Asymptotic Solutions at the Tip of Interface Cracks and Multi-Material Corners with Frictional Contact in Linear Elastic Anisotropic Solids

Abstract: This study focuses on point singularities in the solutions of linear elastic BVPs for anisotropic solids in 2.5D (generalised plane strain). The stresses in these BVPs can be unbounded at singular points, also known as corners, where discontinuities exist in the solid geometry, material properties or boundary/interface conditions. The behaviour of elastic solutions at singular points is described by asymptotic expansions expressed as series of products of power-logarithmic terms in the radial coordinate and characteristic angular functions. The exponents of these terms are known as singularity exponents, while the coefficients of the series are referred to as generalised stress intensity factors (GSIFs).

This work aims to develop:

1) a specific semi-analytic procedure to determine the terms of these asymptotic series at the tip of interface cracks with frictional sliding contact between the crack faces; and

2) a general semi-analytic procedure to determine the terms of these asymptotic series at the tip of multi-material corners with frictional sliding contact at the outer faces and/or interfaces between the wedges, considering the Coulomb friction law.

These procedures are novel in that they lead to nonlinear eigenproblems for both the singularity exponents and the angles of frictional shear stresses in frictional contact zones. Both procedures are based on the Stroh formalism in complex variable for linear anisotropic elasticity.

The application of these procedures is demonstrated by some interesting examples. Finally, SingSol, an online app that implements the general semi-analytic procedure for singularity analysis of multimaterial corners, is briefly presented.

MathematicsPhysics

Audience: researchers in the topic

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Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)

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