(sect:tiedJoints)=
# Tied Joints

The `Tied Joint` provides an interface to the whole joint models.
Multiple connection methods are supported, including weighted
constraint equations.

Separate shear and normal forces are supported. The separation also reduces
requirements on the constraints. The whole surface is no longer required to
have $6$ rigid body modes. The normal tied interface keeps surfaces together.
This relaxes the requirements for shear constraints. The Tied Joint permits
constraints that look more like a collection of trusses, not a collection of
beams.

Rotational DOFs are necessary for the structure to move as a rigid body.
However, the adjacent elements may have no rotational stiffness. This
introduces singularities. Avoiding the rotational DOFs is important.

Normal direction constraints are tied surfaces. Shear direction constraints
are a truss network. For curved surfaces, constraints may be inconsistent.

(sect:tiedjointlapjoint)=
## Lap joint

A lap joint contains regions of "welded" contact, microslip, and macroslip as
shown in {numref}`lapjoint`. An elastic spring approximates normal forces.
Tied surfaces approximate shear behavior of the "welded" region. The
macroslip region is free. The region of microslip depends on the loading.
Microslip introduces loss into the structure. This region is well approximated
by an Iwan element.

:::{figure-md} lapjoint

![](lapjoint.png)

Lap Joint with Contact Regions. The physics of bolted lap joints is complex. Tied Joints use a combination of constraints, springs and optionally Iwan elements to generate a reduced order model of the structure.
:::

Without a Tied Joint, this lap joint can be modeled using a whole joint
model. Each of the contact surfaces is rigidized (using a rigid set). A
Joint2G connects the surfaces.
The mesh is represented in {numref}`lapfem`.
{numref}`conventional:lap` illustrates the conventional means of connecting this structure.
This method reduces all the behavior of the joint to a single Joint2G
element. That element must be included as part of the mesh. Because the
surfaces are allowed to translate and rotate independently,
interpenetration can occur. Nevertheless, the method is effective in
representing the energy loss that occurs in this structure.

:::{figure-md} lapfem

![](lapfem.png)

Lap Joint Finite Element Mesh. The physical lap joint is represented by a reduced order model which uses disconnected meshes of the top and bottom material. These are shown separated in the cartoon but may have overlapping nodes. In a conventional connection the Joint2G which represents the bolt must be explicitly meshed. The Tied Joint approach generates that element internally.
:::

:::{input}
:caption: Conventional Input for Whole Lap Model.
:name: conventional:lap

Rigidset
  sideset 1
end
Rigidset
  sideset 2
end

Block 3
  Joint2G
    Kz = Elastic 1e6
    Kx = Iwan 1
    Ky = Iwan 1
    Krx = Elastic 1e9
    Kry = Elastic 1e9
    Krz = Elastic 1e9
end
:::

The input included in {numref}`tied:whole:lap` represents the same
physics. The normal definition is `none` because the normal stiffness is
part of the Joint2G structure. The shear side definition is `rigid`
corresponding to a rigid set definition on each of the surfaces. No mesh of
block 3 is required.

:::{input}
:caption: Tied Joint Input for Whole Lap Model.
:name: tied:whole:lap

Tied Joint
   Normal Definition = none
     surface 1,2
   Shear Definition
     side = rigid
     connect to Block 3
end
Block 3
   Joint2G
    Kz = Elastic 1e6
    Kx = Iwan 1
    Ky = Iwan 1
    Krx = Elastic 1e9
    Kry = Elastic 1e9
    Krz = Elastic 1e9
end
:::

## Joint with Slip

The whole joint model of {numref}`sect:tiedjointlapjoint`
can be modified to prevent
penetration of the two surfaces. The models are shown in
{numref}`whole:slide` and {numref}`whole:tiedjoint:slide` for the conventional and Tied Joints.

Sliding contact or *slip* keeps two surfaces in contact with no resistance
to transverse motion. Because the sliding contact constrains the normal behavior, the
Joint2G parameters for that direction are irrelevant. Because the surfaces are
flexible, properly constraining the transverse motion of the connection nodes
is challenging. The constraint method is specified using the `side`.
The `Rrod` and `average` methods are available.
{numref}`whole:slide` uses the `Rrod` approach.

:::{input}
:caption: Conventional Input for Whole Lap Model with Sliding Contact.
:name: whole:slide

Rigidrod
   sideset 1
end
Rigidrod
   sideset 2
end
Block 3
   Joint2G
    Kx = Iwan 1
    Ky = Iwan 1
    Krz = Elastic 1e9
END
    
Tied Data
     name = 'block_3_tj'
     surface 1,2
     transverse slip
end
:::

:::{input}
:caption: Tied Joint Input for Whole Lap Model with Sliding Contact.
:name: whole:tiedjoint:slide

Tied Joint
   Normal Definition = slip
     surface 1,2
   Shear Definition
     side = Rrod
     connect to Block 3
end

Block 3
   Joint2G
    Kx = Iwan 1
    Ky = Iwan 1
    Krz = Elastic 1e9
end
:::
