Soft-Bond Model
The soft-bond model is referred to in commands and FISH by the name softbond.
Introduction
The soft-bond model can be used to simulate both unbonded and bonded systems.
In an unbonded state, it behaves essentially similar to the contact model proposed by [Jiang2015a], providing the ability to transmit both a force and a moment at the contact point, with frictional strength parameters limiting the shear force, bending moment and twisting moment.
In its bonded formulation, the behavior is similar to that of a linear parallel bond model, with the possibility for the bond to fail if the bond strength is exceeded either in shear or in tension. However, contrary to the linear parallel bond model, the bond is not removed upon failure. Instead, it may enter into a softening regime until the bond stress reaches a threshold value at which the bond is removed and considered broken. The slope and tensile breakage strength during softening can be specified by the user (via the softening factor and the softening tensile strength factor, respectively). Another difference with the linear parallel bond model is that only one set of stiffnesses is used for both the unbonded and bonded formulations. This behavior is essentially similar to that proposed by [Ma2018], with the difference that the bond elongation used to update the normal stress in the softening regime accounts for both the normal displacement and bending increments.
Behavior Summary
A soft-bond contact can be envisioned as a set of elastic springs with constant normal and shear stiffnesses, uniformly distributed over a {rectangular in 2D; circular in 3D} cross-section lying on the contact plane and centered at the contact point. Relative motion at the contact causes a force and moment that act on the two contacting pieces to develop. The maximum normal and shear stresses at the bond periphery are tracked. The bond can be inactive or active. If the bond is inactive, then frictional-strength parameters limit the shear force and moment (but not the normal force). If the bond is active, then it can break in shear or soften before breaking in tension: (a) if the maximum shear stress exceeds the shear strength, then the bond breaks, (b) if the maximum normal stress exceeds the tensile strength, then the bond may soften until the maximum normal stress reaches some fraction (that may be zero) of the tensile strength, at which point, the bond breaks. The bond becomes inactive after it breaks.
Activity-Deletion Criteria
A contact with the soft bond model is active if it is bonded or if the surface gap is less than or equal to zero. The force-displacement law is skipped for inactive contacts.
Force-Displacement Law
The force-displacement law for the soft-bond model updates the contact force and moment:
where \(\mathbf{F}\) is the linear force, \(\mathbf{F^{d}}\) is the dashpot force, and \(\mathbf{M}\) is the moment. These forces and moments are updated as described below.
The linear force is resolved into a normal and shear force, and the moment is resolved into a twisting and bending moment:
where \(F_n > 0\) is tension. The shear force and bending moment lie on the contact plane and are expressed in the contact plane coordinate system:
The cross-sectional properties of the soft-bond contact are updated as:
(4)\[\begin{split}\begin{array}{l} R = \lambda \left\{ \begin{array}{rl} \min\left( R^{(1)}, R^{(2)} \right), & \mbox{ball-ball} \\ R^{(1)}, & \mbox{ball-facet} \end{array} \right. \\[3mm] A = \left\{ \begin{array}{rl} 2 R t, & \mbox{2D $(t = 1)$} \\ \pi R^2, & \mbox{3D} \end{array} \right. \\[3mm] I = \left\{ \begin{array}{rl} \tfrac{2}{3} t R^3, & \mbox{2D $(t = 1)$} \\ \tfrac{1}{4} \pi R^4, & \mbox{3D} \end{array} \right. \\[3mm] J = \left\{ \begin{array}{rl} 0, & \mbox{2D} \\ \tfrac{1}{2} \pi R^4, & \mbox{3D} \end{array} \right. \end{array}\end{split}\]
where \(A\) is the cross-sectional area, \(I\) is the moment of inertia of the cross section (about the line passing through \(\mathbf{x_{c}}\) and in the direction of \(\mathbf{M_b}\)), and \(J\) is the polar moment of inertia of the cross section (about the line passing through \(\mathbf{x_{c}}\) and in the direction of \(\hat{\mathbf{n}}_\mathbf{c}\)). The cross section is {rectangular in 2D; circular in 3D}. The property user_area can be used to specify a different cross-sectional area that remains constant, independent of the piece geometries.
