Search
An isogeometric finite element formulation for boundary and shell viscoelasticity based on a multiplicative surface deformation split
Abstract
This work presents a numerical formulation to model isotropic viscoelastic material behavior for membranes and thin shells. The surface and the shell theory are formulated within a curvilinear coordinate system,which allows the representation of general surfaces and deformations. The kinematics follow from Kirchhoff–Love theory and the discretization makes use of isogeometric shape functions. A multiplicative split of the surface deformation gradient is employed, such that an intermediate surface configuration is introduced. The surface metric and curvature of this intermediate configuration follow from the solution of nonlinear evolution laws—ordinary differential equations—that stem from a generalized viscoelastic solid model. The evolution laws are integrated numerically with the implicit Euler scheme and linearized within the Newton–Raphson scheme of the nonlinear finite element framework. The implementation of membrane and bending viscosity is verified with the help of analytical solutions and shows ideal convergence behavior. The chosen numerical examples capture large deformations and typical viscoelasticity behavior, such as creep, relaxation, and strain rate dependence. It is also shown that the proposed formulation can be straightforwardly applied to model boundary viscoelasticity of 3D bodies.
Citations
-
5
CrossRef
-
0
Web of Science
-
5
Scopus
Authors (2)
-
Karsten Paul
Cite as
Full text
- Publication version
- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.1002/nme.7080
- License
-
open in new tab
Keywords
Details
- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
-
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
no. 123,
pages 5570 - 5617,
ISSN: 0029-5981 - Language:
- English
- Publication year:
- 2022
- Bibliographic description:
- Paul K., Sauer R.: An isogeometric finite element formulation for boundary and shell viscoelasticity based on a multiplicative surface deformation split// INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING -Vol. 123,iss. 22 (2022), s.5570-5617
- DOI:
- Digital Object Identifier (open in new tab) 10.1002/nme.7080
- Sources of funding:
-
- Free publication
- Verified by:
- Gdańsk University of Technology
seen 73 times
Recommended for you
Isogeometric Shell FE Analysis of the Human Abdominal Wall
- B. Borzeszkowski,
- T. X. Duong,
- R. A. Sauer
- + 1 authors