Category 9: Stress Equations#
The following conditions provide a means to set boundary conditions for the hyperbolic viscoelastic stress equations
STRESS_DEVELOPED#
BC = STRESS_DEVELOPED SS <bc_id>
Description / Usage#
(SIC/POLYMER_STRESS)
This is a fully developed flow condition from Xie and Pasquali for viscoelastic flows
 <bc_id>
The boundary flag identifier, an integer associated with <bc_type> that identifies the boundary location (side set in EXODUS II) in the problem domain.
Examples#
BC = STRESS_DEVELOPED SS 1
BC = S11_1 NS 7 4.0 1.0
Technical Discussion#
Replaces boundary contributions of stress equations with stress equations where the advective term is removed (\(v\cdot\nabla S \rightarrow 0\))
References#
Xie, Xueying, and Matteo Pasquali. “A new, convenient way of imposing openflow boundary conditions in twoand threedimensional viscoelastic flows.” Journal of nonnewtonian fluid mechanics 122, no. 13 (2004): 159176.
S11#
BC = {bc_name} NS <bc_id> <float1> [float2]
Description / Usage#
(DC/STRESS11)
This Dirichlet boundary condition specification is used to set a constant xxstress for any given mode of the stress tensor. Each such specification is made on a separate input card. Definitions of the input parameters are as follows:
{S11  S11_1  S11_2  S11_3  S11_4  S11_5  S11_6  S11_7} 
Boundary condition name (<bc_name>) that defines the xxstress for a given mode, where: 

S11 
xxcomponent of stress tensor for mode 1 

S11_1 
xxcomponent of stress tensor for mode 2 

S11_2 
xxcomponent of stress tensor for mode 3 

S11_3 
xxcomponent of stress tensor for mode 4 

S11_4 
xxcomponent of stress tensor for mode 5 

S11_5 
xxcomponent of stress tensor for mode 6 

S11_6 
xxcomponent of stress tensor for mode 7 

S11_7 
xxcomponent of stress tensor for mode 8 

NS 
Type of boundary condition (<bc_type>), where NS denotes node set in the EXODUS II database. 

<bc_id> 
The boundary flag identifier, an integer associated with <bc_type> that identifies the boundary location (node set in EXODUS II) in the problem domain. 

<float1> 
Value of xxstress. 

[float2] 
An optional parameter (that serves as a flag to the code for a Dirichlet boundary condition). If a value is present, and is not 1.0, the condition is applied as a residual equation. Otherwise, it is a “hard set” condition and is eliminated from the matrix. The residual method must be used when this Dirichlet boundary condition is used as a parameter in automatic continuation sequences. 
Examples#
Following are sample cards for applying a Dirichlet condition on the xxstress component for mode 2 on node set 7:
BC = S11_1 NS 7 4.0
BC = S11_1 NS 7 4.0 1.0
where the second example uses the “residual” method for applying the same Dirichlet condition.
Technical Discussion#
See the technical discussion for the UVW velocity boundary condition for a discussion of the two ways of applying Dirichlet boundary conditions.
For details of the stress tensor and its use for solving viscoelastic flow problems, please see the viscoelastic flow tutorial (Rao, 2000).
References#
GT014.1: Tutorial for Running Viscoelastic Flow Problems with GOMA, June 21, 2000, R. R. Rao
S12#
BC = {bc_name} NS <bc_id> <float1> [float2]
Description / Usage#
(DC/STRESS12)
This Dirichlet boundary condition specification is used to set a constant xystress (also known as the shear stress) for any given mode of the stress tensor. Each such specification is made on a separate input card. Definitions of the input parameters are as follows:
{S12  S12_1  S12_2  S12_3  S12_4  S12_5  S12_6  S12_7} 
Boundary condition name (<bc_name>) that defines the xystress for a given mode, where: 

S12 
xycomponent of stress tensor for mode 1 

S12_1 
xycomponent of stress tensor for mode 2 

S12_2 
xycomponent of stress tensor for mode 3 

S12_3 
xycomponent of stress tensor for mode 4 

S12_4 
xycomponent of stress tensor for mode 5 

S12_5 
xycomponent of stress tensor for mode 6 

S12_6 
xycomponent of stress tensor for mode 7 

S12_7 
xycomponent of stress tensor for mode 8 

NS 
Type of boundary condition (<bc_type>), where NS denotes node set in the EXODUS II database. 

<bc_id> 
The boundary flag identifier, an integer associated with <bc_type> that identifies the boundary location (node set in EXODUS II) in the problem domain. 

<float1> 
Value of xystress. 