The forces and moment are updated as described below for the unbonded or bonded soft-bond contact model.
Unbonded Behavior
When unbonded, the forces and moment are updated with the following steps.
Update \(F_n\) based on the normal-force update mode \(M_l\):
If \(M_l=0\) (absolute update), the normal force is computed as:
(5)\[\begin{split}F_n = \left\{ \begin{array}{rl} k_n A g_s, & g_s < 0 \\ 0 , & \mbox{otherwise} \end{array} \right.\end{split}\]where \(g_s\) is the surface gap (opposite of the overlap).
If \(M_l=1\) (incremental update), the normal force is computed as:
(6)\[F_n := \min\left(F_n + k_n {\kern 1pt} A \, \Delta \delta _n, 0\right)\]where \(\Delta \delta _n\) is the relative normal-displacement increment of Equation (12) of the “Contact Resolution” section.
Note that the unbonded behavior cannot sustain tensile normal force.
Update \(\mathbf{F_s}\):
The shear force \(\mathbf{F_s}\) is first updated with:
(7)\[\mathbf{F_s} := \mathbf{F_s} - k_s {\kern 1pt} A{\kern 1pt} \Delta \pmb{δ} _\mathbf{s}\]where \(\Delta \pmb{δ}_\mathbf{s}\) is the relative shear-displacement increment of :Equation (12) of the “Contact Resolution” section.
Update \(M_t\):
(8)\[\begin{split} M_t := \left\{ \begin{array}{rl} 0, & \mbox{2D} \\ M_t - k_s J \Delta \theta_t, & \mbox{3D} \end{array} \right.\end{split}\]where \(\Delta \theta _{t}\) is the relative twist-rotation increment of Equation (12) of the “Contact Resolution” section.
Update \(\mathbf{M_b}\):
(9)\[\mathbf{M_b} := \mathbf{M_b} - k_n {\kern 1pt} I{\kern 1pt} \Delta \pmb{θ}_\mathbf{b}\]where \(\Delta \pmb{θ}_\mathbf{b}\) is the relative bend-rotation increment of Equation (12) of the “Contact Resolution” section.
Enforce the slip criteria.
A Coulomb friction criterion is enforced on the shear force such that
(10)\[\begin{split}\mathbf{F_s} = \left\{ \begin{array}{rl} \mathbf{F_s} , & \| \mathbf{F_s} \| \le - \mu F_n \\ - \mu F_n \bigl( \mathbf{F_s} / \| \mathbf{F_s} \| \bigr), & \mbox{otherwise.} \end{array} \right.\end{split}\]The shear slip state is updated as
(11)\[\begin{split}s = \left\{ \begin{array}{rl} \mbox{true}, & \| \mathbf{F_s} \| = - \mu F_n \\ \mbox{false}, & \mbox{otherwise.} \end{array} \right.\end{split}\]Maximum bending and twisting moment criteria are enforced as
(12)\[\begin{split} \begin{array}{l} \mathbf{M_b} = \left\{ \begin{array}{rl} \mathbf{M_b} , & \| \mathbf{M_b} \| \le M_b^*\\ M_b^* \bigl( \mathbf{M_b} / \| \mathbf{M_b} \| \bigr), & \mbox{otherwise.} \end{array} \right. \\ M_t = \left\{ \begin{array}{rl} M_t , & \|M_t\| \le M_t^* \\ M_t^* \bigl( M_t / \|M_t\| \bigr), & \mbox{otherwise.} \end{array} \right. \end{array}\end{split}\]where the critical bending and twisting moments are
(13)\[\begin{split}\begin{array}{l} M_b^* & = - 2.1 \lambda_b F_n R {\kern 1pt} / {\kern 1pt} 4 \\ M_t^* & = - 0.65 \lambda_t \mu F_n * R \end{array}\end{split}\]and \(\lambda_b\) and \(\lambda_t\) are respectively the bending and twisting friction multiplier, that default to 1. The critical bending and twisting moments with \(\lambda_b=1\) and \(\lambda_t=1\) correspond to the values proposed by [Jiang2015a].
