cohesion model fiber

Purpose

Basic contact model for fibers

Syntax

cohesion fiber [other model_type/model_name pairs as described here ] general_keyword general_value

zero or more general_keyword/general_value pairs may be appended to the end (using the settings keyword)

keep_original_shape general_value = 'on' or 'off'
    on = fibers will attempt to return to their original shape
    off = fibers will attempt to return to a straightened form [default]

Associated material properties

Material properties

fiberStiffnessYM ( $Y_f$ ): The Youngs Modulus of a fiber material, i.e. its stiffness [pressure]
fiberPoissonsRatio ( $\nu_f$ ): The Poisson’s ratio, i.e. the ratio of transverse to axial strain, of the fiber [ $\cdot$ ]

Material interaction properties

fiberNormalDampingRatio ( $D_n$ ): The damping ratio in normal direction [ $\cdot$ ]
fiberTangentialDampingRatio ( $D_t$ ): The damping ratio in tangential direction [ $\cdot$ ]
maxDistanceBond ( $s_{max}$ ): The maximum separation distance of two particles in a fiber [length]

Description

This model can be used as part of a particle_contact_model.

The current implementation creates the bond with zero forces and torques between the bonded particles. Due to relative motion forces and torques will act on the particles, where the normal force $F_n$ and the tangential force $F_t$ are calculated explicitly:

$F_n = k_n (s_0 - s) - d_n v_n F_t = k_t s_t - d_t v_t$

with the stiffness coefficient $k$ , the damping coefficient $d$ ,the relative velocity $v$ , the initial distance $s_0$ , and the current distance $s$ . The indices $n$ and $t$ stand for normal and tangential, respectively.

The maximum distance two spheres may have is the maxDistanceBond, $s_{max}$ . Since the centre-point distance between two spheres is used as breakage criterion and also used for bond creation, this value needs to be above the initial distance and below the distance to the next neighbor. Otherwise the bonds would not be created or a bond with the neighbor and the next neighbor would be created.

The stiffness and damping coefficients are calculated from several material properties, namely fiberStiffnessYM, fiberPoissonsRatio, fiberNormalDampingRatio, and fiberTangentialDampingRatio:

$k_n &= Y_f^* A / s_0 k_t &= G_f^* A / s_0 d_n &= 2 D_n \sqrt{k_n m^*} d_t &= 2 D_t \sqrt{k_t m^*}$

where the effective Young’s modulus $Y^*$ and Shear modulus $G^*$ depend on the Young’s modulus $Y$ and the Poisson’s ratio $\nu$ from the material/particle combination (i and j). $m^* = \frac{m_i m_j}{m_i + m_j}$ is the effective mass, and $A$ is the corresction area of the bond, computed as $A = {r^*}^2 \pi$ with $r^* = \frac{r_i r_j}{r_i + r_j}$ being the effective radius. The effective Young´s modulus and Shear modulus are computed as

$\frac{1}{Y_f^*} &= \frac{1-\nu_{f,i}^2}{Y_{f,i}} + \frac{1-\nu_{f,j}}{Y_{f,j}}, \frac{1}{G_f^*} &= \frac{2(2-\nu_{f,i})(1+\nu_{f,i})}{Y_{f,i}} + \frac{2(2-\nu_{f,j})(1+\nu_{f,j})}{Y_{f,j}},$

$D_n$ and $D_t$ are the fiberXXXDampingRatio. In theory, valid values can vary from $0 < D < 1$ underdamped, $D = 1$ critically damped to $D > 1$ overdamped. Due to numerical accuracy the simulated behaviour may be slightly shifted (e.g. still oscillating although $D = 1$ ). In most cases a damping ratio of 1 is a good first starting point. An undamped system $D = 0$ will lead to an unstable system in nearly all cases.

Note

Stronger damping yields to higher forces. To guarantee a stable simulation this may require to lower the time step.

If keep_original_shape is not enabled a fiber will always attempt to relax itself into a completely straight state. If it is enabled then the fiber will try to relax into the state it had upon insertion.

There are also several advanced fiber models which can model plastic deformation or buckling and cohesion between disjoint fibers.

Restrictions

This model cannot be used as a wall contact model.

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