<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The scattering of time-harmonic waves by a finite, blunt nano-crack in a graded, viscoelastic bulk material with a free surface is considered in this work. Non-classical boundary conditions and a localized constitutive equation at the interface between crack and matrix, following the Gurtin-Murdoch surface elasticity theory are introduced. An efficient numerical technique is developed using integro-differential equations along the nano-crack line that is based on an analytically derived Green‘s function for the quadratically inhomogeneous half-plane. The dependence of the diffracted and scattered waves and of the local stress concentration fields on key problem parameters such as viscosity, inhomogeneity, surface elasticity, and interaction between the nano-crack and the free surface are all examined through an extensive parametric study.</p></abstract>

The scattering of time-harmonic waves by a finite, blunt nano-crack in a graded, viscoelastic bulk material with a free surface is considered in this work. Non-classical boundary conditions and a localized constitutive equation at the interface between crack and matrix, following the Gurtin-Murdoch surface elasticity theory are introduced. An efficient numerical technique is developed using integro-differential equations along the nano-crack line that is based on an analytically derived Green‘s function for the quadratically inhomogeneous half-plane. The dependence of the diffracted and scattered waves and of the local stress concentration fields on key problem parameters such as viscosity, inhomogeneity, surface elasticity, and interaction between the nano-crack and the free surface are all examined through an extensive parametric study.

Numerical Solution of Integro-Differential Equations Modelling the Dynamic Behavior of a Nano-Cracked Viscoelastic Half-Plane

Cybernetics and Information Technologies

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

The scattering of time-harmonic waves by a finite, blunt nano-crack in a graded, viscoelastic bulk material with a free surface is considered in this work....

Numerical Solution of Integro-Differential Equations Modelling the Dynamic Behavior of a Nano-Cracked Viscoelastic Half-Plane

Published Online: Dec 31, 2020

Page range: 105 - 115

Received: Sep 15, 2020

Accepted: Oct 30, 2020

DOI: https://doi.org/10.2478/cait-2020-0065

Keywords
Viscoelasticity, graded half-plane, nano-crack, integro-differential equations, stress concentration, wave scattering, wave diffraction

© 2020 Tsviatko V. Rangelov et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Numerical Solution of Integro-Differential Equations Modelling the Dynamic Behavior of a Nano-Cracked Viscoelastic Half-Plane

Published Online: Dec 31, 2020

Page range: 105 - 115

Received: Sep 15, 2020

Accepted: Oct 30, 2020

DOI: https://doi.org/10.2478/cait-2020-0065

KeywordsViscoelasticity, graded half-plane, nano-crack, integro-differential equations, stress concentration, wave scattering, wave diffraction

© 2020 Tsviatko V. Rangelov et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Viscoelasticity, graded half-plane, nano-crack, integro-differential equations, stress concentration, wave scattering, wave diffraction