MultiMechanics Blog

A Brief History of Finite Element Analysis: Looking Forward

Posted by MultiMechanics on May 23, 2018 8:00:00 AM

In our first two posts (Part I and Part II), we talked about the history of FEA and hinted at what the future may hold. 

From a hardware standpoint, companies are continuing to uphold Moore's law as they target 500-fold increases in performance by 2018. However, the speed of a processor does not necessarily improve the accuracy of a finite element solution; it only helps you get your inaccurate results faster. 

This lack of accuracy is being magnified as new, advanced materials are introduced into our toolbox. For composite materials, such as fiber-reinforced plastics, the damage initiates at the microstructural level due to the inconsistent material properties and interactions between constituent materials. Thus, in order to predict a composite's behavior using FEA, you need to explicitly model these interactions. 

To many engineers, the thought of creating an accurate finite element model of a microstructure seems either foreign or prohibitively labor-intensive; not to mention that it will likely take days to compute even on the world's most powerful processor. For this reason, these engineers often their composites as a homogenized orthotropic media and account for the uncertainty through expensive destructive testing and/or the age-old technique of over-design. 

In very simple terms, it is easy to plot the consequences of over-design for just a single part. Assume that a part for a car suspension weighs one pound when perfectly designed and that the material costs $16/lb (as high-performance carbon fiber does). If we plot the cost of excess material for different factors of safety, as the number of manufactured parts grows, we will see the results. 

cost_of_over-1

After manufacturing only 2,000 units, the cost of extra carbon fiber already exceeds $25,000. When you look at the average production rates for a single part in the automobile industry (sometimes over 10 million units of a single part per year), the cost of over-design is around $128 million per year.

The point is that the added cost of accurate FEA becomes negligible as the number of manufactured units increases. When it comes to improving FEA accuracy of a composite part, the three competing approaches are direct numerical simulation, rule of mixtures, and multiscale simulation. 

At MultiMechanics, we believe that a multiscale simulation approach is bridging the gap between the simplified FEA of the past and the ideal-but-costly "direct numerical simulation." For example, consider a composite bar with a single layer of cylindrical fibers, periodically placed along the bar. 

 dissertation_beam-1

When examining tension in this beam, transverse to the fiber direction, you see very clear stratification between the DNS and rule of mixtures approaches. Additionally, as the number of cells in the DNS solution increases (ie the FE model grows in size), it converges towards the computationally modest multiscale results! 

Multiscale_v_DNS-1

Further and most importantly, when running these simulations on a 3.0 GHz Dell workstation, the multiscale simulation runs over 140 times faster than the comparably accurate DNS solution. 

Case Time
Rule of mixture 40 seconds
5 cells 20 minutes
25 cells 6.5 hours
100 cells 6 days
MultiMech multiscale (4 processors)  53 minutes

While the past 50 years of Finite Element Analysis has been bright and prosperous, in order to ensure its utility for the next 50 years, new and innovative approaches need to be adopted. We believe that a multiscale simulation approach allows engineers to take advantage of the advances in computing, accurately model their novel material microstructures, and stay within the practical DOF limits set within industry. 

Topics: Composite Failure, Composite Design, Composites Analysis, Engineering Tools, Composites Engineering, Finite Element Analysis, Multiscale

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