Transient dynamic impact of inelastic solids with rough surfaces
|Bearbeitung:||Prof. Dr.-Ing. Udo Nackenhorst, M.Sc. Anuwat Suwannachit|
|Förderung durch:||This work is supported by German Research Foundation (DFG)|
In this project a simulation technique for transient dynamic impact between tire tread rubber and rough road surface is developed. A finite-strain viscoelastic damage model in [Proj. AS] is used for the constitutive description of tread rubber. Different from the others, the model can build up a consistent connection between inelastic effects at low frequencies, such as large viscoelastic deformations and Mullins effect, and the frequency-dependent damping behavior which is predominant in high-frequency domain. The constitutive model has been well established in finite element environment and in addition allows for the computation of complex modulus under arbitrary static pre-deformation.
|Figure 1: Real road surface||Figure 2: Reconstructed surface texture using inverse 2D-FFT|
For the modeling of contact the road surface is assumed to be rigid and fixed in space. To reduce the computational effort by avoiding the discretization of entire road surface texture, we introduce a new technique for the characterization of road surface in a closed form using an inverse computation of 2D-Fast Fourier Transform. A good agreement between the measurement data and reconstructed surface is depicted in figure 1. The contact-stabilized Newmark scheme suggested by Deuflhard et al. is used for time integration. With the fully implicit treatment of contact contribution the problem of “energy blow-up” can be avoided. Moreover, an artificial oscillation in contact force arising from an interplay between space and time discretization has also been removed.
Figure 2: Force-displacement diagram
For the numerical test, a tread block is pressed against the road surface with a time-dependent displacement function applied on the top surface. The identified constitutive parameters in the recent publication [Suwannachit&Nackenhorst, 2010] are used for the tread model. The resulting vertical reaction forces and contact forces during two load cycles are presented in figure 2 and 3, respectively. Effects of viscous dissipation and damage, as well as the smooth behavior of contact forces, are obtained. Snapshots of contact pressure (nodal projection) and stress distribution are illustrated in figure 4 and 5. Obviously, only the peaks of surface asperities carry the load and extremely large contact pressure is found on this area.
Figure 3: Development of contact forces
|Figure 4: Contact pressure distribution [MPa] at maximum deformed state during the second load cycle||Figure 5: Von Mises stress [MPa] at maximum deformed state during the second load cycle|