cohesion model asphalt

Purpose

Modelling the normal cohesion force for asphalt-like materials as proposed in the publication from the TU Bergakademie Freiberg.

Syntax

cohesion asphalt

Associated material properties

Global scalars 

bondYoungsModulus ( $Y_b$ ): the Youngs modulus of the bond [Pa]
maxBondStrength ( $s_{max}$ ): maximum bond strength [Pa s]
tsCreateBond ( $t_s$ ): time-step number at which the bonds are initialized [ $\cdot$ ]

Description

The asphalt cohesion model creates a normal force between two bonded particles based on the following relation:

$F_c = k_b \delta_n\qquad if\quad \delta_n \leq 0 F_c = 0\qquad if\quad \delta_n > 0$

where $k_b = 4.0 r_{ave} Y_b$ is the bond stiffness, $r_{ave} = 0.5(r_1 + r_2)$ is average radius of the two particles forming the bond and $\delta_n$ is the particles overlap. As can be seen, the force is purely elastic and acts when the bonded particles are not in contact (i.e., when their overlap is negative).

A bond is formed when two particles come in contact and is broken when the bond strength reaches zero. The bond strength is defined as follows:

$p_{b}(t_i) = p_{b}(t_{i-1}) + k_b \delta_n(t_i) \Delta t$

where $t_i$ is a generic time instant and $\Delta t$ is the DEM time-step.

At the time of creation, the bond strength is initialized to a certain value $p_{b,0}$ and changes over time based on the particles overlap. In case of the particles overlapping ( $\delta_n > 0$ ), the bond strength increases with time, as $k_b \delta_n(t_i) \Delta t > 0$ . The bond strength is capped at a maximum bond strength $p_{b,max} = 4.0 r_{ave} s_{max}$ . When the particles do not overlap anymore ( $\delta_n < 0$ ), the bond strength decreases with time, as $k_b \delta_n(t_i) \Delta t < 0$ . If the bond strength reaches zero, then the bond breaks.

It is possible to initialize the strength of the bonds which are created at a certain instant of time by specifying that time instant via $t_s$ . Note that the time instant needs to be specified as time-step number and that the bonds created at that instant are initialized to the maximum strength, i.e., $p_{b,0} = p_{b,max}$ . All other bonds created during the simulation are initialized to zero, i.e, $p_{b,0} = 0$ .

More information about this model can be found in the publication from TU Bergakademie Freiberg in Section 6.1.3.

Restrictions

Coarse-graining information:

Using coarsegraining in combination with this command might lead to different dynamics or system state and thus to inconsistencies.

Literature

[1] Untersuchungen und modelltechnische Beschreibung heterogener Strukturen aus Bindemittel und Zuschlag : Abschlussbericht des Institut für Geotechnik und des Institutes für Bergbau und Spezialtiefbau über die im Projekt durchgeführten Arbeiten, TU Bergakademie Freiberg, https://doi.org/10.2314/GBV:655187480