The most accurate finite-element analysis today models multiple physical properties interactively.

**David Kan, Ph.D. COMSOL Inc. Burlington, Mass.**

Edited by Robert Repas

Soon after computers entered the technology landscape, finiteelement analysis (FEA) emerged as a method to solve real-world engineering problems. The work of engineers, applied mathematicians, and physicists over the years showed that FEA could potentially solve for any system of physical phenomena through its use of partial differential equations (PDEs). Those equations mathematically describe physical effects such as fluid motion, electromagnetic fields, and structural mechanics. FEA was a way to translate these well-known mathematical models into an approximate digitally rendered display.

While these early FEA tools tackled a particular aspect of a design, such as stress and fatigue, it became apparent that physics phenomena rarely act alone in nature.For example, heat is generated whenever there are dynamics; and heat always affects other material properties such as electrical conductivity, chemical reaction rates, and the viscosity of fluids, to name but a few. These coupled systems of physics, known as multiphysics, demanded more sophisticated calculations than then-current FEA systems could address effectively. The need for multiphysics analysis tools, though, was obvious.

For the most part, multiphysics simulation remained just a theory throughout the 1980s and 90s because the computational resources did not exist. So, as FEA modeling became a natural part of the research, design, and development cycle, its scope was limited to a single type of physics at a time. The most common types were mechanics, heat transfer, fluids, and electromagnetics. It seemed that FEA was destined to widespread use as a single physics solver simulating mechanical parts.

That landscape has now changed. Decades of advances in computational science have brought us smarter algorithms and faster, more powerful hardware that puts multiphysics-capable FEA tools within reach for all engineers and scientists. The revitalization of FEA toward multiphysics opens up new opportunities for modeling and simulating real-world applications as well as a world of technological investigation. The future of FEA lies in its innate capacity to leverage PDEs for multiphysics analysis.

They say a picture is worth a thousand words, so here is a series of examples that give you a more complete picture of the inherent possibilities of multiphysics FEA.

Piezoacoustic transducers can transform an electric current into an acoustic pressure field or, conversely, generate an electric current from an acoustic field. Typically, these devices go into applications that need sound generation in air or liquid, such as phased-array microphones, ultrasound and bioimaging equipment, sonar transducers, and acousto-biotherapeutics. They are also found in mechanical applications such as inkjet-droplet actuators and piezoelectric motors.

A piezoacoustic device model needs three different physics: piezoelectric stress-strain, an electric field, and pressure acoustics in a fluid. Only a multiphysicscapable simulation can define a computer model that couples the involved phenomena.

The piezoelectric domain is formed from a PZT5-H crystal — a common material in piezoelectric transducers. The boundary condition for the acoustics sets the pressure equal to the normal acceleration of the solid domain at the air and crystal interface. This drives the pressure in the air domain. On the other hand, the crystal domain is subjected to the acoustic pressure changes in the air domain. The simulation conducted studied the acoustic wave propagating from the crystal when applying an electric signal with an amplitude of 200 V and an excitation frequency of 300 kHz. The description of this model and its elegant result indicate that a significant amount of mathematics is behind the compact interface.

One area where multiphysics modeling excels is in the classroom. Students intuitively grasp the visual representation of what had been heretofore invisible. The ease of understanding the displayed model can make students cheer. That’s just what Dr. Krishan Kumar Bhatia experienced after introducing modeling and simulation tools in an undergraduate heat-transfer course conducted at Rowan University in Glassboro, N.J. His students were tasked with cooling a motorcycle engine block. Dr. Bhatia taught the class using the “design-build-test” concept to help students learn by encountering problems, making mistakes, and overcoming them. Obviously that method could not be used in a classroom without computerized modeling as the cost would be prohibitive.

The custom user interface in package like Comsol Multiphysics lets students rapidly set up the heat-transfer problem and gives them direct access to the underlying equations. “One of my main goals was to make the students comfortable with PDEs so that the next time they ran into one, they wouldn’t be afraid to deal with it,” says Bhatia. “This wouldn’t have been possible with many other simulation tools. Almost universally, the feeling among the students is that ‘modeling is really cool!’”

The improved engineering efficiency high-tech organizations see from multiphysics modeling helps them keep their competitive edge. Multiphysics modeling lets engineers run more what-if analyses while building fewer physical prototypes. Thus, they can quickly and cost effectively develop the optimal design of products. One such example comes from a group of researchers at **Medrad Innovations Group **in Indianola, Pa. Led by Dr. John Kalafut, the researchers used multiphysics modeling to investigate the injection of blood cells, a non-Newtonian fluid, with high shear-rates through thin syringes.

From this study the engineers at Medrad developed a particularly novel device known as the Vanguard Dx Angiographic Catheter. The diffusion-tip nozzle produces a more uniform distribution of injected contrast materials compared to a traditional end-hole catheter. Contrast materials are fluids that enhance the visibility of objects within the body during medical imaging using techniques such as X-rays.

Another problem with traditional end-hole catheters is that they tend to cause the contrast material to stream from the exit hole at high velocities, potentially endangering blood vessel walls. The Vanguard Dx Angiographic Catheter reduces the reaction forces associated with contrast material streaming from the nozzle and therefore minimizes the likelihood of the catheter contacting and damaging the blood vessel walls.

The crucial question that needed an answer was what ideal configuration of holes or slits around the catheter tip optimized fluid delivery while preventing a structural deflection? Kalafut’s research team used multiphysics modeling to couple forces from laminar flow with a stress-strain analysis and then model the fluid-structure interaction in the catheters with various hole configurations, geometries, and flow patterns.

