Multiphysics problems are encountered when the response of a system is affected by the interaction between several distinct physical fields (e.g., structural deformation, fluid flow, electric field, temperature, pore-pressure,etc.).

Many problems in engineering and science involve some level of coupling between different physical fields. In the past, due to the lack of computational capabilities, these coupling effects were either ignored or taken into account very approximately. However, with the current analysis capabilities available in ADINA, many important multiphysics coupling effects can now be included accurately. By including these coupling effects, the analyses provide deeper insight into the performance of designs, leading to more economical and safer products, and also to a better understanding of the causes and consequences of natural phenomena [1].

Mathematically, multiphysics problems are described by a set of coupled partial differential equations (PDEs). The solution of these equations poses a challenge regarding the robustness of the algorithms to handle such interactions in a general and efficient manner.

The ADINA Multiphysics package includes all ADINA solvers for solids and structures, heat transfer, CFD, and also a comprehensive array of multiphysics capabilities tightly integrated in one program:

• Fluid-structure interaction (FSI)
• Thermo-mechanical coupling (TMC)
• Structural-pore pressure coupling (porous media)
• Thermal-fluid-structural coupling
• Electric field-structural coupling (piezoelectric)
• Thermal-electrical coupling (Joule heating)
• Acoustic fluid-structural coupling
• Fluid flow-mass transfer coupling
• Fluid flow-electromagnetic coupling

The multiphysics capabilities of ADINA are unique both in their breadth and depth. Using these capabilities, not only a wide range of interactions between different physical fields can be considered, but each of these fields is treated in a general form without compromise on accuracy.

### Fluid-Structure Interaction (FSI)

ADINA FSI offers comprehensive capabilities for solving problems involving the interaction between general nonlinear structures and general Navier-Stokes or Reynolds fluid flow all tightly integrated in a single program.

Examples of Industrial Applications

• Automotive Systems
• Biomedical Applications
• Nuclear Power Plants
• Compressors, Pumps and Pipe Systems
• Valves
• Micro-Electro-Mechanical Systems (MEMS)

For detailed information on ADINA FSI, refer to our page on fluid-structure interaction capabilities of ADINA.

### Thermo-Mechanical Coupling (TMC)

The solution of fully coupled thermo-mechanical problems can be performed with ADINA TMC. In this class of problems, the temperature distribution affects the structural deformation and the structural deformation may affect the temperature distribution.

Examples of Industrial Applications

• Automotive systems
• Metal forming
• Welding
• MEMS (Micro-Electro-Mechanical Systems)
• Pressure vessels

For detailed information on ADINA TMC, refer to our page on thermal-mechanical coupling capabilities of ADINA.

### Structural-Pore Pressure Coupling (Porous Media)

This multiphysics problem is characterized by the coupling between the pore pressure and the deformation of a porous material (e.g., soil, biological tissues…) consisting of a solid skeleton and pore fluid. Mechanical deformation changes the pore pressure and change in the pore pressure causes mechanical deformation.

A variety of constitutive models can be used for the skeleton, such as: elastic isotropic, orthotropic, thermo-isotropic, thermo-orthotropic, thermo-plastic, Drucker-Prager, Mohr-Coulomb, Cam-clay, creep, plastic-creep, etc.

Examples of Industrial Applications

• Soil mechanics and geotechnical engineering
• Slope stability
• Earthquake analysis of earth dams
• Consolidation
• Biomedical applications
• Wave propagation in saturated media

### Thermal-Fluid-Structural Coupling

In this class of multiphysics problems, heat transfer, fluid flow and the mechanical deformation are all coupled. As an example, the fluid flow changes the temperature in the system and this change of temperature causes mechanical deformation changing the boundary conditions for the flow, thus affecting the flow.

Examples of Industrial Applications

• Exhaust manifolds
• Electronic packaging
• Combustion systems
• Metal hydroforming

For detailed information, refer to our page on thermal-fluid-structure interaction capabilities of ADINA.

### Electric Field-Structural Coupling (Piezoelectric)

Piezoelectric problems are characterized by the coupling of the electric field and mechanical deformation. Applying an electric field to a piezoelectric material causes mechanical deformation and the mechanical deformation causes an electric field. This phenomenon is the basis for the design of many sensors and actuators.

An iterative solution of the electric field and structural deformation is implemented in ADINA TMC. Users can also implement nonlinear constitutive relations between the electric displacement (electric flux) and the strain tensor (piezoelectric matrix).

Examples of Industrial Applications

• Microphones
• Micropumps
• Active vibration control devices

Piezo-electric analysis of a beam

### Thermal-Electrical Coupling (Joule Heating)

Joule heating is characterized by heat being generated by an electric current. The heat affects the surrounding media.

Examples of Industrial Applications

• Fuses
• Circuit breakers
• Electronic packaging
• MEMS (Micro-Electro-Mechanical Systems)
• Tissue ablation

### Acoustic Fluid-Structural Coupling

In some practical applications, the fluid can be assumed to be inviscid. This assumption significantly reduces the computational effort required for calculation of the fluid response and also in the fluid-structure interaction problems.

This multiphysics capability is particularly useful when the frequency response of coupled fluid-structure systems is of interest.

Examples of Industrial Applications

• Dams
• Liquid storage tanks
• Nuclear power plants
• Loudspeakers
• Underwater explosions
• Vibration of submerged structures

### Fluid Flow-Mass Transfer Coupling

This class of multiphysics problems is characterized by the coupling between the momentum, continuity and energy equations governing the flow of a mixture of a fluid and other species (solute). The coupling is due to the dependence of the mixture’s density and viscosity on the solute concentration. Transfer of the solute due to the flow changes the spatial distribution of the mixture density and also its viscosity, consequently affecting the flow pattern, which in turn affects the movement of the solute.

Examples of Industrial Applications

• Oil & gas industry
• Ground water modeling
• Nuclear waste
• Drug delivery

For detailed information, refer to our page on thermal-fluid-structure interaction capabilities of ADINA.

### Fluid Flow-Electromagnetic Coupling

In this class of multiphysics problems, the fluid flow is driven by the Lorentz forces caused by the electromagnetic field.

Examples of Industrial Applications

• Electromagnetically-driven pipe mixers

References

1. K. J. Bathe, The Finite Element Method, in Encyclopedia of Computer Science and Engineering, B. Wah (ed.), J. Wiley and Sons, 1253-1264, 2009.

2. For many examples of applications of ADINA in multiphysics problems, see our Publications page.