User-Defined Interfacial Constitutive Behavior

User subroutines UINTER, VUINTER, and VUINTERACTION provide a very general interface for you to define the constitutive behavior across the interface between two surfaces. These subroutines replace all built-in interfacial constitutive behavior models; hence, no other contact property definitions (e.g., friction, thermal conductance, etc.) can be specified in conjunction with them.

In a stress/displacement analysis you must define the stresses, both normal and tangential, at the secondary node (or points on the secondary surface) at the current point in time. In a coupled temperature-displacement analysis and a coupled thermal-electrical-structural analysis you must also define the heat flux across the interface. The constitutive calculation thus involves computing the stresses and heat fluxes based on the increments in relative position of the secondary node with respect to the main surface (which act as strains in this context), temperature at the surface, and predefined field variables. The calculations would typically involve solution-dependent state variables, which can be updated inside these routines. If contact damping is to be included in the interfacial constitutive model, you must include the damping contribution in the stress definition.

When a user subroutine is used to define the interfacial constitutive behavior, all decisions regarding the contact status of a secondary node must be made inside the subroutine based on the information provided. You can make such decisions based on the values of the relative position of the point on the secondary surface with respect to the main surface and appropriately defined solution-dependent state variables. Thus, usage of this feature involves not only developing a constitutive behavior of the interface but also developing conditions under which contact is active at a given point on the secondary surface. The interface is always assumed to be massless.

User subroutine UINTER will be called for each contact constraint location of affected contact pairs in each iteration of an Abaqus/Standard analysis. The input to this user subroutine includes the current relative position of a particular constraint point on the secondary surface with respect to the corresponding closest point on the main surface, as well as the incremental relative motion between these two points. Values of temperature and field variables at the constraint point on the secondary surface and the corresponding closest point on the main surface and several other variables are also provided as input. In addition to defining the contact stress or heat flux, appropriate Jacobian terms must also be defined to ensure proper convergence characteristics in Abaqus/Standard.

User subroutine VUINTER will be called multiple times for the affected contact pairs in each time increment of an Abaqus/Explicit analysis. All secondary nodes are processed in each call to VUINTER, whereas only a single constraint is processed in each call to UINTER. Similar input is provided to VUINTER as UINTER.

User subroutine VUINTERACTION will be called multiple times for each interacting surface in each time increment of an Abaqus/Explicit analysis. Points of potential contact for a given interaction are processed in blocks in calls to VUINTERACTION. Similar input is provided to VUINTERACTION as VUINTER.

You must specify the number of interfacial constants that are needed in user subroutine UINTER, VUINTER, or VUINTERACTION; and you must provide values for all these constants. All surface constitutive behavior calculations and all decisions regarding the contact status at a secondary node (or a point on the secondary surface in question) must be programmed in the user subroutine. Any other contact property definitions included in the analysis are reported as an error.

Computations to determine the precise distance to a main surface are avoided if a secondary node can be easily determined to be separated from the main surface, accounting for all thickness effects and built-in contact property models, by more than a threshold distance called the tracking thickness. Abaqus/Explicit uses an internal default value for the tracking thickness. If a built-in contact property model is in effect, the tracking thickness is quite small to help reduce computation time. However, if user subroutine VUINTER or user subroutine VUINTERACTION is in effect, the default tracking thickness is infinite so that all secondary nodes are supplied to the user subroutines as having potential interactions. Alternatively, you can specify the tracking thickness in conjunction with a user-defined surface interaction model. In this case secondary nodes whose proximity to their main surfaces are within this thickness are available for user-defined interactions. Use of a user-specified tracking thickness is supported only with node-to-surface contact and not with edge-to-edge contact.

Constitutive models used to define the interfacial behavior may require the storage of solution-dependent state variables. You must allocate storage space for these variables by indicating the number of variables. There is no restriction on the number of state variables associated with a user-defined constitutive behavior for the interface.

