Subspring Network Model
The subspring network model is referred to in commands and FISH by the name subspringnetwork
.
Introduction
The subspring network model can be used to simulate unbonded and bonded systems. Like the Spring Network Model, the bonded formulation is based on the Rigid Body Spring Network (RBSN) lattice model introduced by [Bolander1998] based on the work of [Kawai1978].
RBSN is a lattice formulation that can eliminate particlescale heterogeneity and provide elasticallyhomogeneous material behavior in bonded Voronoi block models. [Asahina2015], [Asahina2017], [Rasmussen2018b] and [Rasmussen2022] have expanded the capabilities of RBSN by introducing a fictitious stress scheme capable of generating bondedblock models that directly match the macroscale elastic properties of isotropic, transversely isotropic and bimodular materials without the need for timeconsuming calibrations. [Rasmussen2018a], [Rasmussen2018b] and [Rasmussen2019] applied the RBSN to model hard and anisotropic rocks as well as failure modes of deep underground excavations, including rock fall and spalling. Building on these developments, [Rasmussen2021b] introduced the Hybrid Lattice / Discrete Element Method (Hybrid LDEM), which integrates RBSN into the explicit DEM scheme. This approach is highly effective in bonded block simulations of rocks, allowing accurate control over various aspects of the nonlinear behavior of rocks under compression loading, such as crack initiation and damage stress thresholds. Subsequently, [Rasmussen2022] introduced breakable particles, further expanding the range of macroscale properties that the combined RBSNDEM bondedblock models can reproduce while preserving their simplicity.
Unlike the Spring Network Model, {2 in 2D; 3 in 3D} subcontacts are present. The forcedisplacement law is run independently for each subcontact and subcontact gaps are incrementally tracked; each subcontact can fail independently of the others, similar to the FlatJoint Model formulation. The total contact forces and moments, summed over all subcontacts, are applied to the pieces in contact.
When all subcontacts are bonded, the behavior is identical to the Spring Network Model. In other words, one can effectively remove particlescale heterogeneity in elastic response and match bonded material elastic response without calibration. When a subcontact is not bonded, the fictitious forces are zero for that subcontact, and the unbonded forcedisplacement law is used provided the subcontact gap is less than or equal to zero. All subcontacts have the same stiffnesses, areas, frictional properties, strengths, etc. However, the subcontact forces/moments and gaps may differ between subcontacts.
Behavior Summary
A subspring network bond combines three concepts: incremental forces/moments due to relative motion, the RBSN approach to computing contact stiffnesses/fictitious forces, and subcontacts. The first envisions a bond as a set of elastic springs with constant normal and shear stiffnesses, uniformly distributed over a {rectangular in 2D; circular in 3D} crosssection lying on the contact plane and centered at the subcontact point. Relative motion at the subcontact causes the development of a linear force and moment. The total force and moment, summed over all subcontacts, acts on the two contacting pieces. The RBSN paradigm provides a method to compute contact stiffnesses that are consistent—when bonded—with an elastic material with a target Young’s modulus and zero Poisson’s ratio. If a nonzero Poisson’s ratio is specified then a fictitious force, derived from linear elasticity, is computed and added to the total force to produce the desired Poisson effect for each bonded subcontact. Unlike the Spring Network Model, failure can occur at each subcontact independently. Unbonded or failed subcontacts utilize frictional strength parameters to govern slip with potential dilation and/or healing if the tracked subcontact gap is less than or equal to zero.
ActivityDeletion Criteria
A contact with the subpring network model is active if any subcontact is active. A subcontact is active if it is bonded or if its gap is less than or equal to zero. The forcedisplacement law is skipped for inactive subcontacts.
Contact Stiffness Computation
The subspring network model uses the method outlined here to compute stiffnesses for bonded assemblies. The stiffnesses are stored per unit area, and the subcontact stiffness are uniform.
Fictitious Stress Correction
The subspring network model uses the method outlined here to compute fictitious forces consistent with nonzero Poisson ratio materials. This fictitious force is computed once per contact if any subcontact is bonded, with {1/2 in 2D, 1/3 in 3D} of the value being contributed to the total force for each bonded subcontact. If all subcontacts are unbonded, no fictitious force is computed.