“One of our intern students generated many configurations of hole designs in different fluid regimes,” says Dr. Kalafut. “We used these results to determine the feasibility of new ideas while limiting the number of benchtop models the mechanical engineers had to fabricate.”

Patented in 1991, friction-stir welding (FSW) has since been widely used to create strong joints in aluminum alloys. The aircraft industry was one of the first to adapt this technology and is now studying how to cut manufacturing costs with it.

During FSW, a cylindrical tool made up of a shoulder and a threaded pin is spun and inserted into the joint between two pieces of metal. The rotating shoulder and the pin generate heat — but not enough heat to melt the metal. Instead, the softened, plasticized metal forms a solid phase made up of a fine-grained material with no entrapped oxides or gas porosity. The crushing, stirring, and forging action produces a joint with a finer microstructure than the parent material and with twice the strength. The process even joins dissimilar aluminum alloys.

Airbus funded several investigations to study FSW. Dr. Paul Colegrove of Cranfield University looked at modeling to help his group fully understand the process before manufacturers made massive investments in retooling their manufacturing lines.

The first creation of the research was a mathematical model for FSW that let **Airbus** engineers look “inside” a weld to examine temperature distributions and changes in microstructures. Dr. Colegrove and his team created a GUI-driven simulation tool so Airbus engineers could look at the thermal properties and ultimate strength of the weld.

The multiphysics model used for the FSW simulation calculates heat flow from a 3D thermal analysis that’s coupled with a 2D axisymmetric swirl flow simulation. The thermal analysis calculates the 3D temperature field from the heat flux imposed at the tool surface. It captures the effect of the tool movement, the thermal-boundary conditions, and the thermal properties of the material being welded. The model then projects the temperature distribution near the tool surface from the 3D boundary to the domain in the 2D model. The combined model thus calculates the interaction between heat and flow generated during the FSW action.

The ability to couple the electromagnetic behavior of a substrate to electrical resistance and heat transfer through conduction and radiation takes a true multiphysics model. A typical example where these physical properties interact are in hot-wall furnaces that use induction heating and radiation for semiconductor manufacturing and annealing. The furnace reactors are used to grow layers on semiconductor wafers and for epitaxial growth, a key technology in the fabrication of electrical devices.

For example, growth in wideband- gap silicon carbide takes place in graphite susceptors at temperatures around 2,000°C. The susceptors are heated with radiofrequency (RF) coils, using power levels in the 10-kW range. The furnace chamber design is crucial to create efficient heating that produces uniform temperatures with proper control at such a high temperature. The multiphysics model of the chamber shows that the heat flux is dominated by radiation at these high temperatures. Not only does the model show the temperature distribution over the wafer, it shows the temperature on the outer Quartz tube of the furnace as well.

Important aspects in the choice of materials used in electronic designs are the durability and lifetime of the materials. The drive to miniaturize electronic devices gives rise to an extensive use of surface-mount electronic components. A well-known problem for surface-mounted resistors and other components that produce heat is that temperature cycling can lead to cracks in solder joints and thus premature failure of the circuit board.

The multiphysics model of a surface-mount component can look at the heat transport, structural mechanical stresses, and deformations that result from rising temperatures. The detailed examination can lead to improved mounting techniques and material selections that better withstand the elevated temperatures and stresses, thus mitigating failure.

Advanced computational power made true the predictions that FEA could become the basis for multiphysics simulation. Over the next few years, the wide accessibility of multiphysics modeling will noticeably impact science and engineering. Turnaround times for what-if simulations will shrink, virtual prototypes will offer expanded design ideas, and the understanding gained directly from performing simulations will spark innovation. It is not too much to claim that multiphysics simulation is an enabling factor for the future progress of science and engineering.

**Make Contact Comsol Inc.,** (781) 273-3322, comsol.com

**cranfield.ac.uk**

Cranfield University,

Cranfield University,

**medrad.com**

Medrad,

Medrad,

**calumet.purdue.edu**

Purdue University-Calumet,

Purdue University-Calumet,

**rowan.edu**

Rowan University,

Rowan University,

**unlv.edu**

University of Nevada, Las Vegas,

University of Nevada, Las Vegas,

**Benchmarking multiphysics**

The development of simulation software drives the need for objective measurements of performance. One crucial indicator of software performance derives from benchmark tests.

Dr. Darrell W. Pepper of the University of Nevada, Las Vegas, and Dr. Xiuling Wang of Purdue University-Calumet have published a suite of benchmark problems. The purpose of their benchmarking project was to create four standard 3D benchmark problems to compare performance in computational cost, efficiency, and accuracy between the different multiphysics modeling software. The quartet of benchmark tests simulated fluid-structure interaction (FSI), fully coupled electronic current conduction with Joule heating and structural analysis, electromagnetic wave propagation, and the magnetic fields around and inside a rotating electric generator.

A 46-page report on *Benchmarking Comsol Multiphysics 3.4* gives complete descriptions of all benchmark problem definitions as well as the testing criteria, environment, and individual test methodologies. Scientific literature and experimental data are well annotated and compared with simulation results whenever possible. Simulation results include extensive comparison tables as well as a rich complement of full-color charts and screens shots for each benchmark test.

Benchmarks like these take on more importance as multiphysics technology becomes a standard tool in science and engineering. Still, comparing different codes in terms of performance raises an interesting observation: a multiphysics code can be as fast, or faster, than specialized codes. Whether you are doing structural, fluid-flow, heat-transfer, or electromagnetics analysis, solution speed hinges on solving a PDE system. All systems rely on similar solvers, and multiphysics codes share the same core algorithms for the computationally intensive tasks.