The bend and twist slip states are updated as
(14)\[\begin{split}\begin{array}{rl} s_b = \left\{ \begin{array}{rl} \mbox{true}, & \| \mathbf{M_b} \| = M_b^* \\ \mbox{false}, & \mbox{otherwise.} \end{array} \right. \\ s_t = \left\{ \begin{array}{rl} \mbox{true}, & \| \mathbf{M_t} \| = M_t^* \\ \mbox{false}, & \mbox{otherwise.} \end{array} \right. \\ \end{array}\end{split}\]Whenever the shear, bend, or twist slip states change, the slip_change callback event occurs where the first argument is the contact pointer, the second argument is an integer ranging from 1 to 7 denoting which slip state(s) has(have) changed, and 3 additional arguments holding the current values of the shear, bend, and twist slip states.
Update the dashpot forces:
The dashpot force is updated as in the linear model.
Bonded Behavior
The bonded behavior of the soft-bond model is like that of the linear parallel bond model when the tensile-softening factor \(\zeta = 0\) or the tensile strength reduction factor \(\gamma = 1\). Softening behavior in tension can occur when \(\zeta \neq 0\) and \(\gamma \neq 1.0\). Softening applies only to the extension response; the shear response does not soften. Once the maximum normal stress at the bond periphery is exceeded during extension, the normal stress is not automatically set to 0 as in the linear parallel bond model. Instead, the normal stress is reduced with continued extension past the tensile strength. Softening continues until the normal stress during extension is less than the product of \(\gamma\) and the tensile strength. Thus, when \(\gamma = 0\), tensile softening occurs until the normal stress reaches 0 during extension. The rate at which softening occurs is governed by the tensile-softening factor \(\zeta\). This behavior is inspired by the model of [Ma2018], although the soft-bond behavior is different in a number of ways.
When bonded, the forces and moment are updated with the following steps.
Update \(F_n\) and \(\mathbf{F_s}\) using an incremental formulation:
(15)\[\begin{split}\begin{array}{rl} F_n & := F_n + k_n {\kern 1pt} A \Delta \delta _n \\ \mathbf{F_s} & := \mathbf{F_s} - k_s {\kern 1pt} A{\kern 1pt} \Delta \pmb{δ} _\mathbf{s} \end{array}\end{split}\]where \(\Delta \delta _n\) and \(\Delta \pmb{δ}_\mathbf{s}\) are respectively the relative normal-displacement and shear-displacement increments of Equation (12) of the “Contact Resolution” section.
Update \(\mathbf{M_b}\) and \(M_t\):
(16)\[\begin{split}\begin{array}{rl} \mathbf{M_b} & := \mathbf{M_b} - k_n {\kern 1pt} I{\kern 1pt} \Delta \pmb{θ}_\mathbf{b} \\ M_t & := \left\{ \begin{array}{rl} 0, & \mbox{2D} \\ M_t - k_s J \Delta \theta_t, & \mbox{3D} \end{array} \right. \end{array}\end{split}\]where \(\Delta \pmb{θ}_\mathbf{b}\) and \(\Delta \theta _{t}\) are respectively the relative bend-rotation and twist-rotation increments of Equation (12) of the “Contact Resolution” section.
Update the maximum normal (\(\sigma\), \(\sigma > 0\) is tension) and shear (\(\tau\)) stresses at the bond periphery:
(17)\[\begin{split}\begin{array}{l} \sigma = \displaystyle \frac{F_n} {A} + \beta \frac{\left\| \mathbf{M_b} \right\| R}{I} \\ \tau = \frac{\left\| \mathbf{F_s} \right\|}{A} + \left\{ \begin{array}{rl} 0, & \mbox{2D} \\ \beta \frac{\left| M_t \right| R}{J}, & \mbox{3D} \end{array} \right. \\ \mbox{with }\quad \beta \in [0, 1]. \end{array}\end{split}\]
Update the bond state:
If the bond is intact (\(B=3\)) and the maximum normal stress at bond periphery exceeds the bond tensile strength (\(\sigma > \sigma_c\)), then the bond enters in softening regime (\(B=4\)), and the maximal bond elongation is set to:
(18)\[\begin{split}\begin{array}{l} l^*= l_c (1.0 + \zeta) \\ \mbox{with } l_c = \displaystyle\frac{F_n} {k_n A} + \beta \frac{\left\| \mathbf{M_b} \right\| R}{k_n I} \end{array}\end{split}\]
where \(l_c\) is the critical bond elongation (at peak strength) and \(\zeta\) is the bond softening factor.