One important aspect of the fictitious force correction is that it requires a stress estimate from the bodies attached to the pieces at each end of the contact. This method was initially developed using Voronoi cells in contact along shared faces. That geometrical arrangement allows for contacts at many orientations around each Voronoi cell. As the stress is computed via the outer product of the contact branch vector and the contact force, having more contacts with diverse orientations provides a more robust estimate of the stress state. Now imagine that contacts exist along the facets of a very elongate {triangle in 2D; tetrahedra in 3D}. The number of contacts will be reduced relative to the Voronoi cell case and some of the contact normals may be nearly coincident, meaning that the body stress may be poorly defined. This can potentially lead to instabilities when bodies with few contacts are bonded and the fictitious force is computed. The subspring network model can automatically detect this condition by assessing the convergence of the associate bodies. If the convergence of either body is greater than a specified value (changed with the sn_conv property) for some number of forcedisplacement law computations (changed with the sn_cntconv property  it is 1 by default, disabling the check), the fictitious force correction is disabled.
Subcontact Area and Geometry
The area associated with each subcontact is {1/2 in 2D; 1/3 in 3D} the total contact area. Unlike in the FlatJoint Model, one cannot control the number of subcontacts. The subcontacts are located on the contact plane. In 2D, the two subcontacts are located on either side of the contact position, at a distance of half the contact length (i.e., assuming a unit thickness). In 3D, the three subcontacts are located at a distance of the radius of an equivalent disk from the contact position, 120 degrees apart (i.e., equally distributed around the contact position). The locations of the subcontacts in 3D depend on the local coordinate system, which is arbitrarily assigned. This means that the 3D subcontacts do not represent the actual contacting surface for touching polyhedra, but are rather a useful abstraction of this area. Numerical experiments with tetrahedral and Voronoi packings demonstrated that this abstraction is capable of producing very similar failure responses to a model where the subcontacts are defined based on the faces in contacts. One ramification of this abstraction is that the subspring network model can be used for contacts between any types of pieces.
Bond State
Each subcontact carries an associated bond state
Individual subcontacts cannot be unbonded, meaning that \(B_{sub}=0\) and \(B_{sub}\ne0\) cannot happen for subcontacts that are part of the same contact. Above corresponds to the case when sn_index is nonzero (i.e., when one is querying the bond state of a specific subcontact). By default, sn_index is zero, meaning that \(B_{sub}\) returns the sum of all subcontact bond states. Take the letters \(U\), \(B\), \(T\) and \(S\) to stand for an unbonded subcontact, a bonded subcontact, a subcontact broken in tension and for a subcontact broken in shear, respectively, as shown in the equation above. Healing is left out of this presentation as it is less common situation. In 2D, the \(B_{0}\) (sn_index = 0) represents:
3D differs due to the number of subcontacts:
The sn_states property returns state strings as in the equations above.
ForceDisplacement Law
Each subcontact has an associated gap, force, moment and failure state. All subcontacts lie on the contact plane. Suppose that the vector from the contact position to the position of subcontact \(sub\), in the local coordinate system, is given by \(\mathbf{r}_{sub}\). The relative displacement increment at the subcontact position is computed as:
where \(\Delta \pmb{θ}\) is the increment of relative rotation and \(\Delta \pmb{δ}\) is the increment of relative displacement of Equation (12) of the i Contact Resolution section. The subcontact relative displacement increment can be decomposed as:
The subcontact gap is incremented as:
The total contact force/moment is the sum of the subcontact forces/moments:
where {\(ns = 2\) in 2D; \(ns = 3\) in 3D}, \(\mathbf{F}_{sub}\) is the force of subcontact \(sub\) and \(\mathbf{M}_{sub}\) is the moment of subcontact \(sub\).
The forcedisplacement law for the subspring network model updates the subcontact force and moment:
where \(\mathbf{F}_{sub}^{l}\) is a linear force, \(\mathbf{F}_{sub}^{d}\) is a dashpot force, \(\mathbf{F}_{sub}^{f}\) is the fictitious force corresponding to the Poisson effect, and \(\mathbf{M}\) is a linear moment. Take \(\mathbf{F} = \mathbf{F}_{sub}^{l} + \mathbf{F}_{sub}^{f}\) as the total elastic subcontact force, including the Poisson correction. These forces and moments are updated as described below.
The elastic subcontact force is resolved into a normal and shear force:
where \(F_n > 0\) is tension. The subcontact shear force lies on the contact plane and is expressed in the contact plane coordinate system:
The subcontact gap is zero when the contact is created. Specifying the contact force, either directly or using a stress initialization strategy (i.e., ball tractions
or rblock tractions
), initializes the subcontact gap:
where \(g\) is the contact gap, \(k_n\) is the normal stiffness per unit area, \(A\) is the contact area and \(A_{sub} = A / ns\). The reference gap is likewise initialized to the same value if a stress initialization strategy is used; this ensures that the forcedisplacement law continues to be called even if the physical contact gap becomes positive when stresses have been installed.
Subcontact Moment Update
The subcontact moment is updated, when the subcontact is active, via:
