# How to find Young's Modulus using stress strain curve using Python?

I am trying to find the

• The Young's Modulus of an aluminum alloy
• The yield stress

Below is the data for the stress-strain curve. I tried finding the region where the slope is constant and to my surprise, I found that only 4 data points, in the beginning, give me a straight line. After that, there is another straight line that gives me a different slope. I am confused as to which line to use for the calculation of Young's Modulus. If I use the second line I get an answer that does not conform with the reality of the alloy.

So, I tried to find a package for the same : Here is a link for the package which seems very useful. I wanted to download it but could not find it on conda( I am using Jupyter). I was hoping if someone would provide me with the link too.

PS: If there is no such package I would be grateful to receive help with the question without the package, too using Python.

Eng. Strain Eng. Stress
0.000000    4.174826667
0.00000444  4.188426667
0.0000103   4.164346667
-3.28E-06   4.202586667
4.294E-05   7.26848
0.0001964   16.04202667
0.0003372   22.67858667
0.00048938  27.47632
0.00065652  30.70698667
0.00083308  32.89658667
0.00101768  34.41408
0.0012028   35.57272
0.001385    36.52789333
0.0015676   37.36733333
0.00173426  38.04624
0.00193392  38.65781333
0.00210862  39.24997333
0.00228426  39.80757333
0.00245992  40.32866667
0.00263822  40.91192
0.00280184  41.40042667
0.00298324  41.87698667
0.00315386  42.37184
0.00333258  42.77624
0.00347468  43.24722667
0.00365992  43.64136
0.003817    44.06544
0.00399314  44.49149333
0.0041544   44.90893333
0.00432732  45.32496
0.0044855   45.73408
0.00464472  46.13429333
0.00482466  46.54008
0.00499114  46.85842667
0.00514588  47.30917333
0.00529986  47.64224
0.00546718  48.00805333
0.0056278   48.38162667
0.00578708  48.74576
0.005939    49.07576
0.00609224  49.42216
0.00626128  49.75216
0.00640792  50.1016
0.00658574  50.41605333
0.0067529   50.76744
0.00688528  51.10133333
0.00705596  51.44245333
0.0072123   51.75136
0.00736482  52.06888
0.00752996  52.38224
0.00769128  52.68725333
0.00782884  53.04141333
0.00800278  53.30536
0.00814314  53.62370667
0.00831612  53.94037333
0.00844992  54.23848
0.0086224   54.51992
0.00876314  54.81496
0.00893086  55.08557333
0.00907164  55.37144
0.00924458  55.67368
0.00939518  55.95234667
0.00955464  56.2632
0.00971818  56.518
0.00986798  56.79248
0.01000268  57.03533333
0.01016506  57.32344
0.01033396  57.64594667
0.0104826   57.85688
0.01062482  58.13832
0.01079106  58.40506667
0.01093044  58.66234667
0.01109734  58.91434667
0.01124544  59.14917333
0.01140076  59.39784
0.0115488   59.66208
0.01170736  59.91490667
0.01186224  60.14085333
0.01202728  60.42061333
0.01216586  60.62210667
0.01231978  60.91189333
0.01248044  61.14253333
0.01262062  61.37677333
0.01277486  61.60464
0.01293878  61.84056
0.01308824  62.07674667
0.01324216  62.28269333
0.01339498  62.50834667
0.0135425   62.72845333
0.01370544  62.95021333
0.01386166  63.14504
0.0140343   63.40565333
0.01417988  63.62189333
0.01433782  63.81394667
0.014485    64.04514667
0.01463944  64.2572
0.01477906  64.45786667
0.01495412  64.68738667
0.01508752  64.85781333
0.01524908  65.06986667
0.01539768  65.29994667
0.01555352  65.47256
0.01569838  65.70794667
0.0158504   65.90362667
0.0160023   66.07208
0.0161674   66.28496
0.01631316  66.43429333
0.01647162  66.63189333
0.0166194   66.86005333
0.0167683   67.02157333
0.0169192   67.21392
0.01708108  67.40792
0.01723832  67.59722667
0.01737604  67.76485333
0.0175355   67.97274667
0.01769274  68.17978667
0.01784858  68.32938667
0.01799818  68.49093333
0.01815954  68.68466667
