Tolerances in Fatigue Life Prediction with Endurica

I get this question a lot: how well can the Endurica software predict fatigue life?  Is it as good as a metal fatigue code, where a factor of 2x is often quoted as a target tolerance?

The answer is yes, fatigue life predictions can reach and beat this level of accuracy. But as always, knowledge and control of the problem at hand is key.  We must keep in mind that fatigue behavior varies on a logarithmic scale.  It depends on many variables.  It depends on how failure is defined in the simulation and in the test.  Small variations of an input may lead to large variations of the fatigue life.  So, to achieve the best tolerances, careful specification, measurement, and control are required of both simulation and test.

Analysis tolerances depend on whether the analysis workflow is “open loop” or “closed loop”.  In an open loop workflow, the analyst is typically in the position of having to accept without question the as-given material properties, geometry, boundary conditions and load history.  The analysis is completed and reported.  Decisions are made and life goes on.  In a closed loop workflow, there are additional steps.  These include a careful review of differences between the test and the simulation, as well as identification and correction of any erroneous assumptions (about material properties, geometry, boundary conditions, and load history).

Open loop workflows produce larger tolerances.  Every situation is different, but do not expect tolerances tighter than perhaps a factor of 3x-10x in life, when working in open loop mode.  There is just too much sensitivity, too many variables, and too little control in this mode.  The open loop mode does have a few advantages though.  It takes less work, less time, less cost.  And it is often useful for ranking alternatives (ie A vs. B comparisons).

For high accuracy, a closed loop workflow is required.  It is rarely the case that initial assumptions are sufficiently error-free to support tight tolerances on fatigue life prediction.  Therefore, careful measurement and validation of material property inputs, part dimensions, load-deflection behavior, pre-stresses, etc. should be made.  Where gaps are found between test and simulation, appropriate amendments to the test and/or to the simulation should be adopted.  This approach yields high confidence in the simulation results, and good accuracy in fatigue life predictions.  We have seen users hit life predictions to better than a factor of 1.1x with this approach!  Although this approach requires more effort, it results in more complete mastery of part design, and it yields a much stronger starting position for subsequent products.

While “right the first time” engineering is possible with either open or closed loop, the closed loop approach benefits from progressive refinement of the analysis inputs and it ultimately gives the highest success rate.

 

 

twitterlinkedinmail

What is the Price of Standing Still?

What if we don't change at all and something magical just happens? Technical equation for entropy

“We have always done it this way.” No longer simply a hated phrase, this statement is a warning of impending disaster. Entropy – the disorder that happens when energy disperses and systems simply fall into chaos – happens when things do not change. But it’s a slow process you don’t see day-to-day. Continuing with traditional “build and break” development methods instead of embracing CAE and simulation has many long-term risks but it will only be after stagnating for some time that rubber parts manufacturing firms, and even the entire rubber industry, will realize the pitfalls:

Talent Loss
People are the key to it all and we start here since intelligent, hard-working, productive people are the fundamental reason any business succeeds. When the best and brightest employees leave a company, the fundamental reasons often include the lack of opportunity, learning, and career development. When not allowed to work with emerging technologies and are no longer challenged to grow, top performers find new opportunities taking not only raw potential but also institutional memory with them. And if they don’t see the industry as a viable long-term option, switching companies can also mean leaving the sector completely.

Warranty Issues/Payouts
Liability issues arise when product usage, applications and environments bring risks that may not have been factored in to the original designs and/or production methods. Traditional testing methods cannot be used to investigate “what if?” scenarios the way CAE and simulation can. Recalls and litigation can be significantly more costly than new technology implementations.

Lost Opportunity Costs
While harder to measure than fixed and variable business costs, there is an expense to every choice known as opportunity cost. Refusing to enter a new business sector may result in significant loss of revenue and profit. Taking on a big client project may strain production capabilities. “Standing still” eliminates those risks, but at what potential gain? As the rubber industry wrestles to “go green” we are all weighing and measuring the opportunity costs involved. The real lost opportunity is in refusing to embrace a fundamentally better design platform.