User subroutine UINTER is called for points on the secondary surface at each iteration of every increment. User subroutine VUINTER is called in every time increment for each main-secondary view of each contact pair it affects, as discussed earlier. User subroutine VUINTERACTION is called in every time increment for each pair of surfaces actively interacting, as discussed earlier. Each subroutine is provided with the state of the secondary node or potential contact point at the start of the increment (the state includes stress, flux, solution-dependent state variables, temperature, and any predefined field variables) and with the increments in temperature, predefined state variables, relative position, and time.

If the constitutive Jacobian matrix, $\partial \mathrm{△}\mathit{\sigma }/\partial \mathrm{△}\mathbf{u}$, is not symmetric, you should invoke the unsymmetric equation solution capability in Abaqus/Standard (see Defining an Analysis).

In addition to defining the constitutive behavior, in Abaqus/Standard you may also update the flags LOPENCLOSE, LSTATE, and LSDI. The flag LOPENCLOSE is useful when UINTER is used to model standard contact between two surfaces (similar to the default hard contact in Abaqus). It should be set to 0 to indicate an open status and to 1 to indicate a closed status. At the beginning of the analysis it is set to −1 before UINTER is called. A change in this flag from one iteration to the next will have two consequences. It will result in output related to the change in contact status if detailed contact output has been requested to the message file (see The Abaqus/Standard Message File), and it will also trigger a severe discontinuity iteration. The flag LSTATE can be used to store the current contact status of the points on the secondary surface in non-standard situations where a simple open/close status is not appropriate. An example of such a situation is debonding, where three different states can be defined—fully bonded, partially bonded or debonding, and fully debonded. You can assign an integer to each of these states and set LSTATE accordingly. At the beginning of the analysis LSTATE is set to −1 before UINTER is called. When this flag is used and it changes from one iteration to the next, you can output messages to the message file (unit 7) related to such a change in state directly from user subroutine UINTER. The flag LPRINT is provided to allow you to output messages related to change in contact status only when you request detailed contact output to the message file. In such a situation the LSDI flag may be set to 1 to trigger a severe discontinuity iteration (this issue is discussed in detail later).

An example of a situation where both the flags LOPENCLOSE and LSTATE can be used arises in the modeling of debonding between two surfaces. When the surface is in a state of transition from bonded to debonded, the flag LSTATE may be used, while the flag LOPENCLOSE may be left to its original value of −1. However, once complete debonding has taken place, the contact between the two surfaces may be modeled using standard hard contact. In that situation the LSTATE flag may be set to −1, and the LOPENCLOSE flag used. Any time one of these two flags is set to −1, Abaqus/Standard assumes that it is not being used. A change of these flags from some other value to −1 does not result in contact-status related output or severe discontinuity iterations. Similarly, a change of these flags from −1 to some other value will not result in contact-status related output or severe discontinuity iterations.

If these flags are not used, there will be no output related to change in contact status unless you decide to output messages that are not based on these flags directly from UINTER.

Abaqus/Standard classifies iterations in which the contact state at the end of the iteration is different from the state assumed for that iteration as severe discontinuity iterations. The treatment of severe discontinuity iterations by Abaqus/Standard is discussed in Severe Discontinuities in Abaqus/Standard. When you define the interfacial constitutive behavior through user subroutine UINTER and do not use the LOPENCLOSE flag, it is your responsibility to provide Abaqus/Standard with input on how an iteration should be treated. The flag LSDI is provided in user subroutine UINTER for this purpose. It is set to 0 before each call to UINTER; you should set it to 1 to treat the current iteration as a severe discontinuity iteration. If the LOPENCLOSE flag is used, the value of this flag alone determines whether a severe discontinuity iteration is necessary or not, and the LSDI flag is ignored.

The penalty contact algorithm must be used with user subroutines VUINTER and VUINTERACTION; see Penalty Contact Algorithm.