0.01831758  68.83314667
0.01847322  69.04992
0.01862252  69.21117333
0.0187715   69.39434667
0.01891798  69.56754667
0.0190876   69.7524
0.01923398  69.89256
0.01939434  70.08712
0.0195366   70.22893333
0.01971648  70.34189333
0.01985822  70.55896
0.02002302  70.69912
0.02017412  70.87232
0.0203226   71.05325333
0.02047664  71.22368
0.02063518  71.378
0.02079262  71.49984
0.02095872  71.6772
0.02110058  71.83706667
0.0212731   71.98554667
0.02141456  72.14514667
0.02157642  72.31472
0.0217224   72.45544
0.0218881   72.58008
0.02204202  72.73882667
0.02220198  72.90618667
0.02234996  73.05717333
0.02250912  73.16042667
0.0226554   73.34888
0.02281184  73.45768
0.0229732   73.63141333
0.02311676  73.80461333
0.02328296  73.88509333
0.02343206  74.03997333
0.02359212  74.17874667
0.02374814  74.35861333
0.02391816  74.46602667
0.02405478  74.59314667
0.02421896  74.71914667
0.02437068  74.9076
0.02453578  74.99642667
0.02467912  75.10328
0.02484332  75.27866667
0.02498948  75.3972
0.02517178  75.54706667
0.02531152  75.65808
0.02547098  75.78770667
0.02563648  75.88650667
0.02577992  76.01586667
0.02594008  76.15573333
0.02609704  76.29701333
0.02625378  76.43245333
0.02643204  76.52432
0.02656072  76.63229333
0.0267267   76.73442667
0.02689018  76.89376
0.0270433   77.02032
0.02720226  77.13714667
0.02736182  77.24706667
0.02752298  77.35976
0.02767006  77.468
0.0278426   77.61010667
0.02798816  77.73112
0.02815316  77.84464
0.0283104   77.90069333
0.0284782   78.07165333
0.02864822  78.19074667
0.0288112   78.26538667
0.02897176  78.45469333
0.02913716  78.51962667
0.02929088  78.6176
0.0294621   78.70698667
0.02960114  78.84074667
0.02978062  78.92290667
0.0299273   79.07472
0.03009852  79.14413333
0.03024762  79.23293333
0.03041582  79.36672
0.03057076  79.41834667
0.03072468  79.57042667
0.03088362  79.64592
0.03105124  79.73778667
0.03120838  79.88128
0.03136452  79.96650667
0.03151964  80.06365333
0.03168926  80.17216
0.03184218  80.28456
0.03200576  80.37784
0.03216934  80.47802667
0.03232044  80.52965333
0.03247638  80.68146667
0.03264298  80.69978667
0.03278724  80.82829333
0.03294822  80.95792
0.03311742  81.05642667
0.03327538  81.10861333
0.0334452   81.22048
0.03359166  81.38226667
0.03376652  81.49912
0.03391038  81.58461333
0.03407878  81.68341333
0.03423976  81.74005333
0.03440254  81.85717333
0.0345623   81.95264
0.03472748  82.05312
0.03487094  82.10474667
0.035047    82.18466667
0.03520916  82.2624
0.0353812   82.36562667
0.03552828  82.43002667
0.03569588  82.55048
0.03585182  82.63096
0.03601058  82.74032
0.03616732  82.79362667
0.03634498  82.85578667
0.03649106  82.95016
0.0366649   83.07117333
0.03682908  83.16330667
0.03698662  83.22381333
0.03714678  83.31541333
0.03732324  83.39701333
0.03747414  83.4936
0.03763572  83.56464
0.03782082  83.61794667
0.03797092  83.68733333
0.03813632  83.77336
0.03830854  83.83554667
0.0384661   83.93712
0.03862746  84.03925333
0.03879688  84.11253333
0.03894456  84.15082667
0.03911498  84.26296
0.03929084  84.29237333
0.03944556  84.41450667
0.03961096  84.48
0.03978278  84.56384
0.03993792  84.60490667
0.04009688  84.69261333
0.0402832   84.74978667
0.0404331   84.8336
0.04059326  84.90021333
0.04076308  84.96738667
0.04092102  85.06786667
0.04109364  85.1256
0.04126306  85.19165333
0.04143128  85.25104
0.04157474  85.33709333
0.04174676  85.41978667
0.04192444  85.47864
0.04209686  85.54525333
0.0422381   85.61685333
0.0424186   85.6496
0.04257452  85.77506667
0.04274174  85.84333333
0.04291396  85.87885333
0.04307834  85.95546667
0.04324334  86.05317333
0.04341436  86.11256
0.0435689   86.18194667
0.04373328  86.22024
0.04391194  86.28853333
0.04407714  86.36568
0.04423408  86.37122667