Incompatibility or Obsolescence
At some point, everything being produced right now will become obsolete. Even if you produce the best “widgets” anywhere, the environment around that “widget” will change and will no longer be needed in its current form. The rubber industry standard procedure of building a product then breaking it in physical testing to determine the next design rendition is incompatible with the time available for new product development. It just does not work anymore.

How quickly your business can adapt to or anticipate change is a key factor in continued success. The reasons companies do not make continued progress often include:

Change is expensive
Investments in training, new production systems, updated software and computers add up, but these numbers are not insurmountable when factored against the ongoing and often increasing costs of waste, repairs and downtime associated with outdated systems and equipment.

Learning new technology is time-consuming
Remember when you were thinking about going to college and four (6-8-10) years seemed like FOREVER? What was your ROI? What will it be now? Time invested in learning reaps many rewards beyond the subject at hand and often provides renewed overall energy.

The status quo works
For today, yes. For a brighter future for you company and the industry, NO. Companies that don’t evolve face certain death. Day-to-day operations may appear stable, but firms who do not keep up with technology do not stay in business. Covid forced many to embrace technology in new ways and those firms continuing to provide progressive working arrangements are gathering more than their fair share of the best and brightest talent. Enabling people to work beyond traditional geographic boundaries requires accountability and processes for measuring valued contributions rather than simply time at a desk.  Firms embracing CAE and simulation technologies have realized this and are at the top of the leading rubber industry rankings.

 Six reasons to adopt Endurica workflows

  1. Technically superior (click for details)
  2. Save big on development out of pocket costs (click for details)
  3. Reduce the need for physical testing (see page 2, blue box on right)
  4. Speed to market (able to use the tools immediately)
  5. Accuracy in meeting client needs (click for details)
  6. Easier answers down the road (click for details)
twitterlinkedinmail

My SAE WCX 2022 Top Takeaway

 

SAE WCX | Detroit, Michigan | April 5-7, 2022

There were several papers on fatigue life prediction for elastomers at SAE WCX 2022, but the highlight for us was this one from Automotive OEM Stellantis: “Fatigue Life Prediction and Correlation for Powertrain Torque Strut Mount Elastomeric Bushing Application” by Dr. Touhid Zarrin-Ghalami, Durability Technical Specialist at FCA US LLC Fiat Chrysler Automobiles logowith coauthors C Elango, Sathish Kumar Pandi, and Roshan N. Mahadule from FCA Engineering India Pvt, Ltd.  Check out the abstract or buy the paper here…

The study shows that very accurate fatigue life prediction results are possible for elastomeric components under block cycle loading using Critical Plane Analysis.  A key feature of the analysis is the characterization and modeling of rubber’s hyperelastic properties, fatigue crack growth properties, crack precursor size, and strain crystallization behavior.  Careful measurement of these analysis ingredients led to a nearly perfect correlation of the predicted life (520 blocks) with the tested life (523 blocks, average of 4 replicate tests), and of predicted failure mode with observed failure mode.

Endurica users like Stellantis are developing a solid track record of routine and successful fatigue life prediction.  We soon expect to see the day when CAE fatigue life prediction for rubber components is regarded as obligatory, given the risk and cost avoided with “right the first time” engineering.

Congratulations to the Stellantis team on this impressive success!

 Fatigue Life (block) demonstrating the accuracy of the CAE Virtual Simulation compared to a physical test

Citation: Elango, C., Pandi, S.K., Mahadule, R.N., and Zarrin-Ghalami, T., “Fatigue Life Prediction and Correlation of Engine Mount Elastomeric Bushing using A Crack Growth Approach,” SAE Technical Paper 2022-01-0760, 2022, doi:10.4271/2022-01-0760.

twitterlinkedinmail

Virtual vs. Physical in 2021 and Beyond

An insight to how Endurica stayed connected during Covid-19, by using Microsoft teams to meet virtually.These days everybody’s talking about whether to meet in person or online.  There are great tools available for online meetings, and these have helped us navigate Covid-19. Like everyone else, Endurica teammates regularly use online meeting technology.  But if there is one thing we learned over the last year, it is that sometimes physical presence really matters. Living and working in isolation is just not healthy in the long run.