where \(\mathbf{k_r}\) is the rotational stiffness per unit area. In 2D the rotational stiffness is a scalar quantity, while in 3D it is given by
where these quantities are defined in Equation (2) of the Spring Network Model section. The subcontact moment update applies when either the contact is bonded or if it is unbonded with \(g_{sub} \le 0\).
Subcontact Force Update  Unbonded Behavior
When unbonded, there is no fictitious (\(\mathbf{F}_{sub}^f = 0\)). The forcedisplacement law is computed for all unbonded subcontacts with \(g_{sub} \le 0\). The force is updated with the following steps.
The normal subcontact force is updated incrementally as:
(14)\[F_n := \max\left(F_n + k_n {\kern 1pt} A_{sub} \Delta \delta _{n,sub} , 0\right)\]Note:
the unbonded behavior cannot sustain tensile normal force,
the normalforce update is always incremental, and
there are no fictitious forces when unbonded.
Update \(\mathbf{F_s}\):
The shear subcontact force \(\mathbf{F_s}\) is first updated with:
(15)\[\mathbf{F_s} := \mathbf{F_s}  k_s {\kern 1pt} A{\kern 1pt} \Delta \pmb{δ} _{\mathbf{s},sub}\]Enforce the subcontact slip criteria:
If the critical slip distance, \(c^{dc}\), is not specified, nor any entries in the cohesion table, a Coulomb friction criterion is enforced on the subcontact shear force such that:
(16)\[\begin{split}\mathbf{F_s} = \left\{ \begin{array}{rl} \mathbf{F_s} , & \ \mathbf{F_s} \ \le  \mu F_n \\  \mu F_n \bigl( \mathbf{F_s} / \ \mathbf{F_s} \ \bigr), & \mbox{otherwise.} \end{array} \right.\end{split}\]The subcontact slip state is updated as:
(17)\[\begin{split}s_{sub} = \left\{ \begin{array}{rl} \mbox{true}, & \ \mathbf{F_s} \ =  \mu F_n \\ \mbox{false}, & \mbox{otherwise.} \end{array} \right.\end{split}\]If the subcontact slip state is true, then the subcontact is sliding. The entire contact is sliding if all active subcontacts are sliding.
If \(c^{dc}\) is specified then the shear displacement is tracked and the shear force is linearly interpolated from the peak value to \( \mu F_n \bigl( \mathbf{F_s} / \ \mathbf{F_s} \ \bigr)\) when the shear displacement achieves \(c^{dc}\). If multiple entries are specified in the cohesion table, the shear force is linearly interpolated between entries based on the displacement where entries are multiplicative factors on the failure strength. If healing is specified, then once sliding ceases the shear strength instantaneously recovers to its peak value and the subcontact is in a bonded state where it cannot sustain tension but can sustain shear.
If slipping, subcontact dilation may occur. Dilation occurs until the total shear displacement reaches \(u_{cs}\), at which time it ceases. The increment of shear displacement over a timestep adds a normal force to the subcontact in the form
(18)\[F_n = F_n + k_n {\kern 1pt} A{\kern 1pt} \tan (\psi \pi /180 ) \lVert \Delta \pmb{δ}_{\mathbf{s},sub} \rVert\]where \(\psi\) is the dilation angle in degrees.
Update the subcontact dashpot forces:
The subcontact dashpot force is updated as in the linear model.
Subcontact Force Update  Bonded Behavior
As mentioned above, the computestiffness
method computes stiffnesses consistent with a zero Poisson’s ratio material. If the target Young’s modulus is uniform throughout the specimen when bonded, elastic heterogeneity can effectively be removed. In addition, specifying a nonzero Poisson’s ratio results in a fictitious stress correction that produces a realistic Poisson effect.
When bonded, the subcontact force is updated with the following steps.
Update \(F_n\) and \(\mathbf{F_s}\) using an incremental formulation:
(19)\[\begin{split}\begin{array}{rl} F_n & := F_n + k_n {\kern 1pt} A_{sub} \Delta \delta _{n,sub} + {F_n}^f/{ns} \\ \mathbf{F_s} & := \mathbf{F_s}  k_s {\kern 1pt} A_{sub}{\kern 1pt} \Delta \pmb{δ} _{\mathbf{s},sub} + \mathbf{{F_s}^f}/{ns} \end{array}\end{split}\]Update the subcontact normal (\(\sigma\), \(\sigma > 0\) is tension) and shear (\(\tau\)) stresses:
(20)\[\begin{split}\begin{array}{l} \sigma = \displaystyle \frac{F_n} {A_{sub}} \\ \tau = \frac{\left\ \mathbf{F_s} \right\}{A_{sub}} \end{array}\end{split}\]The effective subcontact normal stress, \(\sigma_e\), is used for subsequent failure computations, using the pore pressure \(P_p\):
(21)\[\sigma_e = \sigma  P_p\]Update the bond state:
Take the subcontact shear strength \(\tau_c = c  \sigma_c tan \phi\).
If the bond has healed then it cannot sustain tensile stresses (i.e., \(\sigma_c = 0\)) but can sustain shear stresses. If \(\sigma_e > 0\) then the bond breaks in tension (\(B_{sub}=1\)). If \(\tau > \tau_c\) then the bond breaks in shear (\(B_{sub}=2\)).
If the bond is intact (\(B_{sub}=3\)) and the effective normal stress exceeds the bond tensile strength (\(\sigma_e > \sigma_c\)) then the bond breaks in tension (\(B_{sub}=1\)).
If the bond is intact (\(B_{sub}=3\)) and the maximum shear stress exceeds the shear strength (\(\tau > \tau_c\)), then the bond fails in shear (\(B_{sub}=2\)).
Energy Partitions
The subspring network model provides three energy partitions that are updated per subcontact:
strain energy, \(E_{k}\), stored in the linear springs plus the fictitious stress correction;
slip energy, \(E_{\mu }\), defined as the total energy dissipated by frictional slip; and
dashpot energy, \(E_{\beta }\), defined as the total energy dissipated by the dashpots
Keyword 
Symbol 
Description 
Range 
Accumulated 