If the bond is in softening regime (\(B=4\)), then the normal stress at bond periphery is checked against the softening envelope as follows.
The maximum stress is given by:
(19)\[\sigma^* = \displaystyle\frac{\sigma_c (l^*-l) }{ \zeta l_c}\]where the current bond elongation \(l\) is given by:
(20)\[l = l_c + \delta l + R |\pmb{\delta θ}_\mathbf{b}|\]where \(\delta l\) is a measure of the bond elongation since softening started:
(21)\[\delta l := \delta l + \Delta \delta _n\]and \(|\pmb{\delta θ}_\mathbf{b}|\) is a measure of the accumulated bending since softening started.
If the current tensile stress is greater than \(\sigma^*\), then it is projected back on the softening envelope, otherwise the bond enters in compression:
(22)\[\begin{split}\begin{array}{l} \mbox{if } \sigma \ge \sigma^* \qquad \mbox{ then} \\ \qquad \left\{ \begin{array}{l} F_n & := F_n {\kern 1pt} \left(\sigma^* / \sigma \right) \\ \mathbf{M_b} & := \mathbf{M_b} {\kern 1pt} \left(\sigma^* / \sigma \right) \end{array} \right. \\ \mbox{else } \\ \qquad \left\{ \begin{array}{l} B & = 5 \mbox{ (compression starts)} \\ \sigma_{m} & = \sigma \\ l_m & := l_c + \delta l + R |\pmb{\delta θ}_\mathbf{b}| \end{array} \right. \end{array}\end{split}\]where \(\sigma_{m}\) and \(l_m\) are respectively the tensile stress and elongation at which the bond enters in compression.
If the bond is in softening regime and in compression (\(B=5\)) and the maximum normal stress at bond periphery exceeds the bond tensile strength at which compression initiated, then the bond state is set to be back in softening regime (\(B=4\)) and the tensile force and bending moment are scaled to project the tensile stress on the softening envelope as discussed above.
Check for bond failure:
Tensile failure is first checked if the bond is in softening regime (\(B=4\)):
(23)\[\begin{split}\begin{array}{l} \mbox{if } B=4 \mbox{ and } \sigma \le \sigma_c {\kern 1pt} \gamma \qquad \mbox{ then} \\ \qquad \left\{ \begin{array}{l} B & = 1 \mbox{ (tensile failure)} \\ \mathbf{F} & = \mathbf{0} \\ \mathbf{M} & = \mathbf{0} \end{array} \right. \end{array}\end{split}\]If the bond has not failed in tension, then shear failure is assessed. The shear strength \(\tau_c = c - \sigma \tan \phi\), where \(\sigma = F_n / A\) is the average normal stress acting on the parallel bond cross section. If the shear-strength limit is exceeded \((\tau > \tau_c)\), then break the bond in shear:
(24)\[\begin{split}\begin{array}{l} \mbox{if } \tau > \tau_c \qquad \mbox{ then} \\ \qquad B = 2 \mbox{ (shear failure)} \end{array}\end{split}\]
If the bond has broken, then the bond_break callback event is triggered, and the behavior becomes that of an unbonded soft-bond model.
Energy Partitions
The soft-bond model provides three energy partitions:
strain energy, \(E_{k}\), stored in the linear springs;
slip energy, \(E_{\mu }\), defined as the total energy dissipated by frictional slip;
dashpot energy, \(E_{\beta }\), defined as the total energy dissipated by the dashpots; and
Keyword |
Symbol |
Description |
Range |
Accumulated |
|---|---|---|---|---|
Soft-Bond: |
||||
|
\(E_{k}\) |
strain energy |
\([0.0,+\infty)\) |
NO |
|
\(E_{\mu}\) |
total energy dissipated by slip |
\((-\infty,0.0]\) |
YES |
Dashpot Group: |
||||
|
\(E_{\beta}\) |
total energy dissipated by dashpots |
\((-\infty,0.0]\) |
YES |
If energy tracking is activated (see the model energy command), the energy partitions are updated as described below.
