Gap Contact Elements

Clearance between GAPUNI Nodes

Abaqus/Standard defines the current clearance between two nodes of the gap, h, as

where ${\mathbf{u}}^1$ and ${\mathbf{u}}^2$ are the total displacements at the first and the second node forming the GAPUNI element. Figure 1 shows the configuration of the GAPUNI element. When h becomes negative, the gap contact element is closed and the constraint $h=0$ is imposed.

Figure 1. GAPUNI and GAPUNIT contact elements.

You specify a value for d. If you provide a positive value, the gap is open initially. If d=0, the gap is initially closed. If d is negative, the gap is considered overclosed at the start of the analysis and an initial interference fit problem is defined. Details about modeling interference fit problems with gap elements are discussed below.

GAP
d

Specifying the Contact Direction

You can specify the contact direction. Otherwise, Abaqus/Standard will calculate the gap direction, $\mathbf{n}$, by using the initial positions of the two nodes forming the element, ${\mathbf{X}}^1$ and ${\mathbf{X}}^2$:

An error message is issued if ${\mathbf{X}}^2={\mathbf{X}}^1$ (if the two gap element nodes have the same initial coordinates). In this situation you must define $\mathbf{n}$. The normal $\mathbf{n}$ usually points from the first node of the element to the second, unless the gap is overclosed at the start of the analysis. In that case specify $\mathbf{n}$ so that the correct contact direction is used for the gap element.

If you specify the gap direction $\mathbf{n}$ rather than allowing Abaqus/Standard to calculate it, the contact calculations consider only $\mathbf{n}$, the displacements of the gap element's nodes, and the ordering of the nodes in the element definition: the initial coordinates of the nodes play no role in the calculations.

The orientation of $\mathbf{n}$ does not change during the analysis.

GAP
 , X-direction cosine, Y-direction cosine, Z-direction cosine

Local Basis System for GAPUNI Element Output

Abaqus/Standard reports the pressure transmitted across the gap and the shear stresses that are orthogonal to the contact direction as element output for GAPUNI elements. You must supply the contact area associated with these elements for Abaqus/Standard to compute the pressure and the shear stress values. It also reports the current clearance in the gap, h, and the relative motions of the GAPUNI nodes orthogonal to the contact direction. The relative motions and the shear stresses are reported in local surface directions that are formed using the standard Abaqus convention for defining directions on surfaces in space (see Conventions). The contact direction defines a surface in space on which the local axes are formed.

GAP
 , , , , cross-sectional area

Defining the Gap Clearance for Case 1 (When d Is Positive)

If d is positive, the GAPCYL element models contact between two rigid tubes of different diameter, where the smaller tube is located inside the larger tube (see Case 1 in Figure 2). In this case d is the maximum allowable separation. Each tube is represented by a node on its axis, with the axes connected by the GAPCYL element; and d corresponds to the difference between the radii of the tubes. The gap between the tubes closes when the two nodes become separated by more than d in any direction in the plane defined by the axis of the GAPCYL element.

Abaqus/Standard defines the current gap opening, h, in GAPCYL elements for Case 1 as

where ${\mathbf{x}}^N$ is the current position of node N, d is the specified initial separation, and a is the axis of the GAPCYL element.

If the initial position of the tube axes is such that the distance between them is less than d, the GAPCYL element is open initially. If the distance is equal to d, the element is closed initially; and if the distance is greater than d, an initial overclosure (interference) is defined. Details about modeling interference fit problems with gap elements are discussed below.

Defining the Gap Clearance for Case 2 (When d Is Negative)

If d is negative, the GAPCYL element models external contact between two parallel rigid cylinders (see Case 2 in Figure 2). In this case $\left|d\right|$ is the minimum allowable separation of the nodes. Each cylinder is represented by a node on its axis connected by the GAPCYL element, and $\left|d\right|$ corresponds to the sum of the radii of the cylinders. The gap closes when the two nodes approach each other to within $\left|d\right|$ in any direction in the plane defined by the axis of the GAPCYL element.

Abaqus/Standard defines the current gap opening, h, in GAPCYL elements for Case 2 as

If the initial position of the cylinder axes is such that the distance between them is greater than $\left|d\right|$, the GAPCYL element is open initially. If the distance is equal to $\left|d\right|$, the element is closed initially; and if the distance is less than $\left|d\right|$, an initial overclosure (interference) is defined. Details about modeling interference fit problems with gap elements are discussed below.