[float2] 
An optional parameter (that serves as a flag to the code for a Dirichlet boundary condition). If a value is present, and is not 1.0, the condition is applied as a residual equation. Otherwise, it is a “hard set” condition and is eliminated from the matrix. The residual method must be used when this Dirichlet boundary condition is used as a parameter in automatic continuation sequences. 
Examples#
Following are sample cards for applying a Dirichlet condition on the xystress component for mode 5 on node set 10:
BC = S12_4 NS 10 1.25
BC = S12_4 NS 10 1.25 1.0
where the second example uses the “residual” method for applying the same Dirichlet condition.
Technical Discussion#
See the technical discussion for the UVW velocity boundary condition for a discussion of the two ways of applying Dirichlet boundary conditions.
For details of the stress tensor and its use for solving viscoelastic flow problems, please see the viscoelastic flow tutorial (Rao, 2000).
References#
GT014.1: Tutorial for Running Viscoelastic Flow Problems with GOMA, June 21, 2000, R. R. Rao
S13#
BC = {bc_name} NS <bc_id> <float1> [float2]
Description / Usage#
(DC/STRESS13)
This Dirichlet boundary condition specification is used to set a constant xzstress for any given mode of the stress tensor. Each such specification is made on a separate input card. Definitions of the input parameters are as follows:
{S13  S13_1  S13_2  S13_3  S13_4  S13_5  S13_6  S13_7} 
Boundary condition name (<bc_name>) that defines the xzstress for a given mode, where: 

S13 
xzcomponent of stress tensor for mode 1 

S13_1 
xzcomponent of stress tensor for mode 2 

S13_2 
xzcomponent of stress tensor for mode 3 

S13_3 
xzcomponent of stress tensor for mode 4 

S13_4 
xzcomponent of stress tensor for mode 5 

S13_5 
xzcomponent of stress tensor for mode 6 

S13_6 
xzcomponent of stress tensor for mode 7 

S13_7 
xzcomponent of stress tensor for mode 8 

NS 
Type of boundary condition (<bc_type>), where NS denotes node set in the EXODUS II database. 

<bc_id> 
The boundary flag identifier, an integer associated with <bc_type> that identifies the boundary location (node set in EXODUS II) in the problem domain. 

<float1> 
Value of xzstress. 

[float2] 
An optional parameter (that serves as a flag to the code for a Dirichlet boundary condition). If a value is present, and is not 1.0, the condition is applied as a residual equation. Otherwise, it is a “hard set” condition and is eliminated from the matrix. The residual method must be used when this Dirichlet boundary condition is used as a parameter in automatic continuation sequences. 
Examples#
Following is a sample card for applying a Dirichlet condition for the xzstress component for mode 5 on node set 10:
BC = S13_4 NS 10 1.3
BC = S13_4 NS 10 1.3 1.0
where the second example uses the “residual” method for applying the same Dirichlet condition.
Technical Discussion#
See the technical discussion for the UVW velocity boundary condition for a discussion of the two ways of applying Dirichlet boundary conditions.
For details of the stress tensor and its use for solving viscoelastic flow problems, please see the viscoelastic flow tutorial (Rao, 2000).
References#
GT014.1: Tutorial for Running Viscoelastic Flow Problems with GOMA, June 21, 2000, R. R. Rao
S22#
BC = {bc_name} NS <bc_id> <float1> [float2]
Description / Usage#
(DC/STRESS22)
This Dirichlet boundary condition specification is used to set a constant yystress (also known as the shear stress) for any given mode of the stress tensor. Each such specification is made on a separate input card. Definitions of the input parameters are as follows:
{S22  S22_1  S22_2  S22_3  S22_4  S22_5  S22_6  S22_7} 
Boundary condition name (<bc_name>) that defines the yystress for a given mode, where: 

S22 
yycomponent of stress tensor for mode 1 

S22_1 
yycomponent of stress tensor for mode 2 

S22_2 
yycomponent of stress tensor for mode 3 

S22_3 
yycomponent of stress tensor for mode 4 

S22_4 
yycomponent of stress tensor for mode 5 

S22_5 
yycomponent of stress tensor for mode 6 

S22_6 
yycomponent of stress tensor for mode 7 

S22_7 
yycomponent of stress tensor for mode 8 

NS 
Type of boundary condition (<bc_type>), where NS denotes node set in the EXODUS II database. 

<bc_id> 
The boundary flag identifier, an integer associated with <bc_type> that identifies the boundary location (node set in EXODUS II) in the problem domain. 

<float1> 
Value of yystress. 