Update the strain energy:
(25)\[{\rm E} _{k} =\frac{1}{2} \left( \frac{F_n^{2} }{k_{n}{\kern 1pt} A} + \frac{\left\| \mathbf{F_s} \right\| ^{2} }{k_{s} {\kern 1pt} A} + \frac{\left\| \mathbf{M_b} \right\| ^{2} }{k_n {\kern 1pt} I} + \frac{M_t^{2} }{k_s {\kern 1pt} J} \right).\]Update the slip energy:
(26)\[\begin{split}\begin{array}{l} E_{\mu } := E_{\mu} + \Delta E_{\mu}^s + \Delta E_{\mu}^b + \Delta E_{\mu}^t \\ {\rm where} \\ \qquad \begin{array}{l} \Delta E_{\mu}^s := - {\tfrac{1}{2}} \left(\left(\mathbf{F_{s}} \right)_{o} +\mathbf{F_{s}} \right)\cdot \Delta \pmb{δ} _\mathbf{s}^{\mu } \\ \Delta E_{\mu}^b := - {\tfrac{1}{2}} \left(\left(\mathbf{M_{b}} \right)_{o} +\mathbf{M_{b}} \right)\cdot \Delta \pmb{\theta} _\mathbf{b}^{\mu } \\ \Delta E_{\mu}^t := - {\tfrac{1}{2}} \left(\left(M_{t} \right)_{o} + M_{t} \right)\cdot \Delta \pmb{\theta} _\mathbf{t}^{\mu } \\ \end{array} \\ {\rm with} \\ \qquad \begin{array}{l} \Delta \pmb{δ} _\mathbf{s}^{\mu } =\Delta \pmb{δ} _\mathbf{s} -\Delta \pmb{δ} _\mathbf{s}^{k} =\Delta \pmb{δ} _\mathbf{s} -\left(\frac{\mathbf{F_{s}} -\left(\mathbf{F_{s}} \right)_{o} }{k_{s} {\kern 1pt} A} \right) \\ \Delta \pmb{\theta} _\mathbf{b}^{\mu } =\Delta \pmb{\theta} _\mathbf{b} -\Delta \pmb{\theta} _\mathbf{b}^{k} =\Delta \pmb{\theta} _\mathbf{b} -\left(\frac{\mathbf{M_{b}} -\left(\mathbf{M_{b}} \right)_{o} }{k_{n} {\kern 1pt} I} \right) \\ \Delta \pmb{\theta} _\mathbf{t}^{\mu } =\Delta \pmb{\theta} _\mathbf{t} -\Delta \pmb{\theta} _\mathbf{t}^{k} =\Delta \pmb{\theta} _\mathbf{t} -\left(\frac{M_{t} -\left(M_{t} \right)_{o} }{k_{s} {\kern 1pt} J} \right) \\ \end{array} \end{array}\end{split}\]Update the dashpot energy:
(27)\[E_{\beta } :=E_{\beta } - \mathbf{F^{d}} \cdot \left(\dot{\pmb{δ} }{\kern 1pt} {\kern 1pt} \Delta t\right)\]where \(\dot{\pmb{δ} }\) is the relative translational velocity of Equation (10) of the “Contact Resolution” section.
Properties
The properties defined by the soft-bond model are listed in the table below for a concise reference; see the “Contact Properties” section for a description of the information in the table columns. The mapping from the surface inheritable properties to the contact model properties is also discussed below.
