February 28,2006 The Focus Issue 45 February 28, 2006 A Publication for ANSYS Users Issue 45 Modeling the “Plastic Knee” in Workbench By Doug Oatis best analyst would get models that would So you’ve mastered the basics of Work- not solve because the first slope was slightly bench and are ready to tackle a plastic off of the Young’s modulus. This approach analysis. If you look at your stress-strain used a TB,MISO material property to define curve and it looks like a bilinear model is multi-linear plasticity. not going to work, you need to be aware of Based upon this issue and several others, how the WB multilinear model works to the new multilinear plasticity model, TB, make sure you are capturing all of your PLAS was developed so that users only had plastic behavior, especially if your material to define the plastic portion of the stress- has a big “plastic knee”. To understand the strain curve. You do this by defining the why and how, we first need to look at the Total Strain - 0.2% (Yield Strain) for the way it used to be done in ANSYS. x-axis and the total stress for the y-axis. In olden days, you gave the elastic behavior Since this is simpler and produces a lot less as Young’s modulus (EX), a yield stress, user frustration, it was chosen for the multi- linear plasticity model in Workbench. Figure 1: Typical Stress Strain Curve and the whole stress-strain curve. If the havior, you should be using the elastic limit equivalent stress was under the yield stress, So for Workbench the following rules apply: or proportional limit (which are often very ANSYS calculated strain using the Young’s close), as your yield stress and use that point 1: The first data point must be at 0 for plastic modulus. If it was over, it used the curve. strain (X) and the Yield Stress for stress (Y) as zero for your strain. There were three rules that you had to meet: 2: The slopes of all the multi-linear segments If you do this, however, you run into two 1: The initial slope of the curve MUST equal the must have a slope less than or equal to the problems. The first is that you need to Young’s modulus Young’s modulus redefine the yield strength of your material 2: The slopes of all the multi-linear segments 3: No segment can have a slope less than zero in Workbench. This is because Workbench must have a slope less than or equal to the does an internal check to make sure all rules Young’s modulus So instead of calculating a total strain from are met with the plastic curve. If the pre- 3: No segment can have a slope of less than zero a curve when stress is above yield, the solver calculates a plastic strain and adds it defined yield stress doesn’t equal the initial The first rule proved to be especially trou- to the elastic strain. For many materials this y-value of the plasticity curve, the solve blesome. But if you didn’t have it, ANSYS is perfect and saves a lot of headache. But, won’t be executed. This problem gets even would predict a jump in strain when a stress if you can remember back to your Strength more complicated if you have a stress tool moved from below to above yield. Even the of Materials textbook (like “Introduction to calculating margin off of the yield strength, Mechanics of Solids”, since your yield strength is now actually Popov, Pg 111) a lot of your elastic limit. You will need to set the materials show behav- criteria to calculate margin from a user-de- ior like the curve shown fined value. in Figure 1. Pulling out The second problem this creates is that the a definitive yield point elastic limit is not a commonly listed mate- is tough so a 0.002 in/in rial property. Finding this point on an ac- offset of the linear por- tual curve obtained from MIL-HDBK can tion of the curve is used prove to be a long and tedious task. to set a yield stress. (Continued on Page 2) So, if your material Contents doesn’t have a large non-linear “knee” be- Plastic Material Model in fore the yield stress, Workbench ...................................1 you can move on to Substructuring Review....................2 reading other articles in ANSYS Buys Fluent........................3 this issue. But if your material shows this be- 2006 IAC.........................................4 www.padtinc.com 1 1-800-293-PADT February 28,2006 The Focus Issue 45 (“Plastic Knee” cont.) The same geometry, element types, and x-axis and define the non-linear portion of loading were used for each model. The the stress strain curve. ANSYS Classic model used the tried-and- true method which requires the first slope equal the Young’s Modulus. Aluminum shows a significant “knee” between Fel and Fty so it was chosen for this study. Figure 2 shows the data used and is based on a MIL- HDBK-5 graph. The results between the models are shown below in Figures 3 and 4. Figure 2: Material Curve Used As you can see, all three models obtain Figure 3: Comparison of Strain So now you must be asking, “Well, is it similar strain results. However, when really worth the extra effort to use my start- equivalent stresses are viewed, the Work- ing point as the elastic limit instead of using bench model which used 0,Fty as it’s start- the easy-to-obtain 0.2% yield stress?” ing point is different from the other two, and In order to answer this, I created three mod- by a considerable amount. els: So, after all is said and done, if you want to Platform Plasticity Model Starting Point more closely match ANSYS Classic meth- Workbench PLASTIC,,,MISO 0,Fty odology, you need to define 0,Fel as your Workbench PLASTIC,,,MISO 0,Fel Classic MISO 0,0 starting point. Just ignore the values on the Figure 4: Comparison of Stress Reviewing Substructuring By Rod Scholl ces… a method to break a matrix into Substructuring, once a cornerstone of FEA say, quarters, and solve four (N/2 x N/2) system analysis, has continued to fade in matrices can represent significant sav- popularity as computer speed and available ings in solution time and memory re- memory have increased dramatically. It still quirements. Of course these matrices has its place in structural analysis, but it is have to be relatively independent of one definitely diminished. And when this tech- another as we will see. Also, for some nique is applicable, the savings can be huge nonlinear problems, the predominately and makes a nice implement on the Bat Belt linear portion can be scuttled away as a of the FEA analyst. substructure to be solved essentially once, leaving only the nonlinear portion What it isn’t to be iterated upon. Afterward the whole First let’s note that performing a substructred solution is reassembled. Of course not modal anlaysis (prerequisite for many types all problems lend themselves to substruc- of dynamic analysis) requires Component turing… (if not, why would one ever Mode Synthesis (CMS) and although a type mess with the huge NxN global stiffness of substructuring, is not covered in this arti- matrix?!) So expect that only a limited cle, but was covered in the a previous issue class of problems are benefited by the Again, read the manual for more details, but Further, the term “submodeling” is often con- substructuring method. substructuring analysis can be broken into fused with the term “substructuring”. Sub- these steps: modelling refers to the method of taking a How It Works coarsely-meshed solution, remodeling a por- The help manual is decent in this re- Get the macros at: tion of it , meshing with greater refinement, spect… but with all the files and naming ftp.padtinc.com/public/downloads to keep track of, an extra example is and applying the results of the previous run as 1) TSUB1.mac – Generation Pass useful. (attach macros 1,2,3). These boundary conditions (CBDOF) to the new Define how the model will be sliced up into three macros can be run sequentially to model and resolving. chunks, and form a Matrix50 Super-Element model two blocks pushed into contact. (couldn’t resist making the graphic here, get What it Is The majority of the block is sub-struc- it, “Super Element”) of each chunk. What Substructuring is about breaking a model up tured, leaving only the contact surfaces exactly is a super-element? Well, you know into a set of smaller models, or to be solved during the contact iterations. that feeling when you lean back in a chair… “superelements” and then solving them si- The only real trick to substructuring is and you lean back too far, and you thrash multaneously. Since we know solution time getting the file naming correct. There are is roughly related to N^3 for (NxN) matri- a bunch of ways to do this. (Continued on Page 3) www.padtinc.com 2 1-800-293-PADT February 28,2006 The Focus Issue 45 quickly and barely recover? That was a lit- system level results at the superelement tle help from the often invisible, but ever- boundaries and applies them to the superelement present Super-Element… fighting evil in our and solves. Some people still call this an “Unwind” daily lives. Okay, okay, it’s an element with pass.