A Three-Dimensional Finite Element Formulation for Thermoviscoelastic Orthotropic Media

Abstract

SUMMARYThis paper is concerned with the development of a numerical algorithm for the solution of the uncoupled, quasistatic initial/boundary value problem involving orthotropic linear viscoelastic media undergoing thermal and/or mechanical deformation. The constitutive equations, expressed in integral form involving the relaxation moduli, are transformed into an incremental algebraic form prior to development of the ÿnite element formulation. This incrementalization is accomplished in closed form and results in a recursive relationship which leads to the need of solving a simple set of linear algebraic equations only for the extraction of the ÿnite element solution. Use is made of a Dirichlet-Prony series representation of the relaxation moduli in order to derive the recursive relationship and thereby eliminate the storage problem that arises when dealing with materials possessing memory. Three illustrative example problems are included to demonstrate the method.

Computational Constitutive Model for Predicting Nonlinear Viscoelastic Damage and Fracture Failure of Asphalt Concrete Mixtures

“…In an attempt to place the viscoelastic constitution into a computational finite-element model, it must be incrementalized so that the history dependence is retained at each time step. A more detailed description of the numerical implementation for viscoelastic media can be found in a study by Zocher et al (1997).…”

Damage-Induced Modeling of Asphalt Mixtures through Computational Micromechanics and Cohesive Zone Fracture

“…A more detailed description of the numerical implementation can be found elsewhere (Zocher et al 1997;Seidel 2002).…”

Method for Performing Accelerated Characterization of Viscoelastic Constitutive Behavior of Asphaltic Concrete

“…The second author and coworkers at Texas A&M University have developed a finite-element algorithm that can be used to predict the response of thermoviscoelastic asphaltic roadways to arbitrary quasi-static mechanical and thermal loading, including cyclic loadings (Allen et al 1994;Zocher et al 1997). Therefore, the characterization of the material properties described above constitutes a significant impediment to modeling the predicted response of an asphaltic roadway.…”

“…Unfortunately, computational algorithms that use viscoelastic material properties are generally more convenient to construct when a strain formulation is used such as that described in constitutive Equation (3) (Allen et al 1994;Zocher et al 1997). Therefore, it is usually necessary to convert the experimentally determined creep compliances to relaxation moduli.…”