Keyword |
Symbol |
Description |
Type |
Range |
Default |
Modifiable |
Inheritable |
|---|---|---|---|---|---|---|---|
softbond |
Model name |
||||||
Soft-Bond Group: |
|||||||
kn |
\(k_n\) |
Normal stiffness [stress/length] |
FLT |
\([0.0,+\infty)\) |
0.0 |
YES |
YES |
ks |
\(k_s\) |
Shear stiffness [stress/length] |
FLT |
\([0.0,+\infty)\) |
0.0 |
YES |
YES |
fric |
\(\mu\) |
Friction coefficient [-] |
FLT |
\([0.0,+\infty)\) |
0.0 |
YES |
YES |
sb_bmul |
\(\lambda_b\) |
Bending-friction multiplier [-] |
FLT |
\([0.0,+\infty)\) |
1.0 |
YES |
YES |
sb_tmul |
\(\lambda_t\) |
Twisting-friction multiplier [-] |
FLT |
\([0.0,+\infty)\) |
1.0 |
YES |
YES |
emod |
\(E^*\) |
Effective modulus [force/area] |
FLT |
\([0.0,+\infty)\) |
0.0 |
NO |
N/A |
kratio |
\(\kappa^*\) |
Normal-to-shear stiffness ratio [-] |
FLT |
\([0.0,+\infty)^*\) |
0.0\(^*\) |
NO |
N/A |
\(\kappa^* \equiv \frac{k_n}{k_s}\) |
|||||||
rgap |
\(g_r\) |
Reference gap [length] |
FLT |
\(\mathbb{R}\) |
0.0 |
YES |
NO |
sb_mode |
\(M_l\) |
Normal-force update mode [-] |
INT |
\(\{0,1\}\) |
0 |
YES |
NO |
\(\;\;\;\;\;\;\begin{cases} \mbox{0: update is absolute} \\ \mbox{1: update is incremental} \end{cases}\) |
|||||||
sb_rmul |
\(\lambda\) |
Radius multiplier [-] |
FLT |
\((0.0,+\infty)\) |
1.0 |
YES |
NO |
sb_radius |
\(R\) |
Radius [length] |
FLT |
\((0.0,+\infty)\) |
N/A |
NO (set via \(\lambda\)) |
NO |
sb_area |
\(A\) |
Cross-sectional area |
FLT |
\((0.0,+\infty)\) |
N/A |
NO |
NO |
user_area |
\(A\) |
Cross-sectional area (held constant) |
FLT |
\((0.0,+\infty)\) |
0.0 |
YES |
NO |
sb_ten |
\(\sigma_c\) |
Tensile strength [stress] |
FLT |
\([0.0,+\infty)\) |
0.0 |
YES |
NO |
sb_soft |
\(\zeta\) |
Tensile-softening factor [-] |
FLT |
\([0.0,+\infty)\) |
0.0 |
YES |
NO |
sb_cut |
\(\gamma\) |
Tensile strength reduction factor [-] |
FLT |
\([0.0,1]\) |
1.0 |
YES |
NO |
sb_coh |
\(c\) |
Cohesion [stress] |
FLT |
\([0.0,+\infty)\) |
0.0 |
YES |
NO |
sb_fa |
\(\phi\) |
Friction angle [degrees] |
FLT |
\([0.0,90.0)\) |
0.0 |
YES |
NO |
sb_state |
\(B\) |
Bond state [-] |
INT |
{0,1,2,3,4,5} |
0 |
NO |
NO |
\(\;\;\;\;\;\;\begin{cases} \mbox{0: unbonded} \\ \mbox{1: unbonded & broke in tension} \\ \mbox{2: unbonded & broke in shear} \\ \mbox{3: bonded} \\ \mbox{4: bonded & softening} \\ \mbox{5: bonded & compressing} \end{cases}\) |
|||||||
sb_shear |
\(\tau_{c}\) |
Shear strength [stress] |
FLT |
\([0.0,+\infty)\) |
0.0 |
NO (set via \(c\) and \(\phi\)) |
N/A |
sb_mcf |
\(\beta\) |
Moment-contribution factor [-] |
FLT |
\([0.0,1]\) |
1.0 |
YES |
NO |
sb_sigma |
\(\sigma\) |
Maximum normal stress at bond periphery |
