Nonlinear Viscoelasticity
Development of Nonlinear Viscoelastic Constitutive Model for Asphaltic Materials
Modeling of asphalt and asphalt concrete behavior is complicated by the need to account for nonlinear viscosity, temperature dependency, damage evolution, and the effect of the aggregates. It is widely accepted that asphaltic materials (both asphalt and asphalt concrete) exhibit linear viscosity in the small strain range and that the effect of nonlinearity becomes significant beyond this range. In spite of the nonlinear viscosity exhibited by asphaltic materials, many researchers have approximated its behavior based on the theory of linear viscoelasticity and employed concepts of damage and/or plasticity to account for the nonlinear portion of behavior. In addition, a generalized constitutive model has not yet been proposed that accounts for both linear and nonlinear viscoelastic responses over various temperatures and loading conditions. A nonlinear viscoelastic constitutive model covering both linear and nonlinear range with a single set of material parameter is developed in this study. The premise of the proposed model is that the viscoelasticity of asphaltic materials can be simulated by combining a generalized Maxwell model to handle linear viscosity and a nonlinear damper to model nonlinear viscosity.
The model starts off with a uniaxial version and is then expanded to three-dimensional formulation. To overcome mathematical difficulty caused from nonlinear term of the constitutive equation, a method of time domain numerical integration is introduced for both strain controlled and stress-controlled loading. The response of the model is then calculated from the elemental constitutive relationship of each spring and damper in the mechanical analog. Other factors influencing the behavior of asphaltic materials are temperature dependency and damage. The method of using a shift factor based on time-temperature superposition principle is employed in this study to consider the temperature effect. In addition, since the effect of damage evolution is significant in the deformation of asphalt concrete, a damage parameter is employed within the concept of damage mechanics to account for damage evolution. In addition, a new calibration method tailored to the proposed model is developed. The most important advantage of the suggested calibration process is that all of the viscoelastic material parameters can be calibrated from a single set of constant strain rate tests conducted at several different strain rates, which reduces the number of tests required for material characterization. The ability of the proposed model to represent the behavior of asphalt concrete is verified through the simulation for pure asphalt and asphalt concrete under uniaxial tension, compression, and pure shear loading conditions.
The model starts off with a uniaxial version and is then expanded to three-dimensional formulation. To overcome mathematical difficulty caused from nonlinear term of the constitutive equation, a method of time domain numerical integration is introduced for both strain controlled and stress-controlled loading. The response of the model is then calculated from the elemental constitutive relationship of each spring and damper in the mechanical analog. Other factors influencing the behavior of asphaltic materials are temperature dependency and damage. The method of using a shift factor based on time-temperature superposition principle is employed in this study to consider the temperature effect. In addition, since the effect of damage evolution is significant in the deformation of asphalt concrete, a damage parameter is employed within the concept of damage mechanics to account for damage evolution. In addition, a new calibration method tailored to the proposed model is developed. The most important advantage of the suggested calibration process is that all of the viscoelastic material parameters can be calibrated from a single set of constant strain rate tests conducted at several different strain rates, which reduces the number of tests required for material characterization. The ability of the proposed model to represent the behavior of asphalt concrete is verified through the simulation for pure asphalt and asphalt concrete under uniaxial tension, compression, and pure shear loading conditions.