A robust algorithm for the contact of viscoelastic materials

4th ModTech International Conference - Modern Technologies in Industrial Engineering

Spinu, S.^1,2 ; Cerlinca, D.^1,2

Department of Mechanics and Technologies, Stefan Cel Mare University of Suceava, 13th University Street, 720229, Romania^1

Integrated Center for Research, Development and Innovation in Advanced Materials, Nanotechnologies and Distributed Systems for Fabrication and Control (MANSiD), Stefan Cel Mare University, Suceava, Romania^2

关键词: Linear viscoelasticity;    Numerical differentiation;    Semi-analytical methods;    Static equilibrium equations;    Transcendental equations;    Trial-and-error approach;    Visco-elastic material;    Viscoelastic contact problems;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/145/4/042034/pdf
DOI  :  10.1088/1757-899X/145/4/042034

来源: IOP

【 摘 要 】

Existing solutions for the contact problem involving viscoelastic materials often require numerical differentiation and integration, as well as resolution of transcendental equations, which can raise convergence issues. The algorithm advanced in this paper can tackle the contact behaviour of the viscoelastic materials without any convergence problems, for arbitrary contact geometry, arbitrary loading programs and complex constitutive models of linear viscoelasticity. An updated algorithm for the elastic frictionless contact, coupled with a semi-analytical method for the computation of viscoelastic displacement, is employed to solve the viscoelastic contact problem at a series of small time increments. The number of equations in the linear system resulting from the geometrical condition of deformation is set by the number of cells in the contact area, which is a priori unknown. A trial-and-error approach is implemented, resulting in a series of linear systems which are solved on evolving contact areas, until static equilibrium equations and complementarity conditions are fully satisfied for every cell in the computational domain. At any iteration, cells with negative pressure are excluded from the contact area, while cells with negative gap (i.e. cells where the contacting bodies are predicted to overlap) are reincluded. The solution is found when pressure is stabilized in relation to the imposed normal load. This robust algorithm is expected to solve a large variety of contact problems involving viscoelastic materials.