tangential model asphalt

Purpose

Tangential model with Kelvin and Maxwell spring (example usage: asphalt)

Syntax

tangential burgers_asphalt

Associated material properties

Material properties

maxwellViscosity ( $\eta_m$ ): Viscosity of the Maxwell damper [pressure*time]
kelvinViscosity ( $\eta_k$ ): Viscosity of the Kelvin damper [pressure*time]
maxwellYoungsModulus ( $E_m$ ): Young’s Modulus of the Maxwell spring [pressure]
kelvinYoungsModulus ( $E_k$ ): Young’s Modulus of the Kelvin spring [pressure]

Description

This model can be used in the tangential argument of both particle_contact_model and wall_contact_model. It can only be used in combination with cohesion model asphalt.

This is the tangential part of the contact model as published in the project report. It implements the tangential force that acts between two particles when a bond is present, which is modelled using a Burgers model. A Burgers model consists of a serial combination of a Kelvin and a Maxwell body. The force is given by the second order differential equation

$F_s + \left[ \frac{csk}{ksk} + csm \left(\frac{1}{ksk}+\frac{1}{ksm}\right) \right] \cdot \dot{F}_s + \frac{csk \cdot csm}{ksk \cdot ksm} \cdot \ddot{F}_s = -csm \cdot \dot{u}_s - \frac{csk \cdot csm}{ksk} \cdot \ddot{u}_s$

which is implemented in discretized form. $F_s$ is the force, $u_s$ is the displacement during the last time step. The quantities $ksk = 2r \cdot E_k$ , $ksm = 2r \cdot E_m$ , $csk = 2r \cdot \eta_k$ , $csm = 2r \cdot \eta_m$ are related to the material properties.

Coarse-graining information:

Using coarsegraining in combination with this command should lead to statistically equivalent dynamics in the system.

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