FLT |
\([0.0,+\infty)\) |
0.0 |
NO |
N/A |
sb_tau |
\(\tau\) |
Maximum shear stress at bond periphery |
FLT |
\([0.0,+\infty)\) |
0.0 |
NO |
N/A |
sb_slip |
\(s\) |
Shear slip state [-] |
BOOL |
{false,true} |
false |
NO |
N/A |
\(\;\;\;\;\;\;\begin{cases} \mbox{true: slipping} \\ \mbox{false: not slipping} \end{cases}\) |
|||||||
sb_slipb |
\(s_b\) |
Bend slip state [-] |
BOOL |
{false,true} |
false |
NO |
N/A |
\(\;\;\;\;\;\;\begin{cases} \mbox{true: slipping} \\ \mbox{false: not slipping} \end{cases}\) |
|||||||
sb_slipt |
\(s_t\) |
Twist slip state [-] |
BOOL |
{false,true} |
false |
NO |
N/A |
\(\;\;\;\;\;\;\begin{cases} \mbox{true: slipping} \\ \mbox{false: not slipping} \end{cases}\) |
|||||||
sb_force |
\(\mathbf{F}\) |
Force (contact plane coord. system) |
VEC |
\(\mathbb{R}^3\) |
\(\mathbf{0}\) |
YES |
NO |
\(\left( -F_n,F_{ss},F_{st} \right) \quad \left(\mbox{2D model: } F_{ss} \equiv 0 \right)\) |
|||||||
sb_moment |
\(\mathbf{M}\) |
Moment (contact plane coord. system) |
VEC |
\(\mathbb{R}^3\) |
\(\mathbf{0}\) |
YES |
NO |
\(\left( M_t,M_{bs},M_{bt} \right) \quad \left(\mbox{2D model: } M_{t} \equiv M_{bt} \equiv 0 \right)\) |
|||||||
Dashpot Group: |
|||||||
dp_nratio |
\(\beta_n\) |
Normal critical damping ratio [-] |
FLT |
\([0.0,1.0]\) |
0.0 |
YES |
NO |
dp_sratio |
\(\beta_s\) |
Shear critical damping ratio [-] |
FLT |
\([0.0,1.0]\) |
0.0 |
YES |
NO |
dp_mode |
\(M_d\) |
Dashpot mode [-] |
INT |
{0,1,2,3} |
0 |
YES |
NO |
\(\;\;\;\;\;\;\begin{cases} \mbox{0: full normal & full shear} \\ \mbox{1: no-tension normal & full shear} \\ \mbox{2: full normal & slip-cut shear} \\ \mbox{3: no-tension normal & slip-cut shear} \end{cases}\) |
|||||||
dp_force |
\(\mathbf{F^d}\) |
Dashpot force (contact plane coord. system) |
VEC |
\(\mathbb{R}^3\) |
\(\mathbf{0}\) |
NO |
NO |
\(\left( -F_n^d,F_{ss}^d,F_{st}^d \right) \quad \left(\mbox{2D model: } F_{ss}^d \equiv 0 \right)\) |
|||||||
\(^*\) By convention, \(\kappa^*\) equals zero if either normal or shear stiffness is zero. |
|||||||
Note
Modifying the contact model force will not alter forces accumulated to the bodies. Therefore, any change to \(\mathbf{F^l}\) or \(\mathbf{M}\) may only be effective during the next force-displacement calculation. When \(M_l = 0\), the normal component of the linear force is automatically overridden during the next force-displacement calculation.
Surface Property Inheritance
The linear stiffnesses, \(k_n\) and \(k_s\), and the friction coefficient, \(\mu\), may be inherited from the contacting pieces. See this section from the linear formulation for details on property inheritance.