Local Basis System for GAPCYL Element Output

Abaqus/Standard reports the pressure transmitted across the gap and the shear stresses that are orthogonal to the contact direction as element output for GAPCYL elements. You must supply the contact area associated with these elements for Abaqus/Standard to compute the pressure and the shear stress values. It also reports the current clearance in the gap, h, and the relative motions of the element's nodes that are orthogonal to the contact direction. The relative motions and the shear stresses are reported in local surface directions that are formed using the standard Abaqus convention for defining directions on surfaces in space (see Conventions). The contact direction defines a surface in space on which the local axes are formed, and the slip is calculated from the relative motions in the surface directions.

Abaqus/Standard updates the contact direction for GAPCYL elements based on the motion of the nodes forming the elements. However, the orientation of $\mathbf{a}$ is not updated during the analysis.

GAP
 , , , , cross-sectional area

Defining the Gap Clearance for Case 1 (When d Is Positive)

If d is positive, the GAPSPHER element models contact between a rigid sphere inside another (larger) hollow rigid sphere (see Case 1 in Figure 2). In this case d is the maximum allowable separation of the nodes forming the gap. Each sphere is represented by a node at its center, with the centers connected by the GAPSPHER element; and d corresponds to the difference between the radii of the spheres. The gap closes when the two nodes become separated by more than d.

Abaqus/Standard defines the current gap opening, h, for Case 1 as

with ${\mathbf{x}}^N$ the current position of node N and d the specified separation.

If the initial position of the tube axes is such that the distance between them is less than d, the GAPSPHER element is open initially. If the distance is equal to d, the element is closed initially; and if the distance is greater than d, an initial overclosure (interference) is defined. Details about modeling interference fit problems with gap elements are discussed below.

Defining the Gap Clearance for Case 2 (When d Is Negative)

If d is negative, the GAPSPHER element models external contact between two rigid spheres (see Case 2 in Figure 2). In this case $\left|d\right|$ is the minimum allowable separation of the nodes forming the gap. Each sphere is represented by a node at its center connected by the GAPSPHER element; and $\left|d\right|$ corresponds to the sum of the radii of the spheres. The gap closes when the two nodes approach each other to within $\left|d\right|$.

Abaqus/Standard defines the current gap opening, h, for Case 2 as

If the initial position of the cylinder axes is such that the distance between them is greater than $\left|d\right|$, the GAPSPHER element is open initially. If the distance is equal to $\left|d\right|$, the element is closed initially; and if the distance is less than $\left|d\right|$, an initial overclosure (interference) is defined. Details about modeling interference fit problems with gap elements are discussed below.

Local Basis System for GAPSPHER Element Output

Abaqus/Standard reports the pressure transmitted across the gap and the shear stresses that are orthogonal to the contact direction as element output for GAPSPHER elements. You must supply the contact area associated with these elements for Abaqus/Standard to compute the pressure and the shear stress values. It also reports the current clearance in the gap, h, and the relative motions of the element's node that are orthogonal to the contact direction. The relative motions and the shear stresses are reported in local surface directions that are formed using the standard Abaqus convention for defining directions on surfaces in space; see Conventions. The contact direction defines a surface in space on which the local axes are formed, and the slip is calculated from the relative motions in the surface directions.

Abaqus/Standard updates the contact direction for GAPSPHER elements based on the motion of the nodes forming the elements.

GAP
 , , , , cross-sectional area

Clearance between DGAP Nodes

Abaqus/Standard defines the clearance between two nodes of the gap, h, as

Since there are no displacements in a heat transfer analysis, the clearance remains unchanged. The clearance is used only for clearance-dependent thermal interactions.

You specify a value for d. If you provide a positive value, the gap is open initially. If d=0, the gap is closed initially. If d is negative, the gap is considered overclosed but no interference fit is performed. The contact direction does not need to be specified: any contact direction specified is ignored in the analysis. You must supply the contact area associated with these elements for Abaqus/Standard to compute the heat flux value per unit area.

GAP
d, , , , cross-sectional area