0.04439564  86.47725333
0.0445703   86.56941333
0.04472804  86.58216
0.0449045   86.65210667
0.0450564   86.73594667
0.04523388  86.82309333
0.0454063   86.89637333
0.0455721   86.91968
0.04572482  87.00570667
0.04589806  87.05901333
0.0460562   87.10341333
0.04622744  87.1728
0.04639262  87.24050667
0.04655822  87.28048
0.04673426  87.33712
0.04690388  87.42813333
0.04706606  87.47866667
0.04723628  87.55802667
0.04740208  87.58856
0.04757974  87.65794667
0.0477387   87.68293333
0.0479073   87.76730667
0.04807128  87.85224
0.04822944  87.85778667
0.04841394  87.92608
0.04858176  88.00877333
0.04874936  88.08205333
0.04891334  88.12701333
0.04908194  88.1764
0.04924654  88.22304
0.04940992  88.24690667
0.04958014  88.34626667
0.04975518  88.39290667
0.0499083   88.43232
0.05008898  88.50114667
0.05025638  88.54277333
0.05041856  88.61162667
0.05058616  88.64936
0.05076444  88.70541333
0.05092158  88.74928
0.05108858  88.8292
0.05125376  88.86141333
0.05143364  88.91413333
0.05158676  88.98074667
0.05177086  89.00962667
0.05193686  89.07458667
0.05210448  89.12064
0.05226222  89.19890667
0.05243526  89.24053333
0.05259824  89.2572
0.05276966  89.33269333
0.05293786  89.38765333
0.05310588  89.42816
0.05327832  89.48034667
0.0534455   89.53808
0.05361472  89.60578667
0.05378032  89.63301333
0.0539429   89.70794667
0.05411492  89.72125333
0.05428514  89.754
0.05443022  89.8628
0.05462358  89.88778667
0.05479318  89.95608
0.0549608   89.99602667
0.05512678  90.00824
0.05528696  90.04432
0.05545114  90.07485333
0.05562438  90.14368
0.05578996  90.25304
0.05597306  90.26192
0.05612618  90.30688
0.05629198  90.3352
0.05647266  90.3896
0.05663422  90.42901333
0.05680888  90.48784
0.05697748  90.51448
0.0571465   90.52949333
0.0573137   90.63938667
0.05748734  90.66602667
0.05766038  90.74597333
0.05782256  90.74042667
0.05800444  90.78706667
0.05819176  90.85976
0.05835998  90.88586667
0.0585306   90.92858667
0.05872134  90.98909333
0.05887224  91.04794667
0.05905656  91.05293333
0.05922758  91.12066667
0.05938532  91.1412
0.05956842  91.20448
0.05972698  91.23389333
0.05989358  91.26610667
0.06006944  91.34602667
0.06024608  91.36546667
0.06039578  91.41874667
0.06058612  91.46426667
0.06075594  91.51090667
0.06092696  91.56917333
0.06109196  91.56973333
0.06126418  91.61914667
0.06142636  91.65744
0.0615978   91.67133333
0.06177204  91.74237333
0.06193984  91.79565333
0.0621177   91.82674667
0.0622674   91.85506667
0.06247424  91.92944
0.06261388  91.9472
0.06278894  91.97330667
0.06297766  92.03656
0.06314546  92.06933333
0.06332012  92.09152
0.06347464  92.14981333
0.0636493   92.17757333
0.06382514  92.22477333
0.0639857   92.27082667
0.06415874  92.28637333
0.06433218  92.3108
0.06450924  92.34909333
0.06467384  92.43957333
0.06483722  92.46624
0.06501428  92.49842667
0.06518248  92.50453333
0.0653672   92.59834667
0.0655169   92.58501333
0.0657004   92.62498667
0.06587222  92.67992
0.06604122  92.70269333
0.06620704  92.73378667
0.06637322  92.76488
0.06654586  92.81816
0.06671446  92.87810667
0.06688428  92.88810667
0.06707222  92.94138667
0.06724526  92.97746667
0.06742272  92.98413333
0.0675877   93.02242667
0.06775914  93.05130667
0.0679394   93.13568
0.06809958  93.17453333
0.06828066  93.19285333
0.06844444  93.20008
0.06861788  93.24669333
0.06879374  93.28
0.06896476  93.31053333
0.06913216  93.3616
0.06930642  93.3716
0.06948266  93.41989333
0.06965208  93.42933333
0.06984 93.45597333
0.06999212  93.53533333
0.070172    93.56197333
0.070339    93.58029333
0.07051648  93.60418667
0.07068106  93.61194667
0.07085248  93.70077333
0.07102632  93.71741333
0.0712042   93.72021333
0.07137844  93.77405333
0.07155308  93.8312
0.0717249   93.81957333
0.0718891   93.86784