The new normal during the pandemic had some benefits that were enabled by the virtual world. Time and energy that used to be consumed by travel were rechanneled into improving our software, testing services, and marketing materials. In our personal lives, we had more opportunities to spend quality time with our immediate families and found more time for fitness activities. We previously talked about our pandemic pivots to bring our training courses online and offer webinars to stay in touch with our existing and potential customers.

But virtual meetings can’t replace the full experience of being together in person.  The face-to-face engagement at a trade show, the serendipitous bumping into a client, the spontaneous discussion of ideas with fellow conference-goers with a shared interest, the rapport building that comes from shared experiences.  We fundamentally need physical connection. A hug, delivered via Zoom, will never feel the same.

The world of 2021 and beyond is hybrid: part virtual, part in-person.  The benefits of the virtual are too great to set aside, and the necessity of the physical is too compelling to neglect.  Both are critical to our future, at home and at work.

So, too, with Endurica’s simulation workflows. It was NEVER Simulation OR Build-and-Break. Even the best simulations are not enough to completely skip physical testing. The virtual approach saves significant time and money in product development and design refinement. It allows you to explore a huge space of compound options and of design features before investment in building and testing prototypes. Our simulations enable you to balance difficult trade-offs. Still, before you head into production, you must complete actual physical testing on your rubber part – the physical world is what counts in the end. It is simulation AND build-and-break that are both needed in concert to #GetDurabilityRight.

Just as a Zoom hug will never replace the real thing, software will never replace the role of physical testing.  But just as online meetings are creating new opportunities and efficiencies, Endurica’s tools position you for unprecedented success when it’s time to test.

It's a Hybrid World from Here | Endurica's tools position you for unprecedented success when it’s time to test.

twitterlinkedinmail

Proper tear testing of elastomers: Why you should tear up the Die C tear test

Endurica Fatigue Ninja tearing rubber

I spent an interesting and rewarding part of my career helping to lead an elastomer technical college in Yanbu, Saudi Arabia. One of the rubber technology words that was challenging for the Saudis to say in English was ‘tear’. They initially pronounced it like the heteronym related to crying. It might be a stretch to say that tears will come to your eyes if you don’t get tear testing of elastomers right, but proper measurement of critical tearing energy (tear strength) is essential for effective materials development for durability.

The fatigue threshold (intrinsic strength; T0) is the lower limit of the fatigue crack growth curve shown in the figure below, and we recently reviewed this material parameter including the various measurement options.1 The upper limit is the tear strength, TC. If loads in your elastomer component are near or above TC, then it is not a fatigue problem anymore but rather a critical tearing issue with imminent product failure. It is therefore important to accurately characterize this durability performance characteristic of your materials.

General fatigue crack growth behavior of elastomers

Endurica uses the planar tension (pure shear) geometry for measuring TC in our Fatigue Property Mapping testing services due to the simple relationship between the strain energy density (W) and the energy release rate (tearing energy, T).2,3 The TC is equal to the W at tearing multiplied by the initial specimen height, h. You can see this geometry below along with other tear testing specimens employed in the rubber industry and specified in the ASTM standard.4

Comparison of the different durability tests one can conduct: the differences between Crack Nucleation Test and Tear and Crack Growth Tests.

We sometimes get questions from folks with technical backgrounds in metals or plastics about whether rubber tear properties will be different when tested in distinct testing modes (mode I, mode II, etc.). It turns out that the extensibility of rubber causes the deformation to be predominately tension in the tearing region, irrespective of how the crack is opened, such that TC values are similar for rubber evaluated in different testing modes.2,3 Therefore, trouser tear testing is an alternative to the planar tension testing, as long as any stretching of the legs is accounted for in the data analysis.3,5 With no stretching of the legs, TC is simply given by 2F/t where F is the measured force to propagate the tear and t is the thickness of the specimen. The factor of 2 is surprisingly omitted in the ASTM standard4 even though it is mentioned in the appendix. The image below shows how to convert the ASTM trouser tear strength to TC.

