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deflection due to plasticity manual calculation

deflection due to plasticity manual calculation

deflection due to plasticity manual calculation

(OP)
Hello,
I Like to know how to do manual calculation for finding displacement of cantilever beam due to plasticity. I know to find values without plastic effect using stiffness matrix methods. But when the plastic data is added the deflection increase more due to provided strain values which is reached due to stress. But this happens due to change in elastic modulus values I think. So can you help me in solving this.

A beam of length 102 mm, where left end is fixed and right end is free. From left upto 2 mm the moment of inertia is 0.520833 mm^4
and the rest (remaining 100 mm) upto the tip of beam to right has inertia value of 266.6666667 mm^4. The load at the tip is 6 newton, modulus of elasticity of beam is 70000 N/mm^2 and poisson ratio 0.3.
True Yield stress ------------ true plastic strain
90, ------------ 0
100.2, ----------- 0.00071230266
110.55, ----------- 0.00370184151
120.84, ------------ 0.00568991373
135.2, ------------ 0.037291147

Now if I did not enter plastic data in abaqus and run non linear it gives 3.464 mm but with plastic data it gives 79.91 mm (time period 2 secs) because if the load reaches the max yield stress, strain increases making displacement more. I know how to calculate without plastic effect. So again the question is how to calculate with plastic values what changes during manual calculation and how abaqus changes it?


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