Viscoelastic functionally graded finite element method with recursive time integration and applications to flexible pavements

Abstract

SUMMARYThe finite-element (FE) method is used for modeling geotechnical and pavement structures exhibiting significant non-homogeneity. Property gradients generated due to non-homogeneous distributions of moisture is one such example for geotechnical materials. Aging and temperature-induced property gradients are common sources of non-homogeneity for asphalt pavements. Investigation of time-dependent behavior combined with functionally graded property gradation can be accomplished by means of the non-homogeneous viscoelastic analysis procedure. This paper describes the development of a generalized isoparametric FE formulation to capture property gradients within elements, and a recursive formulation for solution of hereditary integral equations. The formulation is verified by comparison with analytical and numerical solutions. Two application examples are presented: the first describes stationary crack-tip fields for viscoelastic functionally graded materials, and the second example demonstrates the application of the proposed procedures for efficient and accurate simulations of interfaces between layers of flexible pavement.

IlliTC – low-temperature cracking model for asphalt pavements

“…The code is based on the incremental-recursive formulation proposed by Yi and Hilton (1994) and Zocher, Groves, and Allen (1997). The details on the implementation and formulation have been presented by Dave et al (2012). Due to the non-linear nature of the CZM, the FEA was implemented using a modified Newton-Raphson solution scheme.…”

“…The first task of this module is to develop a FE mesh for the pavement geometry selected by user. The details on the mesh generation were previously discussed by Dave, Paulino, and Buttlar (2012). Briefly, the code generates a FE mesh using four node quadrilateral elements (Q4) and it automatically generates a transition mesh with element sizes increasing as the distance from potential thermal crack increases.…”

Application of Linear Viscoelastic Properties in Semianalytical Finite Element Method with Recursive Time Integration to Analyze Asphalt Pavement Structure

“…As mentioned above, asphalt pavements are inherently viscoelastic structures [28], and it is of great importance for pavement engineers to assess the pavement condition when rutting is considered. Extensive research has been conducted in the area of numerical analysis of viscoelastic problems.…”

Applications of the symplectic method in quasi-static analysis for viscoelastic functionally graded materials

“…Both the inappropriate discretization used for spatial derivation and time integration can result in spurious oscillations, and thus affecting the accuracy of a numerical solution (Aryana et al , 2007). Besides, Dave et al (2012) proposed a “graded element” to model complicated boundary value problems. Chen et al (2015) presented a meshless method to solve two-dimensional quasi-static and transient dynamic problems in continuously heterogeneous and linear viscoelastic media.…”