Trouser tear strength testing

A proper tear test includes an initial macroscopic cut/crack in the specimen. This is not the case for Die C tear described in the tear testing standard.4 Die C is thus not a tear test at all but rather is a crack nucleation experiment akin to normal tensile testing of rubber. Because the strange Die C geometry forces failure in a small region in the center of the specimen, it is actually less useful than tensile strength testing of a dumbbell sample which probes the entire gauge region. The Die C test can also have substantial experimental variability related to the sharpness of the die used to punch out the samples. Unfortunately, the Die C “tear” test is the most popular method in the rubber industry to (incorrectly) assess the tear strength of elastomers, and this reality was a key motivator for writing this post. We look forward to seeing the rubber industry shift away from the Die C test, and we hope that the information provided here will help in that path to #GetDurabilityRight. Click here to learn how intrinsic strength and tear strength can be measured quickly and accurately (0:42 video).

References

  1. Robertson, C.G.; Stoček, R.; Mars, W.V. The Fatigue Threshold of Rubber and its Characterization Using the Cutting Method. Advances in Polymer Science, Springer, Berlin, Heidelberg, 2020, pp. 1-27.
  2. Lake, G.J. Fatigue and Fracture of Elastomers. Rubber Chem. Technol. 1995, 68, 435-460.
  3. Rivlin, R.S.; Thomas, A.G. Rupture of rubber. I. Characteristic energy for tearing. J. Polym. Sci. 1953, 10, 291–318.
  4. Standard Test Method for Tear Strength of Conventional Vulcanized Rubber and Thermoplastic Elastomers. Designation: ASTM D 624-00, ASTM International, West Conshohocken, PA, USA, 2020; pp. 1-9.
  5. Mars, W.V.; Fatemi, A. A literature survey on fatigue analysis approaches for rubber. Int. J. Fatigue 2002, 24, 949–961.
twitterlinkedinmail

Is It Validated?

Is it Validated?

“Is it validated?” – that’s often the first question we hear after introducing our durability simulation capabilities. And for good reason, given the weight that hangs on the hinge of product durability. Endurica takes verification and validation (V&V) very seriously. Let’s look at what that means.

First, it means that our tools are built on well-known, well-established foundations.  These foundations include 1) definition of material / crack behavior via fracture mechanics (Rivlin and Thomas, 1953), 2) integration of the crack growth rate law to predict fatigue life (Gent, Lindley and Thomas, 1964), 3) the fact that crack precursors occur naturally in all locations and all orientations in a rubber sample (Choi and Roland 1996, Huneau et al 2016), 4) hyperelastic stress-strain laws compatible with commercial FEA codes (see Muhr 2005 for an excellent review), and 5) rubber’s fatigue threshold (Lake and Thomas 1967).  The validation case thus begins with the cumulative authority of thousands of reports that have confirmed these classical results over nearly 70 years.

Critical plane analysis for rubber has now been around for 20+ years, and it has been validated in multiple ways (material level, component level, system level), across multiple experimental programs (industrial and academic), by multiple independent research groups working on multiple applications (see Google/scholar, for example).  It has been validated that: 1) it correctly predicts crack plane orientation under uniaxial, proportional and nonproportional loadings (Harbour et al 2008), 2) it correctly predicts fatigue life across different modes of deformation (Mars 2002), 3) it correctly accounts for the effects of crack closure (Mars 2002), 4) it correctly predicts the development of off-axis cracks for nonrelaxing cycles in strain-crystallizing materials (Ramachandran 2017), 5) it correctly predicts the effects of finite straining on crack orientation (Mars and Fatemi 2006).

