kikuo Kishimoto

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

By employing the Stroh formalism, a general solution satisfying the basic laws of two-dimensional linear anisotropic elasticity has been written in a complex variable formulation. To study the stress singularity, suitable stress functions have been assumed in the exponential form. The singular order near the anisotropic elastic composite wedge apex can then be found by satisfying the boundary conditions. Since there are many material constants and boundary conditions involved, the characteristic equation for the singular order usually becomes cumbersome or leaves in the form of a system of simultaneous algebraic equations. It is therefore difficult to get any important parameters to study the failure initiation of the composite wedges. Through a careful mathematical manipulation, a key matrix N̂ that contains the information of material properties and wedge geometries has been found to be a dominant matrix for the determination of the singular order. A closed-form solution for the order of stress singularity is thus written in a simple form. Special cases such as the wedge corners, cracks, interfacial joints or cracks, a crack terminating at the interface, etc. can all be studied in a unified manner.

Original language English 40-50 11 JSME International Journal, Series A: Solid Mechanics and Material Engineering 46 1 https://doi.org/10.1299/jsmea.46.40 Published - 2003 Jan 1

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Cracks
Composite materials
Boundary conditions
Elasticity
Materials properties
Geometry

All Science Journal Classification (ASJC) codes

• Materials Science(all)
• Mechanical Engineering

Cite this

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abstract = "By employing the Stroh formalism, a general solution satisfying the basic laws of two-dimensional linear anisotropic elasticity has been written in a complex variable formulation. To study the stress singularity, suitable stress functions have been assumed in the exponential form. The singular order near the anisotropic elastic composite wedge apex can then be found by satisfying the boundary conditions. Since there are many material constants and boundary conditions involved, the characteristic equation for the singular order usually becomes cumbersome or leaves in the form of a system of simultaneous algebraic equations. It is therefore difficult to get any important parameters to study the failure initiation of the composite wedges. Through a careful mathematical manipulation, a key matrix N̂ that contains the information of material properties and wedge geometries has been found to be a dominant matrix for the determination of the singular order. A closed-form solution for the order of stress singularity is thus written in a simple form. Special cases such as the wedge corners, cracks, interfacial joints or cracks, a crack terminating at the interface, etc. can all be studied in a unified manner.",
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A key matrix N̂ for the stress singularity of the anisotropic elastic composite wedges. / Hwu, Chyanbin; Omiya, Masaki; Kishimoto, Kikuo.

In: JSME International Journal, Series A: Solid Mechanics and Material Engineering, Vol. 46, No. 1, 01.01.2003, p. 40-50.

Research output: Contribution to journalArticle

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