When VUINTER is used and balanced main-secondary contact is specified (that is, the contact pair weighting factor is not equal to 0.0 or 1.0), VUINTER will be called for each surface in the contact pair that can act as a secondary surface. The forces and fluxes defined in VUINTER will be multiplied by the weight value for the main-secondary view before they are applied.

Abaqus/Explicit accounts for the contact stiffness and conductance in the stable time increment calculation. Specifying stresses and fluxes in the user subroutine that correspond to large contact stiffness (e.g., large slope of contact pressure versus penetration) and large contact conductance will cause a significant drop in the stable time increment and, therefore, an increase in the solution time. Tangent stiffnesses and conductances are determined by Abaqus/Explicit using a finite difference method. User subroutine VUINTER is called three times per increment for each main-secondary view of each two-dimensional contact pair that references it and four times per increment for each three-dimensional contact pair that references it. User subroutine VUINTERACTION is called four times per increment for each active surface interaction that references it. The user subroutines are called once with the actual configuration and subsequently with perturbed configurations based on displacement perturbations in the normal direction, the ${\mathbf{t}}_1$ tangential direction, and, in three-dimensional cases, the ${\mathbf{t}}_2$ tangential direction, respectively (see the local coordinate system discussion in VUINTER and VUINTERACTION for an explanation of how the ${\mathbf{t}}_1$ and ${\mathbf{t}}_2$ directions are defined). For example, each component of contact stiffness is computed as a difference in contact stress divided by a difference in relative position. You do not have access to the computed values of contact stiffness and conductance, but you can control the constitutive behavior of the model. Estimated default penalty stiffness (and conductance) values are provided to the user subroutines for comparison purposes. Contact stiffnesses or conductances that exceed the default penalty values can significantly reduce the time increment size. The default penalty stiffnesses and conductances are based on an assumption that all secondary nodes are in contact. In the case of VUINTER, if only a fraction of the secondary nodes are in contact, higher penalties than are reported in VUINTER would be assigned in some cases with the default penalty algorithm.

Any changes to state variables are ignored for the perturbation calls.

In the case of VUINTER there can be significant additional CPU expense associated with contact tracking. Since the contact state is unknown on entry to VUINTER, all nodes on the secondary surface must be tracked in every increment. This can increase the cost of an analysis significantly compared to the contact models in Abaqus/Explicit if a large proportion of the secondary nodes are not involved in contact.

In the case of VUINTERACTION there can be significant additional CPU expense associated with contact tracking only if the tracking thickness is large compared to the element facet size on contacting surfaces.

Any other user subroutine that does not deal with constitutive behavior across an interface can be used in conjunction with UINTER, VUINTER, or VUINTERACTION.

For example, user subroutines UMAT and UMATHT can be used in conjunction with UINTER to define the constitutive mechanical and thermal behaviors of the material underlying the contact surfaces. User subroutine VUMAT and VUMATHT can be used in conjunction with VUINTER to define the constitutive mechanical and thermal behaviors of the material underlying the contact surfaces. However, user subroutines FRIC, GAPCON, and GAPELECTR—available in Abaqus/Standard for defining mechanical, thermal, and electrical interactions between surfaces—can be used in conjunction with UINTER only if they are referenced on separate surface interactions. The same restriction applies to user subroutine VFRIC used in conjunction with VUINTER and to user subroutines VFRICTION or VFRIC_COEF used in conjunction with VUINTERACTION.

In Abaqus/Standard contact controls will not have any effect when used at an interface whose constitutive behavior is defined through user subroutine UINTER.

In Abaqus/Explicit contact controls can be specified for a contact pair referencing a user-defined surface interaction. In the case of user subroutine VUINTERACTION the default penalty stiffness argument includes any scale factor specified; whereas with user subroutine VUINTER the scale factor is ignored.

Most of the standard output variables that are normally available in an analysis involving contact are available with this capability.