The literature is full of old experiments that we have used as validation targets.  We have validated Endurica’s strain crystallization models by simulating experimental results published by Cadwell et al (1940) and by Fielding et al (1943).  We have validated the ability to predict deformation mode effects by simulating experimental results for simple and biaxial tension published by Roberts and Benzies (1977).  We have validated Endurica’s temperature dependence against measurements reported by Lake and Lindley (1964).  We have validated against multiaxial fatigue experiments reported by Saintier, Cailletaud and Piques (2006).

We’ve done our own validation experiments.  My PhD dissertation (University of Toledo, 2001) contains an extensive database of tension/torsion/compression fatigue tests against which our critical plane algorithms were validated.  Two additional PhD dissertations that I co-advised generated additional validations.  Dr. Malik Ait Bachir’s thesis (2010) validated mathematically that the scaling law we use for small cracks is valid across all multiaxial loading states.  Dr. Ryan Harbour’s thesis (2006) contains a database of multiaxial, variable amplitude fatigue experiments against which our rainflow and damage accumulation procedures were extensively validated.

Validation from partners.  We partner with several testing labs.  We have invested in testing protocols that produce clean, accurate data and we have run validation programs with our partners to verify the effectiveness of our testing protocols.  We’ve demonstrated significant improvements to test efficiency and reproducibility (Goosens and Mars 2018) and (Mars and Isasi 2019).  We’ve validated techniques for estimating precursor size and size distribution (Robertson et al 2020, Li et al 2015).

Validation from users.  Three (3) of the top 12 tire companies and six (6) of the top 10 global non-tire rubber companies now use our solutions.  Most of our users have run internal validation programs to show the effectiveness of our solutions for their applications.  Most of these studies are unpublished, but the fact that our user base has continued growing at ~20%/year for 12 years (as of this year) says something important both about the technical validation case and the business validation case.  Validation studies have been published with the US Army (Mars, Castanier, Ostberg 2017), GM (Barbash and Mars 2016), Tenneco (Goossens et al 2017) and Caterpillar (Ramachandran et al 2017).

Validation from external groups.  There are several academic groups that have independently applied and validated components of our approach.  There are too many to list completely, but a few recent examples include Zarrin-Ghalami et al (2020), Belkhira et al (2020) and Tobajas et al (2020).

Software verification, benchmarking and unit testing.  In addition to the experimental validations mentioned above, each time we build a new version of our software, we execute a series of automated tests.  These tests verify every line of code against expected function, and they ensure that as we add new features, we do not introduce unintended changes.  The benchmarks include tests that verify things like coordinate frame objectivity (rigid rotations under static load should do no damage and the same strain history written in two different coordinate systems should have the same life), and check known results pertaining to material models and cycle counting rules.  You can read more about our software quality processes here.

It is safe to say that no other solution for fatigue life prediction of rubber has been tested and validated against a larger number of applications than Endurica’s.

References

Aıt-Bachir, M. “Prediction of crack initiation in elastomers in the framework of Configurational Mechanics.” PhD diss., Ph. D. thesis, Ecole Centrale de Nantes, Nantes (France), 2010.

Barbash, Kevin P., and William V. Mars. Critical plane analysis of rubber bushing durability under road loads. No. 2016-01-0393. SAE Technical Paper, 2016.

Belkhiria, Salma, Adel Hamdi, and Raouf Fathallah. “Cracking energy density for rubber materials: Computation and implementation in multiaxial fatigue design.” Polymer Engineering & Science (2020).

Cadwell, S. M., R. A. Merrill, C. M. Sloman, and F. L. Yost. “Dynamic fatigue life of rubber.” Rubber Chemistry and Technology 13, no. 2 (1940): 304-315.

Choi, I. S., and C. M. Roland. “Intrinsic defects and the failure properties of cis-1, 4-polyisoprenes.” Rubber chemistry and technology 69, no. 4 (1996): 591-599.

Fielding, J. H. “Flex life and crystallization of synthetic rubber.” Industrial & Engineering Chemistry 35, no. 12 (1943): 1259-1261.