springnetwork: 


\(E_{k}\) 
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:
(22)\[{\rm E} _{k} =\frac{1}{2} \left( \frac{F_n^{2} }{k_{n}{\kern 1pt} A_{sub}} + \frac{\left\ \mathbf{F_s} \right\ ^{2} }{k_{s} {\kern 1pt} A_{sub}} + \frac{\left\ \mathbf{M_b} \right\ ^{2} }{k_n {\kern 1pt} I ns} + \frac{M_t^{2} }{k_s {\kern 1pt} J ns} \right).\]Update the slip energy:
(23)\[\begin{split}\begin{array}{l} E_{\mu } := E_{\mu} + \Delta E_{\mu}^s \\ {\rm where} \\ \qquad \begin{array}{l} \Delta E_{\mu}^s :=  {\tfrac{1}{2}} \left(\left(\mathbf{F_{s}} \right)_{o} +\mathbf{F_{s}} \right)\cdot \Delta \pmb{δ} _{\mathbf{s},sub}^{\mu } \\ \end{array} \\ {\rm with} \\ \qquad \begin{array}{l} \Delta \pmb{δ} _{\mathbf{s},sub}^{\mu } =\Delta \pmb{δ} _{\mathbf{s},sub} \Delta \pmb{δ} _{\mathbf{s},sub}^{k} =\Delta \pmb{δ} _{\mathbf{s},sub} \left(\frac{\mathbf{F_{s}} \left(\mathbf{F_{s}} \right)_{o} }{k_{s} {\kern 1pt} A_{sub}} \right) \\ \end{array} \end{array}\end{split}\]Update the dashpot energy:
(24)\[E_{\beta } :=E_{\beta }  \mathbf{F}_{sub}^{d} \cdot \left(\dot{\pmb{δ} }{\kern 1pt} {\kern 1pt} \Delta t\right)\]where \(\dot{\pmb{δ} }\) is the relative translational velocity of this equation of the i Contact Resolution section.
Properties
The properties defined by the springnetwork model are listed in the table below for a concise reference; see the i 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 