Methods
Method |
Arguments |
Symbol |
Type |
Range |
Default |
Description |
|---|---|---|---|---|---|---|
Soft-Bond Group: |
||||||
area |
Set user_area to sb_area |
|||||
deformability |
Set deformability |
|||||
emod |
\(E^*\) |
FLT |
\([0.0,+\infty)\) |
N/A |
Effective modulus |
|
kratio |
\(\kappa^*\) |
FLT |
\([0.0,+\infty)^*\) |
N/A |
Normal-to-shear stiffness ratio |
|
bond |
Bond the contact if \(g_c \in G\) |
|||||
gap |
\(G\) |
VEC2 |
\(\mathbb{R}^2\) |
\((-\infty,0]\) |
Gap interval |
|
soft |
\(\zeta\) |
FLT |
\([0.0,+\infty)\) |
\(0.0\) |
Softening parameter |
|
cut |
\(\gamma\) |
FLT |
\([0.0,1.0]\) |
\(1.0\) |
Softening threshold parameter |
|
unbond |
Unbond the contact if \(g_c \in G\) |
|||||
gap |
\(G\) |
VEC2 |
\(\mathbb{R}^2\) |
\((-\infty,0]\) |
Gap interval |
|
\(^*\) By convention, setting \(\kappa^*\) equal to zero sets the shear stiffness to zero but does not modify the normal stiffness. |
||||||
Area
Set the user_area property via the current sb_area. This operation means that the contact area stays constant and is fixed independent of changes to the piece sizes/geometries. In order for the stiffnesses to be recomputed accounting for this area, one should subsequently call the deformabilty method.
Deformability
The deformability can be specified with the deformability method, which sets
The first term in this expression is obtained by equating the normal stiffness to the axial stiffness of the volume of material shown in this figure of the linear model formulation.
Bond
Activate the bond if the contact gap between the pieces is within the bonding-gap interval.
If no gap is specified, then the bond is activated if the pieces overlap.
A single value can be specified with the gap keyword corresponding to the maximum gap.
One can ensure the existence of contacts between all pieces with a contact gap less than a specified bonding gap \((g_b)\) by specifying \(g_b\) with the proximity in the contact cmat default command of the Contact Model Assignment Table (CMAT). If the bond is activated, then the normal force calculation mode sb_mode is automatically set to 1 (incremental).
Unbond
Deactivate the bond if the contact gap between the pieces is within the gap interval. If no gap is specified, then the bond is deactivated if the pieces overlap. A single value can be specified with the gap keyword corresponding to the maximum gap. If the bond is deactivated, then the bond state becomes unbonded \((B=0)\). The force and moment are unaffected and will be updated during the next cycle.
Callback Events
Event |
Array Slot |
Value Type |
Range |
Description |
|---|---|---|---|---|
contact_activated |
Contact has become active |
|||
1 |
C_PNT |
N/A |
Contact pointer |
|
Soft-Bond Group: |
||||
slip_change |
Slip state has changed |
|||
1 |
C_PNT |
N/A |
Contact pointer |
|
2 |
INT |
{1,7} |
Slip change mode |
|
\(\;\;\;\;\;\;\begin{cases} \mbox{1: shear slip state has changed} \\ \mbox{2: bend slip state has changed} \\ \mbox{3: twist slip state has changed} \\ \mbox{4: shear & bend slip states have changed} \\ \mbox{5: shear & twist slip states have changed} \\ \mbox{6: bend & twist slip states have changed} \\ \mbox{7: all slip states have changed} \end{cases}\) |
||||
3 |
INT |
{0,1} |
shear slip state |
|
4 |
INT |
{0,1} |
twist slip state |
|
5 |
INT |
{0,1} |
bend slip state |
|
bond_break |
Bond has broken |
|||
1 |
C_PNT |
N/A |
Contact pointer |
|
2 |
INT |
{1,2} |
Failure mode |
|
\(\;\;\;\;\;\;\begin{cases} \mbox{1: failed in tension} \\ \mbox{2: failed in shear} \end{cases}\) |
||||
3 |
FLT |
\([0.0,+\infty)\) |
Failure strength [stress] (\(\sigma_c\) or \(\tau_c\), according to the failure mode) |
|
4 |
FLT |
\([0.0,+\infty)\) |
Bond strain energy \(\overline{E}_k\) at onset of failure |
|
Usage and Verification Examples
The example “Genesis and Testing of a Soft-Bonded Material” demonstrates usage of the soft-bond contact model.
Model Summary
An alphabetical list of the soft-bond contact model methods is given here. An alphabetical list of the soft-bond contact model properties is given here.
References
| Was this helpful? ... | Itasca Software © 2024, Itasca | Updated: Feb 07, 2025 |
