<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

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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

Publié en ligne: 31 déc. 2020

Pages: 105 - 115

Reçu: 15 sept. 2020

Accepté: 30 oct. 2020

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

Mots clés
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

Publié en ligne: 31 déc. 2020

Pages: 105 - 115

Reçu: 15 sept. 2020

Accepté: 30 oct. 2020

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

Mots clésViscoelasticity, 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.

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