Applied Research Of Symplectic Analytical Singular Element In Quasi-static 2D Linear Viscoelastic Fracture Analysis

Many materials show noticeable time effect in viscoelastic property in room or higher temperature environments.In particular,if structures composed of these materials have cracks or notches which may generate local stress singularity,delayed crack growth may occur in these structures after loaded for a period of time.Delayed fracture failures will occur eventually,and they are extremely dangerous just as fatigue failures.Therefore,studies on viscoelastic fracture problems are of great significance.Numerical methods are effective ways to investigate viscoelastic fracture problems.Since viscoelastic problems are time-varying,they should be analyzed by combining time-domain numerical methods with space-domain ones.In this thesis,by combined with Precise Time-Domain Expansion(PTDE)algorithm or Laplace integral transformation,Symplectic Analytic Singularity Elements(SASEs)are directly extended to analyze quasi-static linear viscoelastic fracture problems.Consequently,we present the high-precision numerical analysis method for the related problems.The main work of this thesis includes:(1)Basic equations of quasi-static viscoelastic problems and two different methods for dealing with the time domain are briefly introduced.Symplectic eigenexpansion solutions for some exsiting planar static elastic problems are sorted out,and then those for two other kinds of bimaterial V-notch problems are derived.These preparatory works lay a foundation for the extended application of SASE to present problems.(2)As for problems of a kind of linear viscoelastic materials with constant poisson ratio,the PTDE algorithm is used to discretize time.A displacement-type recursive scheme,which is more conveniently useful than the existing stress-type recursive scheme,is derived for the first time.The obtained quasi-elastic space boundary value problems in this new scheme are equivalent to standard elastic problems.Consequently,the SASE and the conventional elements,which are constructed in static elastic problems,can be directly applied to numerically solve the viscoelastic fracture problems.The present method shows an advantage that the high-precision viscoelastic displacement field and stress field within the singular element can be obtained via the displacement-type recursive scheme.Furthermore,numerical results of fracture parameters such as the viscoelastic stress intensity factor and the viscoelastic strain energy release rate can be obtained explicitly.(3)As for problems of bimaterial interfacial crack structures and homogeneous material V-notch structures,the Laplace transformation is used to form frequency-domain problems which can be solved by the SASE constructed in static elastic problems.It is the first time to discuss the case that the degree of freedom of the SASE and the number of retained symplectic eigen expanding items are not equal.In the end,numerical results of viscoelastic notch stress intensity factor and viscoelastic strain energy release rate can be obtained via the numerical Laplace inversions.In this thesis,the SASE is effectively extended to numerically analyze the viscoelastic fracture problems.Especially,the SASE used for the viscoelastic fracture problems have the same advantages as that for analyzing the elastic fracture problems.These advantages include that a very large size SASE can be used and fine grids or transition units are totally unnecessary.Besides,the numerical results show that the method presented in this paper is in very high solving accuracy and good numerical stability.Thus,the methods we present are effective means to analyze the linear viscoelastic fracture problems.