A new time-domain boundary element formulation for generalized models of viscoelasticity. (May 2023)

• Record Type: Journal Article
• Authors: Akay, Ahmet Arda; Gürses, Ercan; Göktepe, Serdar
• Is Part Of: Engineering analysis with boundary elements. Volume 150(2023)
• Page Start: 30
• Page End: 43
• Publication Date: 2023-05
• Subjects: Boundary element method -- Linear viscoelasticity -- Meshless domain integration -- Cartesian transformation method -- Radial point interpolation method -- Semi-implicit time integration; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2023.01.031
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: The contribution is concerned with the novel algorithmic formulation for generalized models of viscoelasticity under quasi-static conditions within the framework of the boundary element method (BEM). The proposed update algorithm is constructed for a generic rheological model of linear viscoelasticity that can either be straightforwardly simplified to recover the basic Kelvin and Maxwell models or readily furthered towards the generalized models of viscoelasticity through the serial or parallel extensions. In contrast to the scarce existing rate formulations of inelasticity developed within BEM, the put forward non-iterative formulation exploits the hybrid semi-implicit update of strain-like kinematic history variables. The challenge arising from the indispensable domain integrals is overcome through the mesh-free Cartesian transformation method (CTM), complemented by the radial point integration (RPIM) technique. The excellent performance of the proposed approach is demonstrated in comparison with the corresponding analytical and finite element results for boundary-value problems with uniform and non-uniform strain fields under different representative modes and types of loading. Highlights: A new semi-implicit approach to viscoelasticity within the framework of the BEM. A non-iterative update of history variables using total strains and strain rates. A model-independent and easy-to-extend unified BEM formulation of viscoelasticity. Calculation of domain integrals through the mesh-free CTM supplemented by RPI.