Fully Coupled Thermal-Electrical-Structural Analysis
A fully coupled thermal-electrical-structural analysis is the union of a coupled thermal-displacement analysis (see Fully Coupled Thermal-Stress Analysis) and a coupled thermal-electrical analysis (see Coupled Thermal-Electrical Analysis).
Coupling between the temperature and electrical degrees of freedom arises from temperature-dependent electrical conductivity and internal heat generation (Joule heating), which is a function of the electrical current density. The thermal part of the problem can include heat conduction and heat storage (About Thermal Properties). Forced convection caused by fluid flowing through the mesh is not considered.
Coupling between the temperature and displacement degrees of freedom arises from temperature-dependent material properties, thermal expansion, and internal heat generation, which is a function of inelastic deformation of the material. In addition, contact conditions exist in some problems where the heat conducted between surfaces may depend strongly on the separation of the surfaces and/or the pressure transmitted across the surfaces as well as friction (see About Mechanical Contact Properties and Thermal Contact Properties).
Coupling between the electrical and displacement degrees of freedom arises in problems where electricity flows between contact surfaces. The electrical conduction may depend strongly on the separation of the surfaces and/or the pressure transmitted across the surfaces (see Electrical Contact Properties).
An example of a simulation that requires a fully coupled thermal-electrical-structural analysis is resistance spot welding. In a typical spot welding process two or more thin metal sheets are pinched between two electrodes. A large current is passed between the electrodes, which melts the metal between the electrodes and forms a weld. The integrity of the weld depends on many parameters including the electrical conductance between the sheets (which can be a function of contact pressure and temperature).
Steady-State Analysis
Steady-state analysis provides the steady-state solution directly. Steady-state thermal analysis means that the internal energy term (the specific heat term) in the governing heat transfer equation is omitted. A static displacement solution is assumed. Only direct current is considered in the electrical problem, and it is assumed that the system has negligible capacitance. Electrical transient effects are so rapid that they can be neglected.
Assigning a “Time” Scale to the Analysis
In steady-state cases you should assign an arbitrary “time” scale to the step: you specify a “time” period and “time” incrementation parameters. This time scale is convenient for changing loads and boundary conditions through the step and for obtaining solutions to highly nonlinear (but steady-state) cases; however, for the latter purpose, transient analysis often provides a natural way of coping with the nonlinearity.
Accounting for Frictional Slip Heat Generation
Frictional slip heat generation is normally neglected in the steady-state case. However, it can still be accounted for if user subroutine FRIC provides the incremental frictional dissipation through the variable SFD. If frictional heat generation is present, the heat flux into the two contact surfaces depends on the slip rate of the surfaces. The “time” scale in this case cannot be described as arbitrary, and a transient analysis should be performed.
Transient Analysis
Alternatively, you can perform a transient coupled thermal-electrical-structural analysis. As in steady-state analysis, electrical transient effects are neglected and a static displacement solution is assumed. You can control the time incrementation in a transient analysis directly, or Abaqus/Standard can control it automatically. Automatic time incrementation is generally preferred.
Automatic Incrementation Controlled by a Maximum Allowable Temperature Change
The time increments can be selected automatically based on a user-prescribed maximum allowable nodal temperature change in an increment, . Abaqus/Standard restricts the time increments to ensure that this value is not exceeded at any node (except nodes with boundary conditions) during any increment of the analysis (see Time Integration Accuracy in Transient Problems).
Fixed Incrementation
If you do not specify , fixed time increments equal to the user-specified initial time increment, , will be used throughout the analysis, except when the explicit creep integration scheme is used. In this case Abaqus/Standard might decrease the time increment if the stability limit is exceeded.
Spurious Oscillations due to Small Time Increments
In transient analysis with second-order elements there is a relationship between the minimum usable time increment and the element size. A simple guideline is
where is the time increment, is the density, c is the specific heat, k is the thermal conductivity, and is a typical element dimension (such as the length of a side of an element). If time increments smaller than this value are used in a mesh of second-order elements, spurious oscillations can appear in the solution, in particular in the vicinity of boundaries with rapid temperature changes. These oscillations are nonphysical and may cause problems if temperature-dependent material properties are present. In transient analyses using first-order elements the heat capacity terms are lumped, which eliminates such oscillations but can lead to locally inaccurate solutions for small time increments. If smaller time increments are required, a finer mesh should be used in regions where the temperature changes rapidly.
There is no upper limit on the time increment size (the integration procedure is unconditionally stable) unless nonlinearities cause convergence problems.
Automatic Incrementation Controlled by the Creep Response
The accuracy of the integration of time-dependent (creep) material behavior is governed by the user-specified accuracy tolerance parameter, . This parameter is used to prescribe the maximum strain rate change allowed at any point during an increment, as described in Rate-Dependent Plasticity: Creep and Swelling. The accuracy tolerance parameter can be specified together with the maximum allowable nodal temperature change in an increment, (described above); however, specifying the accuracy tolerance parameter activates automatic incrementation even if is not specified.
Selecting Explicit Creep Integration
Nonlinear creep problems (Rate-Dependent Plasticity: Creep and Swelling) that exhibit no other nonlinearities can be solved efficiently by forward-difference integration of the inelastic strains if the inelastic strain increments are smaller than the elastic strains. This explicit method is efficient computationally because, unlike implicit methods, iteration is not required as long as no other nonlinearities are present. Although this method is only conditionally stable, the numerical stability limit of the explicit operator is in many cases sufficiently large to allow the solution to be developed in a reasonable number of time increments.
For most coupled thermal-electrical-structural analyses, however, the unconditional stability of the backward difference operator (implicit method) is desirable. In such cases the implicit integration scheme may be invoked automatically by Abaqus/Standard.
Explicit integration can be less expensive computationally and simplifies implementation of user-defined creep laws in user subroutine CREEP; you can restrict Abaqus/Standard to using this method for creep problems (with or without geometric nonlinearity included). See Rate-Dependent Plasticity: Creep and Swelling for further details.
Excluding Creep and Viscoelastic Response
You can specify that no creep or viscoelastic response occurs during a step even if creep or viscoelastic material properties have been defined.
Unstable Problems
Some types of analyses may develop local instabilities, such as surface wrinkling, material instability, or local buckling. In such cases it may not be possible to obtain a quasi-static solution, even with the aid of automatic incrementation. Abaqus/Standard offers a method of stabilizing this class of problems by applying damping throughout the model in such a way that the viscous forces introduced are sufficiently large to prevent instantaneous buckling or collapse but small enough not to affect the behavior significantly while the problem is stable. The available automatic stabilization schemes are described in detail in Automatic Stabilization of Unstable Problems.
Units
In coupled problems where two or three different fields are active, take care when choosing the units of the problem. If the choice of units is such that the terms generated by the equations for each field are different by many orders of magnitude, the precision on some computers may be insufficient to resolve the numerical ill-conditioning of the coupled equations. Therefore, choose units that avoid ill-conditioned matrices. For example, consider using units of megapascal (MPa) instead of pascal (Pa) for the stress equilibrium equations to reduce the disparity between the magnitudes of the stress equilibrium equations, the heat flux continuity equations, and the conservation of charge equations.