Extended Finite Element Method Based On Precise Algorithm In Time-Domain And Its Application In Viscoelastic Displacement Field Analysis

For various viscoelastic materials used in engineering,take concrete,polymer and composite materials for instance,the fracture problem caused by little cracks existed in the structures should be highly considered.Because of the aging property of viscoelastic material, the crack could be generated by increase of displacement growing through the period,when the loading is lower than the critical value of elasticity.Thus,the analysis of displacement field is significant for viscoelastic materials.It's difficult to obtain analytical solution due to the complexity of space-time coupling for viscoelastic material which has a crack;therefore,effective numerical methods are in great need when the problem is being solved.The precise algorithm in time-domain is conducted in the paper.For a more accurate description of the variables which change over time,they are expanded to power series in discretized time intervals,and an initial boundary value problem with time and space coupled is converted into a series of spatial boundary value problems. Extended finite element method is used in this paper.Through the control of the expansion power,the adaptive calculation in time-domain can be achieved.According to the proposed method in the paper,a numerical validation is shown.Compared with the analytic solution, numerical examples show satisfactory results.This paper is expected to provide a new numerical approach to displacement field analysis of viscoelastic fracture problems,but it is just a beginning,and there are still a lot of works to do. Its application in practice is looked forward to after further research and investigation.