A non-iterative boundary element formulation for nonlinear viscoelasticity

Date

2024-06-01

Author

Akay, Ahmet Arda
Gürses, Ercan
Göktepe, Serdar

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In this study, we propose a non-iterative boundary element method (BEM) of highly nonlinear viscoelasticity in time domain. The computationally attractive iteration-free algorithmic structure is achieved by the linearization of a power-type evolution equation. Supplementing the consistent linearization about every solution step with a semi-implicit update scheme, we obtain a robust boundary element framework for nonlinear viscoelasticity. The domain integrals emerging in the proposed approach are calculated using truly mesh-free integration techniques. To our best knowledge, this is the first work on a non-iterative time-domain BEM of nonlinear viscoelasticity. The proposed approach is critically assessed through a comprehensive numerical study that involves representative boundary-value problems (BVPs). The analyses of BVPs are also conducted by the corresponding fully implicit nonlinear finite element method (FEM). The rate of loading, the degree of nonlinearity, and the level of spatial non-uniformity are the primary variables considered in the numerical analyses. The quantitative comparisons made in terms of global force-displacement curves and the local contour plots of a viscous strain measure suggest that the proposed non-iterative time-domain BEM formulation is capable of accurately solving nonlinear viscoelasticity problems in nonstandard domains.

Subject Keywords

Boundary element method, Consistent linearization, Meshless domain integration, Nonlinear viscoelasticity, Power-type evolution equation, Semi-implicit time integration

URI

https://hdl.handle.net/11511/108968

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Department of Aerospace Engineering, Article