[float2] 
An optional parameter (that serves as a flag to the code for a Dirichlet boundary condition). If a value is present, and is not 1.0, the condition is applied as a residual equation. Otherwise, it is a “hard set” condition and is eliminated from the matrix. The residual method must be used when this Dirichlet boundary condition is used as a parameter in automatic continuation sequences. 
Examples#
Following are sample cards for applying a Dirichlet condition on the yystress component for mode 8 on node set 20:
BC = S22_7 NS 20 5.0
BC = S22_7 NS 20 5.0 1.0
where the second example uses the “residual” method for applying the same Dirichlet condition.
Technical Discussion#
See the technical discussion for the UVW velocity boundary condition for a discussion of the two ways of applying Dirichlet boundary conditions.
For details of the stress tensor and its use for solving viscoelastic flow problems, please see the viscoelastic flow tutorial (Rao, 2000).
References#
GT014.1: Tutorial for Running Viscoelastic Flow Problems with GOMA, June 21, 2000, R. R. Rao
S23#
BC = {bc_name} NS <bc_id> <float1> [float2]
Description / Usage#
(DC/STRESS23)
This Dirichlet boundary condition specification is used to set a constant yzstress for any given mode of the stress tensor. Each such specification is made on a separate input card. Definitions of the input parameters are as follows:
{S23  S23_1  S23_2  S23_3  S23_4  S23_5  S23_6  S23_7} 
Boundary condition name (<bc_name>) that defines the yzstress for a given mode, where: 

S23 
yzcomponent of stress tensor for mode 1 

S23_1 
yzcomponent of stress tensor for mode 2 

S23_2 
yzcomponent of stress tensor for mode 3 

S23_3 
yzcomponent of stress tensor for mode 4 

S23_4 
yzcomponent of stress tensor for mode 5 

S23_5 
yzcomponent of stress tensor for mode 6 

S23_6 
yzcomponent of stress tensor for mode 7 

S23_7 
yzcomponent of stress tensor for mode 8 

NS 
Type of boundary condition (<bc_type>), where NS denotes node set in the EXODUS II database. 

<bc_id> 
The boundary flag identifier, an integer associated with <bc_type> that identifies the boundary location (node set in EXODUS II) in the problem domain. 

<float1> 
Value of yzstress. 

[float2] 
An optional parameter (that serves as a flag to the code for a Dirichlet boundary condition). If a value is present, and is not 1.0, the condition is applied as a residual equation. Otherwise, it is a “hard set” condition and is eliminated from the matrix. The residual method must be used when this Dirichlet boundary condition is used as a parameter in automatic continuation sequences. 
Examples#
Following are sample cards for applying a Dirichlet condition on the yzstress component for mode 8 on node set 20:
BC = S23_7 NS 20 5.0
BC = S23_7 NS 20 5.0 1.0
where the second example uses the “residual” method for applying the same Dirichlet condition.
Technical Discussion#
See the technical discussion for the UVW velocity boundary condition for a discussion of the two ways of applying Dirichlet boundary conditions.
For details of the stress tensor and its use for solving viscoelastic flow problems, please see the viscoelastic flow tutorial (Rao, 2000).
References#
GT014.1: Tutorial for Running Viscoelastic Flow Problems with GOMA, June 21, 2000, R. R. Rao
S33#
BC = {bc_name} NS <bc_id> <float1> [float2]
Description / Usage#
(DC/STRESS33)
This Dirichlet boundary condition specification is used to set a constant zzstress for any given mode of the stress tensor. Each such specification is made on a separate input card. Definitions of the input parameters are as follows:
{S33  S33_1  S33_2  S33_3  S33_4  S33_5  S33_6  S33_7} 
Boundary condition name (<bc_name>) that defines the zzstress for a given mode, where: 

S33 
zzcomponent of stress tensor for mode 1 

S33_1 
zzcomponent of stress tensor for mode 2 

S33_2 
zzcomponent of stress tensor for mode 3 

S33_3 
zzcomponent of stress tensor for mode 4 

S33_4 
zzcomponent of stress tensor for mode 5 

S33_5 
zzcomponent of stress tensor for mode 6 

S33_6 
zzcomponent of stress tensor for mode 7 

S33_7 
zzcomponent of stress tensor for mode 8 

NS 
Type of boundary condition (<bc_type>), where NS denotes node set in the EXODUS II database. 

<bc_id> 
The boundary flag identifier, an integer associated with <bc_type> that identifies the boundary location (node set in EXODUS II) in the problem domain. 

<float1> 
Value of zzstress. 

[float2] 
An optional parameter (that serves as a flag to the code for a Dirichlet boundary condition). If a value is present, and is not 1.0, the condition is applied as a residual equation. Otherwise, it is a “hard set” condition and is eliminated from the matrix. The residual method must be used when this Dirichlet boundary condition is used as a parameter in automatic continuation sequences. 
Examples#
Following are sample cards for applying a Dirichlet condition on the zzstress component for mode 1 on node set 100:
BC = S33 NS 100 5.0
BC = S33 NS 100 5.0 1.0
where the second example uses the “residual” method for applying the same Dirichlet condition.
Technical Discussion#
See the technical discussion for the UVW velocity boundary condition for a discussion of the two ways of applying Dirichlet boundary conditions.
For details of the stress tensor and its use for solving viscoelastic flow problems, please see the viscoelastic flow tutorial (Rao, 2000).
References#
GT014.1: Tutorial for Running Viscoelastic Flow Problems with GOMA, June 21, 2000, R. R. Rao