SpringNetwork Group: 


\(k_n\) 
Normal stiffness [stress/disp./area] 
FLT 
\([0.0,+\infty)\) 
0.0 
YES 
YES 

\(k_s\) 
Shear stiffness [stress/disp./area] 
FLT 
\([0.0,+\infty)\) 
0.0 
YES 
YES 

\(\mu\) 
Friction coefficient [] 
FLT 
\([0.0,+\infty)\) 
0.0 
YES 
YES 

\(g_r\) 
Reference gap [length] 
FLT 
\(\mathbb{R}\) 
0.0 
YES 
NO 

\(\kappa^*\) 
Normaltoshear stiffness ratio [] 
FLT 
\([0.0,+\infty)^*\) 
0.0\(^*\) 
NO 
N/A 
\(\kappa^* \equiv \frac{k_n}{k_s}\) 


\(\mathbf{k_r}\) 
Rotational stiffness [stress/disp./area] 
VEC 
\(\mathbb{R}^3\) 
\(\mathbf{0}\) 
YES 
NO 

\(A\) 
Bond area [length*length] 
FLT 
\((0.0,+\infty)\) 
N/A 
NO 
NO 

\(A\) 
Constant bond area [length*length] 
FLT 
\((0.0,+\infty)\) 
0.0 
YES 
NO 

\(\sigma_c\) 
Tensile strength [stress] 
FLT 
\([0.0,+\infty)\) 
0.0 
YES 
NO 

\(c\) 
Cohesion [stress] 
FLT 
\([0.0,+\infty)\) 
0.0 
YES 
NO 

\(c_{resid}\) 
Residual cohesion [stress] 
FLT 
\([0.0,+\infty)\) 
0.0 
YES 
NO 

\(c^{dc}\) 
Critical slip distance [length] 
FLT 
\([0.0,+\infty)\) 
0.0 
YES 
NO 

Cohesive strength multiplier as a function of shear displacement 
VEC2 
\(\mathbb{R}^2\) 
YES 
NO 


Number of times the convergence limit has been exceeded to deactivate the fictitious force correction [~]. A negative value disables the check. 
INT 
\([0,+\infty)\) 
1 
YES 
NO 


Convergence limit to deactivate the fictitious force correction [~] 
FLT 
\([0.0,+\infty)\) 
1000.0 
YES 
NO 


