It is a method whereby classical, mathematical, formulations for calculating stress, strain, temperature/heat flow, or flow potential for simple geometries (blocks, simple beams, thin plates, etc.) has been extended to very complex geometries made up of the simple geometric components. The complexity inherent in this "conglomeration" is represented in mathematical matrix forms that are solvable by computer numerical methods.

Genesis of the FEA Method
The finite element method was first employed on truss-like structures and over time expanded to include most physical/mechanical phenomena.

Finite Element Analysis Usage is Expanding
FEA is gaining wider and wider use as the software tools and computing hardware become less costly and more capable, like everything else in this computer age. Academic curricula involving the finite element analysis method are now available at most universities with engineering schools. Application is still somewhat problematic because the method requires good engineering intuition and experience.

Three things are required. First, accurate material properties and material models, i.e., the finite element analysis mathematical model that best represents the material behavior. Second, a good solver, one that meets accuracy requirements and user flexibility. And third, good FEA requires a good analyst. Really, the first two depend on the last.

The Role the Analyst Plays
The analyst chooses the software, sets up the model physics and controls the simulation. The analyst must have a good intuitive grasp of the physics and be able to properly apply the solvers. Remember the adage, "garbage in, garbage out?" The analyst is part engineer and part designer: engineer, to correctly pose the problem and make assumptions or simplifications where necessary; and designer, to imaginatively build the finite element model, apply constraints, and make changes that meet engineering and aesthetic considerations. This is not always straight forward. FEA analysis is a balancing act and that is why it can be difficult for many engineers to apply it successfully.

FEA, on the scale we employ it, cannot model residual stresses generated in parts during machining, or complex temperature dependent processing. It is not always applicable to material or fluid mechanics on micro-structure scales (scales employed in fracture mechanic studies dealing with metal grain sizes and polycrystalline structures, etc.) largely because the real, composite geometry, and material loads at these scales are difficult to know and apply.

Having said that, the factors mentioned above can be accounted for through relative effect studies, which can provide useful information not otherwise available.

Special purpose FEA CFD, reactive gas dynamics, explosive shear rupture phenomena, and mold flow solvers are available, but generally, they are very expensive and involve esoterica that is not useful for all but the most specialized interests.

Another way of asking this question is, What can FEA do? See the Examples page.

Most FEA software vendors provide verification samples that compare FEA results to classical closed-form solutions that are exact. Good FEA solvers deliver answers that compare to the exact answer within a couple of percentage points or better.

Engineering, the Art of Approximation and Inference
As engineers, we realize that in the real world, there are no exact answers, just very good approximations. Again, accuracy depends on what characterizes well executed FEA.

Applycon currently employs FEA software from Autodesk, Inc.: Autodesk Algor Simulation 2010 for three reasons. First, it is the most capable general purpose implicit solver available and is continually improved. Second, for its power, it is easy (a relative term) to use with a coherent and consistent graphical user interface (GUI). Third, it is affordable. Applycon has 25 years experience with other high-end FEA software suites and solid modelers.

As a consulting engineering business, Applycon must provide reliable answers fast and at reasonable rates, or we would not stay in business. Most serious FEA packages are good, let's not quibble. The solvers, whether linear or nonlinear, are very capable. After all, the fundamental mathematics are the same.

Software Flexibility
What it comes down to is this: how much flexibility is the analyst given in how he/she sets up the problem? Here flexibility implies real-world load application and material representation accuracy. This is where Algor Simulation excels. Compare its list of material models, element types, solvers, loads and constraint options, FE meshers to its competition. And don't forget Algor Simulations's unique Mechanical Event Simulation (MES) capability! You'll see the difference.

Most real-world problems involve complex interactions that are not fully captured with the linear static type packages. For example, linear static stress modelers assume a perfectly elastic material. The figure of merit for this elasticity is Young's (Elastic) Modulus. Typically, the neo-analyst assumes that the part will survive if the reported stress does not exceed the yield point, or worst, the tensile strength of the material. However, the yield point assumes a 0.02% strain offset of the Elastic Modulus. There is permanent deformation occurring but has not met the definition of plastic behavior, yet. Okay, this simple analysis has ignored every failure mode but a single, catastrophic one. The questions that need to be asked now are: Does the part see millions of cycles? What effect does a small stress have over many cycles? Is the material really a plastic one? We may be in a fatigue situation. What do we do next? The answer is: "Nothing. You've exceeded the limits of your software."

Today, designs require optimization for cost, strength, wear, manufacturability, etc. These things involve second order effects not visible with pedestrian linear solvers. Nonlinear applies to events and processes as well as materials.

When to Consider Nonlinear Finite Element Analysis
Consider the case where the stresses in a linear finite element (FE) model reported are very low. At this point the part could be considered over-built. Reducing the material could reduce costs in manufacturing. Let's say we want to go from a machined part, to a cast one. How thin can we make a stiffening web, etc.? Again, we are in a situation where we need the horse power of very sophisticated solvers to adequately answer this question since we are designing at the material's limits. Time to consider a nonlinear solver.

Or consider a very common, yet seemingly simple problem. We have a box with internal electronics. We must pass a drop test. How do we orient the boards or components on those boards? First, what is the load? You'll have to guess. How good is your guess? Everything depends on this guess. You can't use a linear static solver. Using a nonlinear solver like Autodesk Algor's we don't have to guess. We just set up a problem in virtual space and perform the drop test. It's that "easy." We can apply initial translation and rotation velocities, orientations, etc. The printed circuit boards inside will actually vibrate after impact. Want a concrete floor or carpet? Done. Set it up as you like. Glad you had a nonlinear solver?