0.07206496  93.88781333
0.0722384   93.97221333
0.0724231   93.98442667
0.07257562  94.01773333
0.07275468  94.02882667
0.07291726  94.07712
0.07311162  94.10821333
0.0732742   94.11986667
0.07343476  94.16317333
0.07360942  94.19370667
0.073774    94.22698667
0.07396594  94.24144
0.07413496  94.30250667
0.07431524  94.32858667
0.0744589   94.32248
0.07464282  94.33746667
0.07481706  94.41296
0.07498968  94.42128
0.07515508  94.45293333
0.07533778  94.49954667
0.07550518  94.53173333
0.07567742  94.55562667
0.07584844  94.58338667
0.07601826  94.62890667
0.07620296  94.63666667
0.07637078  94.68274667
0.07655588  94.68328
0.07671886  94.73768
0.07689068  94.78544
0.07706372  94.79208
0.07724562  94.84984
0.07741704  94.86981333
0.07759692  94.88146667
0.07775748  94.91256
0.077943    94.97194667
0.07811562  94.95696
0.07829028  95.00912
0.0784621   95.04912
0.07864038  95.03245333
0.0788134   95.10904
0.07898486  95.07797333
0.07914662  95.13402667
0.07932488  95.18842667
0.0795116   95.20674667
0.07968102  95.21674667
0.07985042  95.2384
0.08003192  95.29722667
0.08020778  95.30112
0.08038564  95.35717333
0.0805615   95.36885333
0.08072448  95.40714667
0.08090314  95.436
0.08107054  95.44322667
0.08125646  95.47930667
0.08142468  95.50373333
0.08160214  95.54869333
0.0817647   95.54536
0.08194458  95.55981333
0.08211682  95.61418667
0.0822979   95.65192
0.08244882  95.67690667
0.08264078  95.67802667
0.08281662  95.71578667
0.08298764  95.73853333
0.083147    95.71909333
0.08331964  95.78184
0.08350796  95.83624
0.08369188  95.85954667
0.08384358  95.85178667
0.08404076  95.89229333
0.08420092  95.92226667
0.08437918  95.92338667
0.08454136  95.94778667
0.08473008  96.01552
0.08490274  96.02552
0.0850665   96.05493333
0.08524558  96.09656
0.08542264  96.08269333
0.08559528  96.13098667
0.0857655   96.15208
0.08594096  96.17538667
0.08610754  96.20426667
0.08629266  96.20202667
0.08645766  96.25589333
0.08664678  96.27976
0.0868146   96.28864
0.08699084  96.31416
0.087149    96.31861333
0.08734578  96.38357333
0.08750996  96.39410667
0.08769428  96.44962667
0.08787414  96.48293333
0.08804516  96.47461333
0.08822222  96.52845333
0.08839688  96.53453333
0.08857756  96.56674667
0.08874738  96.58952
0.08892926  96.58061333
0.08910592  96.58061333
0.08927656  96.60392
0.08944316  96.66776
0.0896335   96.67888
0.08980572  96.70717333
0.0899868   96.72770667
0.09016186  96.74216
0.09032524  96.77101333
0.09050794  96.78989333
0.090687    96.83373333
0.09086126  96.82597333
0.09103428  96.87704
0.09120572  96.89704
0.09137956  96.92034667
0.09156348  96.95365333
0.09174214  96.96032
0.09192202  96.95864
0.09209062  97.02968
0.09226768  97.03357333
0.0924391   97.05189333
0.09261738  97.05522667
0.09278318  97.11461333
0.0929687   97.10573333
0.09314414  97.11517333
0.0933216   97.12573333
0.09349344  97.13629333
0.09366568  97.17234667
0.09385964  97.23621333
0.09402864  97.22896
0.0941884   97.24784
0.09438278  97.27282667
0.09455178  97.30168
0.09471918  97.32666667
0.09490028  97.32666667
0.09506486  97.36109333
0.09525842  97.41770667
0.0954222   97.38218667
0.0955892   97.4388
0.0957731   97.44936
0.09594936  97.43768
0.0961385   97.47432
0.0963051   97.49930667
0.09648456  97.53650667
0.0966584   97.52429333
0.09684432  97.57536
0.09700812  97.60810667
0.09719322  97.622
0.0973566   97.64141333
0.09754212  97.67637333
0.09771596  97.65306667
0.09789542  97.68581333
0.09806002  97.71136
0.0982407   97.72690667
0.09842058  97.78682667
0.09860328  97.748
0.0987731   97.76853333
0.09894974  97.82570667
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0.21910582  103.6059467
0.21929816  103.6104
0.2195074   103.61816
0.21971826  103.6131733