Goossens, J.R., Mars, W., Smith, G., Heil, P., Braddock, S. and Pilarski, J., 2017. Durability Analysis of 3-Axis Input to Elastomeric Front Lower Control Arm Vertical Ride Bushing (No. 2017-01-1857). SAE Technical Paper. https://doi.org/10.4271/2017-01-1857

Goossens, Joshua R., and William V. Mars. “Finitely Scoped, High Reliability Fatigue Crack Growth Measurements.” Rubber Chemistry and Technology 91, no. 4 (2018): 644-650. https://doi.org/10.5254/rct.18.81532

Harbour, Ryan Joseph. Multiaxial deformation and fatigue of rubber under variable amplitude loading. Vol. 67, no. 12. 2006.

Harbour, Ryan J., Ali Fatemi, and Will V. Mars. “Fatigue crack orientation in NR and SBR under variable amplitude and multiaxial loading conditions.” Journal of materials science 43, no. 6 (2008): 1783-1794.

Huneau, Bertrand, Isaure Masquelier, Yann Marco, Vincent Le Saux, Simon Noizet, Clémentine Schiel, and Pierre Charrier. “Fatigue crack initiation in a carbon black–filled natural rubber.” Rubber Chemistry and Technology 89, no. 1 (2016): 126-141.

Lake, G. J., and P. B. Lindley. “Cut growth and fatigue of rubbers. II. Experiments on a noncrystallizing rubber.” Journal of Applied Polymer Science 8, no. 2 (1964): 707-721.

Li, Fanzhu, Jinpeng Liu, W. V. Mars, Tung W. Chan, Yonglai Lu, Haibo Yang, and Liqun Zhang. “Crack precursor size for natural rubber inferred from relaxing and non-relaxing fatigue experiments.” International Journal of Fatigue 80 (2015): 50-57.

Mars, William Vernon. Multiaxial fatigue of rubber. 2001.

Mars, Will V. “Cracking energy density as a predictor of fatigue life under multiaxial conditions.” Rubber chemistry and technology 75, no. 1 (2002): 1-17.

Mars, W. V., and A. Fatemi. “Analysis of fatigue life under complex loading: Revisiting Cadwell, Merrill, Sloman, and Yost.” Rubber chemistry and technology 79, no. 4 (2006): 589-601.

Mars, W. V., and A. Fatemi. “Nucleation and growth of small fatigue cracks in filled natural rubber under multiaxial loading.” Journal of materials science 41, no. 22 (2006): 7324-7332.

Mars, W. V. “Computed dependence of rubber’s fatigue behavior on strain crystallization.” Rubber Chemistry and Technology 82, no. 1 (2009): 51-61. https://doi.org/10.5254/1.3557006

Mars, William V., Matthew Castanier, David Ostberg, and William Bradford. “Digital Twin for Tank Track Elastomers: Predicting Self-Heating and Durability.” In Proceedings of the 2017 Ground Vehicle Systems Engineering and Technology Symposium (GVSETS). 2017.pdf here

Mars, W. V., and M. Isasi. “Finitely scoped procedure for generating fully relaxing strain-life curves.” In Constitutive Models for Rubber XI: Proceedings of the 11th European Conference on Constitutive Models for Rubber (ECCMR 2019), June 25-27, 2019, Nantes, France, p. 435. CRC Press, 2019.

Muhr, A. H. “Modeling the stress-strain behavior of rubber.” Rubber chemistry and technology 78, no. 3 (2005): 391-425.Lake and Thomas 1967

Ramachandran, Anantharaman, Ross P. Wietharn, Sunil I. Mathew, W. V. Mars, and M. A. Bauman. “Critical Plane Selection Under Nonrelaxing Simple Tension with Strain Crystallization.” In Fall 192nd Technical Meeting of the Rubber Division, pp. 10-12. 2017.

