Christoph Zopf

A continuum mechanical approach to model asphalt

The goal of this paper is to contribute to tire–pavement-interaction analyses from a structural mechanics point of view. The proposed asphalt material model is used to analyse the strain–stress dependencies of an asphalt pavement which is cyclically loaded by a truck tire. For the analysis of tire and pavement as well as its interaction, a finite element approach is utilised. The development of the material model is based on triaxial material tests of cylindrical specimens. The asphalt material is characterised by elastic, viscous (rate-dependent) and plastic behaviour. In order to enable the use of the model also for large deformations within the pavement, it is developed for finite strains. The proposed approach consists of five rheological constitutive branches in parallel. A nonlinear elastic material model is used, which represents the elastic behaviour. The plastic effects are considered by an endochronic frictional element. One Maxwell element and two fractional Maxwell elements represent the viscoelastic behaviour of the model. The consideration of fractional elements is commonly used for the characterisation of cyclicly loaded materials like asphalt. Furthermore, it enables the representation of viscoelastic properties with few material parameters. For the fractional element, a material parameter determines the transition of the rheological elements features between spring () and dashpot (). The proposed model is finally considered within a simulation of a pavement at transient cyclic tire loading. Hence, the increase of the pavement deformation after each load cycle is obtained. Taking this result into account, the long-term behaviour of asphalt pavement is extrapolated and the development of rutting is computed in dependency on the number of load cycles.

Numerical modelling of tyre–pavement-interaction phenomena: constitutive description of asphalt behaviour based on triaxial material tests

As basis for the subsequent numerical modelling of tyre–pavement-interaction phenomena, an adequate representation of asphalt material behaviour is required. Therefore, in the present publication, experimental investigations by the repeated load triaxial test and a new approach of the interpretation of the test results are presented. Based on these results, an appropriate asphalt material model that considers elastic, viscous as well as plastic properties and that allows for large strain theory is selected for the numerical modelling by finite element method. The related material parameters are identified based on the experimental data by an optimisation procedure. Exemplarily, the numerical simulation of data points of the Cole–Cole-plot and the computation of an asphalt test sample in triaxial stress state are conducted. The comparison of experimental and numerical results shows good agreement. Therefore, the material model and the parameters may be used subsequently for structural pavement computations.

A novel method for constitutive characterization of the mechanical properties of uncured rubber

A novel constitutive characterization method for uncured rubber behaviour has been developed in this article. A systematic measuring procedure was designed to fully investigate the uncured rubber complex stress–strain behaviour under different deformation patterns, which integrated three kinds of tests – the uniaxial tensile, the compression test and the shear test. It can be found from the observed behaviour that the uncured rubber has similar but much pronounced non-elastic stress–strain relationship, which is highly non-linear and highly rate dependent. A generalized Maxwell model with modified Yeoh model is developed to constitutively describe the observed phenomena in which parameters are identified by an evolution optimization scheme. Good agreement can be found between the model and the test data. Another finding is that, similar to vulcanized rubber, multi-test data are needed to obtain compatible constitutive models. The test results, findings and the developed model help rubber engineers deeply understand the uncured rubbers mechanical behaviour and provide a base for rubber manufacturing simulation.