Also please tell me how reliable the new python package is.

• +1. Thanks for joining our site, and we hope to see you here more often. However the first link you sent seems to require a username and password for your university (IIT)? Jul 7, 2020 at 18:03
• How do I add a notepad file here? Also, could you tell me more about the second link too?
– user1015
Jul 8, 2020 at 5:48
• @AkshatBakliwal please remain calm. The question has been up for only 2 days, and no one is "working for you" which means they don't "need" to answer your questions. We are all volunteers. I will do my best to advertise this question so that it gets seen by a wide audience. Jul 9, 2020 at 18:13
• @AkshatBakliwal I would echo Nike's sentiment. The site is still fairly small and it really just depends whether someone is willing to invest the time to answer your question. I'm sure your bounty will go a long way towards getting you an answer.
– Tyberius
Jul 9, 2020 at 18:38
• I get the same error with the Python package. I opened an issue on Github, but the person who wrote it has no recent activity so I wouldn't expect a response. How much of a tolerance are you using to define a straightline? As long as the slope is nearly the same, you might be able to include more points in the first line you found.
– Tyberius
Jul 9, 2020 at 20:46

I was able to run the code on your data and got a Young's Modulus of $$2.08236\times10^{-5}$$. This clearly doesn't seem right for an aluminum system, though I don't know the units you are using.

To get this, I had to make a few changes to both the code and your data.

1. As suggested, by Enusi, I commented out from model import stress_strain from the __init__.py file.

2. Line 159 of material_analytics.py (return data[0,1] + young_modulus*(x-offset)) starts with a tab rather than spaces. This needs to be changed for the code to run.

3. If you are using Python3.x, one of the functions uses xrange, which no longer exists after Python2.x. This needs to be replaced with range in order to run.

4. I removed your first and fourth data points. The youngs_modulus function uses a log at some point, so it will give warnings if you pass it numbers that are zero or negative.

I can only guess that something is wrong with your choice of data points. The curve below is an example stress-strain curve for steel and then your aluminum alloy curve. Your curve does not really have a linear section and looks more like the example curve after the yield strength.

I designed the Python program a few years back but haven't looked at it in some time.

The __init__.py line can be commented out for your usage. That "model" was for my team's use case, and it looks like I got rid of it.

You may be better off importing the "material_analytics.py" directly, and using those functions right on your dataset. They are designed to work with data like yours, and each specifies the format it expects for stress/strain samples. Keep in mind these modules are designed for high strain rate samples, and as such this is just an approximation and no guarantees can be made about the results.

Good luck!

• +10. An answer from the author of the program! It doesn't get any better than that! Jul 10, 2020 at 2:43

Unfortunately, due to my reputation, I cannot comment yet. However, to the surprise of Tyberius, I would like to note that the function young_modulus does not return the Young's modulus, but the compliance.

The code looks as follows

 return (lin_elastic_region[-1,1],lin_elastic_region[0,1])/(lin_elastic_region[-1,0]-lin_elastic_region[0,0])


with lin_elastic_region being of type [stress,strain]. If you interchange the columns to

return (lin_elastic_region[-1,0],lin_elastic_region[0,0])/(lin_elastic_region[-1,1]-lin_elastic_region[0,1])


the value of $$2.08236\times10^{-5}$$ actually turns out as $$48022.43$$, which may be interpreted as MPa or equivalently about $$48$$ GPa. This value is still somewhat small for the stiffness of aluminium, but is quite close to an average value of about $$70$$ GPa.

Also I would like to add, that the program calls the adjust function, which aims on making all strain values positive, but actually sets non-positive values to $$1$$. I changed this value to a very small positive number, such as $$1\times10^{-5}$$.

• Welcome to the site, +1! I think this definitely warrants an answer, rather than a comment, as it seems to resolve the main issue with the code.
– Tyberius
Aug 27, 2021 at 14:08