Rivlin, R. S., and A. G. Thomas. “Rupture of rubber. I. Characteristic energy for tearing.” Journal of polymer science 10, no. 3 (1953): 291-318.Gent, Lindley and Thomas, 1964

Roberts, B. J., and J. B. Benzies. “The relationship between uniaxial and equibiaxial fatigue in gum and carbon black filled vulcanizates.” Proceedings of rubbercon 77, no. 2 (1977): 1-13.

Robertson, Christopher G., Lewis B. Tunnicliffe, Lawrence Maciag, Mark A. Bauman, Kurt Miller, Charles R. Herd, and William V. Mars. “Characterizing Distributions of Tensile Strength and Crack Precursor Size to Evaluate Filler Dispersion Effects and Reliability of Rubber.” Polymers 12, no. 1 (2020): 203. Pdf here

Saintier, Nicolas, Georges Cailletaud, and Roland Piques. “Multiaxial fatigue life prediction for a natural rubber.” International Journal of Fatigue 28, no. 5-6 (2006): 530-539.

Tobajas, Rafael, Daniel Elduque, Elena Ibarz, Carlos Javierre, and Luis Gracia. “A New Multiparameter Model for Multiaxial Fatigue Life Prediction of Rubber Materials.” Polymers 12, no. 5 (2020): 1194.

Zarrin-Ghalami, Touhid, Sandip Datta, Robert Bodombo Keinti, and Ravish Chandrashekar. Elastomeric Component Fatigue Analysis: Rubber Fatigue Prediction and Correlation Comparing Crack Initiation and Crack Growth Methodologies. No. 2020-01-0193. SAE Technical Paper, 2020.

 

twitterlinkedinmail

Behind the Scenes Tour of Endurica Software Development and QA Practices

Ever wonder what it takes to consistently deliver quality and reliability in our software releases?  Here’s a brief overview of the systems and disciplines we use to ensure that our users receive timely, trouble-free updates of Endurica software.

Automation:

Throughout the life of our software, changes are made to our source code for a variety of reasons.  Most commonly, we are adding new features and capabilities to our software.  We also make updates to the code to improve performance and to squash the inevitable bugs that occasionally occur.

With each change committed to the code repository, the software needs to be built, tested, and released.  Endurica’s workflow automates these steps so that any change to the source repository triggers a clean build of the software.  A successful build is automatically followed by a testing phase where our suite of benchmarks is executed and compared to known results.  Finally, the build is automatically packaged and stored so that it is ready to be delivered.  At each step along the way, a build error or failed test will cancel the workflow and send an alert warning that the release has been rejected, so that the issue can be addressed, and the workflow restarted.

Endurica's build and testing process ensures that high quality standards are met for every new release. Black arrow: normal flow, Red arrow: an error or failed test
Figure 1: Endurica’s build and testing process ensures that high quality standards are met for every new release. Black arrow: normal flow, Red arrow: an error or failed test.

Reliability:

The automated testing phase that every release goes through helps ensure the reliability of our software.  For example, every Endurica CL release must pass all 70 benchmarks.  Each benchmark is a separate Endurica CL analysis made up of different materials, histories, and output requests.  Results from a new build are compared to known results from the previous successful build.  If results do not agree, or if there are any errors, the benchmark does not pass and the build is rejected.

The testing phase prevents “would-be” bugs from making it into a release and makes sure that any issues get resolved.

Repeatability:

The automated nature of our development workflow naturally helps with repeatability in our releases.  Each build flows through the same pipeline, creating consistent releases every time.  There is less worry, for example, that a component will be forgotten to be included.  It also allows us to recreate previous versions if comparisons need to be made.

Traceability:

Our version control system enables us to easily pinpoint where and when prior changes were introduced into the software.  Each release is tied to a commit in the repository. This allows any future issues to be easily traced back and isolated to a small set of changes in the source for quick resolution.

Responsiveness:

Automating the build and release pipelines greatly increases our responsiveness.  If an issue is discovered in a release, the problem can be resolved, and a fully corrected and tested release can be made available the same day.  We can also quickly respond to user feedback and suggestions by making small and frequent updates.