\(\phi\) 
Friction angle [degrees] 
FLT 
\([0.0,90.0)\) 
0.0 
YES 
NO 

\(\psi\) 
Dilation angle [degrees] 
FLT 
\([0.0,90.0)\) 
0.0 
YES 
NO 

\(u_{cs}\) 
Critical dilation distance [length] 
FLT 
\([0.0,+\infty)\) 
+infty 
YES 
NO 

\(g_{sub}\) 
Incremental gap [disp.] 
FLT 
\((\infty,+\infty)\) 
0 
YES 
NO 
If sn_index is zero, the minimum subcontact gap is returned, otherwise the subcontact gap is returned 


\(h\) 
Healing 
INT 
{0,1} 
0 
YES 
NO 

Subcontact index 
INT 
{0,1,2,3} 
0 
YES 
NO 

\(02/3 \ \mbox{(2D model/3D model)}\) 


\(B_{sub}\) 
Bond state 
INT 
{0,1,2,3,4,5,6,7,8,9} 
0 
NO 
NO 
See equations (2) and (3) of the Bond State section 


Bond state string 
STR 
NO 
NO 

See equations (2) and (3) of the Bond State section 


\(\tau_{c}\) 
Bond shear strength [stress] 
FLT 
\([0.0,+\infty)\) 
0.0 
NO (set via \(c\) and \(\sigma_c\)) 
N/A 

\(\sigma\) 
( ) 
FLT 
\([0.0,+\infty)\) 
0.0 
NO 
N/A 

\(\sigma_e\) 
Effective normal stress at bond periphery [stress] 
FLT 
\([0.0,+\infty)\) 
0.0 
NO 
N/A 

\(\tau\) 
Shear stress at bond periphery [stress] 
FLT 
\((\infty,+\infty)\) 
0.0 
NO 
N/A 

\(\sum \delta _s\) 
Shear displacement [length] 
VEC2 
\(\mathbb{R}^2\) 
\(\mathbf{0}\) 
NO 
N/A 

\(s_{sub}\) 
Slip state [] 
BOOL 
{false,true} 
false 
NO 
N/A 
\(\;\;\;\;\;\;\begin{cases} \mbox{true: slipping} \\ \mbox{false: not slipping} \end{cases}\). If sn_index is zero, true is returned if any subcontact is slipping, otherwise the subcontact slip state is returned 


\(\mathbf{F}_{sub}\) 
Force (contact plane coord. system) 
VEC 
\(\mathbb{R}^3\) 
\(\mathbf{0}\) 
YES 
NO 
\(\left( F_n,F_{ss},F_{st} \right) \quad \left(\mbox{2D model: } F_{ss} \equiv 0 \right)\). If sn_index is zero, the accumulated subcontact force is returned, otherwise the subcontact force is returned 


\(\mathbf{M}_{sub}\) 
Moment (contact plane coord. system) 
VEC 
\(\mathbb{R}^3\) 
\(\mathbf{0}\) 
YES 
NO 
\(\left( M_t,M_{bs},M_{bt} \right) \quad \left(\mbox{2D model: } M_{t} \equiv M_{bt} \equiv 0 \right)\). If sn_index is zero, the accumulated subcontact moment is returned, otherwise the subcontact moment is returned 


\(nd\) 
Offdiagonal computation mode [] 
FLT 
\([0,1]\) 
1 
YES 
NO 

\(\nu\) 
Poisson ratio [] 
FLT 
\([0,+\infty)\) 
0.0 
YES 
NO 

\(\mathbf{F^{p}}_{sub}\) 
Poisson force (contact plane coord. system) 
VEC 
\(\mathbb{R}^3\) 
\(\mathbf{0}\) 
NO 
NO 
If sn_index is zero, the accumulated subcontact fictitious force is returned, otherwise the subcontact fictitious force is returned 