How about this electric sign attached to a wheeled trailer commonly seen around highway construction sites to inform motorists of constructions delays? How should we design the post/base to withstand a steady wind and a destructive wind gust to prevent toppling or some other problem? Well, with a nonlinear solver you can examine the cyclic effect of turbulent eddies that put the structure into rotational oscillation. You don't have to guess at the force generated by the wind, just apply the air fluid flow and let the solver determine the load for a given wind velocity at any vector you choose. Glad you used the nonlinear solver?

In a word, VERY.

Appearance versus Content
Any analyst can produce numbers and present "pretty pictures" showing stress fields, streamlines, and temperature gradients. The answer has to make sense and be believable. The FEA approach must pass scrutiny from all sides until confidence is earned.

Forensic Verification
From a forensic standpoint, it will be necessary to demonstrate the failure mode and location with an FEA simulation. If the new design passes the failure criteria established by the forensic analysis and utilizes the same FEA approach, then the model can be said to be verified and the methodology can be applied to other designs. Failing this, FEA has not accomplished anything.

The Analyst's Grasp
The verification process will ultimately depend on the analyst's ability to capture the event physics and persuasively communicate his/her rationale to the customer. If the problem is really a material property question and no published data is available, then laboratory determination of properties will be suggested.

FEA results are material, load, and geometry dependent. Most real-world problems involve complex interactions between loads, materials, and the geometry that can not be intuitively grasped, much less predicted by closed-form mathematical means, or determined in any other manner.

Stress Concentrations
Failures occur at stress concentrations. There is no better way to predict the location and effects of stress concentration than with finite element analysis for two major reasons. First, to measure stress you need the actual part, or assembly, you need to load it with the actual environmental condition under study, and you need the measurement equipment to collect the stress data. This is usually very time consuming and expensive, especially when the study must include variations in material or geometry. Secondly, in many cases the stresses cannot be experimentally measured because the feature size is too small or in an inaccessible area. The stress concentration, or geometrical load magnification effect, is built into the FEA method, so there is no need to apply (guess at) concentration factors, which are subject to qualification and interpretation.

When we speak of concentrations, this applies as well to fluid flows and heat transfer where we can consider flow bottle-necks, turbulence, or very steep temperature gradients as "stress" concentrations. (See the FEA Examples)

Not all stress concentrations are "bad." The FEA method is well suited to sensor design, where the designer wants high strain in certain locations. This also applies to inclusion of flexible features that must deflect or buckle in certain ways and locations.

FEA is Cost Effective
The final answer goes to the bottom line: FEA is cost effective. Building virtual prototypes is faster and cheaper than building hardware. It has been our experience that even proven designs can be improved with an FEA tweak.

Hyperelastic materials, like rubber, exhibit nonlinear and shallow stress/strain relations at high strains and are nearly incompresible. We employ Algor software to model these rubber-like materials in the FEA virtual world and choose from three types, which depend on the maximum expected strain: Mooney-Rivlin, Ogden, or Arruda-Boyce.

Data Input Requirements
The FEA material models rely on user input material data, like density and a stress/strain relation. This stress/strain data is empirically derived by straining material samples in usually four different ways under laboratory conditions: uniaxial tension, equibiaxial tension, pure strain, and volumetric compression. The first three are usually the easiest to obtain and are provided in units of Engineering Strain and Stress, where Engineering Strain is defined as the average linear strain, obtained by dividing the elongation of the length of the specimen by the original gage length, and Engineering Stress as the load divided by the original cross-sectional area. Volumetric compression requires data in the form of volumetric strain and pressure.

The first three data types above should be provided for every material modeled (the fourth is more difficult to obtain and is not required if the other three are available, see below). The data is entered into the software and a curve fit to the data. That curve which best fits the data, is the curve employed in the analysis.

Uniaxial Tension Data Collection
The test specimen, the classic dog-bone shape, must be pulled in simple tension to achieve a state of pure tensile strain. Therefore, the test specimen must be much longer in the direction of stretching than in the width and thickness dimensions so that there is negligible constraint to lateral thinning. A non-contacting strain measuring device such as a video extensometer or laser extensometer is required to measure strain where the pure strain condition exists.

Equibiaxial Tension Data Collection
Equibiaxial extension of a test specimen generates a strain state equivalent to pure compression. This method is more complex than the simple compression experiment, but a pure state of strain can be achieved, which results in a more accurate material model. The equibiaxial strain state may be achieved by radially stretching a circular disc.

Pure Shear Data Collection
The rubberlike materials are nearly incompressible. So, when a test specimen that is very wide with respect to its length (a fat dog-bone if you will) is pulled in simple tension a state of pure shear exists in the specimen at a 45-degree angle to the stretching direction. The objective is to create an experiment where the specimen is perfectly constrained in the lateral direction so that all specimen thinning occurs in the thickness direction.

Volumetric Compression Data Collection
Here, a cylindrical specimen is constrained in a fixture and compressed to obtain its compressiblity. Care must be taken to measure only the specimen compliance and not the test equipment since the actual displacement during compression is very small.

Complicating Factors for Data Collection of All Types
Hyperelastic materials exhibit the Mullen effect, which is a kind of material hysteresis. The strain rate is a function of material preconditioning and even the test data collected will show signs of "path dependence" under repeated data collection. Therefore, it will be important to collect several data sets, where each data set is collected after a series of preconditioning strains to levels of strain approximating the material's maximum operational strain.

Other complicating factors include temperature dependencies. At a minimum, the test data should be collected at the operational temperature(s) of the material to ensure realism.

Low strain rate materials may follow a creep law. Other material models are available to simulate them.

For more specific information, please contact Applycon directly.