The systems and disciplines we use in our development process make us very efficient, and they protect against many errors. This means we can spend more of our time on what matters: delivering and improving software that meets high standards and helps you to get durability right.

twitterlinkedinmail

EIE – Effect of Map Discretization on Interpolation Accuracy

Overview

The accuracy of the interpolated results performed by EIE is dependent on the discretization of the map. Specifically, the results will become more accurate as the map’s point density increases. This study uses a simple 2D model to quantify the accuracy of results interpolated from maps with different densities.

Model

A 1 mm x 1 mm rubber 2D plane strain model with two channels is used. The square’s bottom edge is fixed and the top edge is displaced in the x and y directions as shown below. The x displacement corresponds to channel 1 and the y displacement corresponds to channel 2. The working space of the model is defined by the x displacement ranging from 0 mm to 0.8 mm and the y displacement ranging from -0.08 mm to 0.8 mm.

Plane strain model with two channels
Plane strain model with two channels

The model is meshed with 100 8-node, quadrilateral, plane strain, hybrid, reduced integration elements (shown below).

100 element mesh
100 element mesh

History

We define as the benchmark reference solution a history that covers the model’s entire working space with a high density of points. An evenly spaced grid of 128×128 points for a total of 16384 points is used as the history (shown below). It is important that this history is more refined than the maps that we will create to ensure that we are testing all regions of our maps.

128 x 128 history points
128×128 history points

These points are used to drive the finite element model and the results are recorded. For this study, we record the three non-zero strain components and the hydrostatic pressure (NE11, NE22, NE12, and HP) for each element at each time point. In summary, there are 4 result components, 100 elements, and 16384 time increments. This set of results is the reference solution since it is solved directly by the finite element model. We will compare this solution to our interpolated results to measure our interpolation accuracy.

Maps

Six maps with different levels of refinement are used to compute interpolated results for our history points. All of the maps structure their points as an evenly spaced grid. The first map starts with two points along each edge. With each additional map, the number of points along each edge is doubled so that the sixth and final map has 64 edge points. The map points for the six maps are shown below.

Six maps with increasing levels of refinement, structuring their points on an evenly spaced grid
Six maps with increasing levels of refinement

The map points for these six maps are used to drive the finite element model’s two channels. The strain and hydrostatic pressure results from the FEA solutions are recorded at each map point in a similar way to how the results were recorded for the FEA solution that was driven by the history points. Next, EIE is used six times to interpolate the map point results at each resolution onto the high resolution reference history points.

We now have seven sets of history results: the true set of results and six interpolated sets of results.

Results

To compare our results, we look at the absolute difference between the sets of results. The absolute error is used, opposed to a relative error, since some regions of the model’s working space will give near zero strain and hydrostatic pressure. Division by these near zero values would cause the relative error to spike in those regions.

Since we have 100 elements and 4 components per element, there are a lot of results that could be compared. To focus our investigation, we look at the element and component that gave the maximum error. The figure below shows contour plots for each of the six maps for this worst-case element and component. The component that gave the maximum error was NE12. The title of each of the contour plot also shows the maximum error found for each of the plots.

Error contours for the worst-case element and component. Titles report the maximum log10 error.
Error contours for the worst-case element and component. Titles report the maximum log10 error.

You can see that the error decreases as the map density increases. Also, you can identify the grid pattern in the contour plots since the error gets smaller near the map points.

Plotting the maximum error for each of the maps against the number of map points on a log scale is shown below. The slope of this line is approximately equal to 1 which is expected since a linear local interpolation was used to compute the results.

Maximum error vs the number of points for each of the six maps
Maximum error vs the number of points for each of the six maps
twitterlinkedinmail
close
Trial License RequestTrial License RequestTrial License RequestTrial License RequestTrial License Request

Our website uses cookies. By agreeing, you accept the use of cookies in accordance with our cookie policy.  Continued use of our website automatically accepts our terms. Privacy Center