\(P_p\) 
Pore pressure [stress] 
FLT 
\((\infty,+\infty)\) 
0.0 
YES 
NO 
Dashpot Group: 


\(\beta_n\) 
Normal critical damping ratio [] 
FLT 
\([0.0,1.0]\) 
0.0 
YES 
NO 

\(\beta_s\) 
Shear critical damping ratio [] 
FLT 
\([0.0,1.0]\) 
0.0 
YES 
NO 

\(M_d\) 
Dashpot mode [] 
INT 
{0,1,2,3} 
0 
YES 
NO 
\(\;\;\;\;\;\;\begin{cases} \mbox{0: full normal & full shear} \\ \mbox{1: notension normal & full shear} \\ \mbox{2: full normal & slipcut shear} \\ \mbox{3: notension normal & slipcut shear} \end{cases}\) 


\(\mathbf{F^d}_{sub}\) 
Dashpot force (contact plane coord. system) 
VEC 
\(\mathbb{R}^3\) 
\(\mathbf{0}\) 
NO 
NO 
\(\left( F_n^d,F_{ss}^d,F_{st}^d \right) \quad \left(\mbox{2D model: } F_{ss}^d \equiv 0 \right)\). If sn_index is zero, the accumulated subcontact dashpot force is returned, otherwise the subcontact dashpot force is returned 

\(^*\) 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 forcedisplacement calculation. When \(M_l = 0\), the normal component of the linear force is automatically overridden during the next forcedisplacement 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 

springnetwork Group: 


Set 


Assign stiffness without Poisson correction 


\(k_n\) 
FLT 
\([0.0,+\infty)\) 
N/A 
Normal stiffness 


\(\kappa^*\) 
FLT 
\([0.0,+\infty)^*\) 
N/A 
Normaltoshear stiffness ratio 


Bond the contact if \(g_c \in G\) 


\(G\) 
VEC2 
\(\mathbb{R}^2\) 
\((\infty,0]\) 
Gap interval 


Compute stiffnesses with Poisson correction 


\(E\) 
FLT 
\([0.0,+\infty)\) 
N/A 
Young’s modulus 


\(\nu\) 
FLT 
\([0.0,+\infty)^*\) 
N/A 
Poisson ratio 


Unbond the contact if \(g_c \in G\) 


\(G\) 
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 sn_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 deformability
method.
assignstiffness
Assign normal and shear stiffness without the Poisson’s ratio correction. This should be used for assigning notional joint stiffnesses for nonbonded, preexisting joints. This computation is outlined above, except one can specify a different shear stiffness and the rotational stiffnesses are 0.
bond
Activate the bond if the contact gap between the pieces is within the bondinggap 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 sn_mode
is automatically set to 1 (incremental).
computestiffness
Compute stiffnesses to match the target Young’s modulus and Poisson’s ratio. This computation is outlined above.
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 has become active 

1 
C_PNT 
N/A 
Contact pointer 

springnetwork Group: 


Subcontact slip state has changed 

1 
C_PNT 
N/A 
Contact pointer 

2 
INT 
{1,2,3} 
Subcontact index for use with sn_index 

3 
INT 
{0,1} 
slip state 


Subcontact bond has broken 

1 
C_PNT 
N/A 
Contact pointer 

2 
INT 
{1,2} 
Failure mode 

See equations (2) and (3) of the Bond State section 

3 
VEC 
\(\mathbb{R}^3\) 
Vector, in the global coordinate system, from the contact position to the subcontact position 

4 
INT 
{1,2,3} 
Subcontact index for use with sn_index 


All subcontacts have broken 

1 
C_PNT 
N/A 
Contact pointer 

2 
INT 
{2,3,4,5,6} 
Accumulated \(B_{sub}\) 

See equations (2) and (3) of the Bond State section 
Usage and Verification Examples
The example i Rigid Block Model of Tunnel Excavation demonstrates usage of the subspring network contact model for the sequential excavation of a tunnel. Note in that model, sn_cntconv
is set to 10.
Model Summary
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