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Basics of plasticity-Crisfield's book

Hi-I'm currently reading the chapter 6 on Basic plasticity from the book by Crisfield on Non Linear Finite element analysis and am finding it a bit too hard  to understand things but am determined to get it right.

I shall be extremely grateful if anyone can help me understand  few introductory sections and I hope once that,I could follow the correct path.

For example, in the introductory paragraphs he states that:

1. The main objective of the present chapter is to concentrate on those aspects that relate to a numerical solution.

2.In particular, we will be mainly thinking of the finite element method but many of the concepts that apply to other discretisation procedures such as finite differences.

3.In contrast, the present chapter will concentrate on the Von Misses yield criteria although much of the workm will be general and applicable to other yield functions.

4.In the present chapter only isotrpic hardening will be trated in depth while the flow rules will generally assumed to be associative.

5.Because the plastic flow rules are incremental in nature,elasto plastic problems sould be solved using small equilibrium steps.

6.For, no matter how accurately we may, within an increment satisfy the flow rules and keep to the yield surface, the solution is only in equilibrium at the end of each increment after the equilibrium iterations.

7.In keeping with the main static theme of work, we will not consider the time dependent visco plasticity but should note that visco palsticity approaches have ben used with a psedo time to analyse time independent elasto plasticity.

8.In relation to such elasto plasticity having reached equilibrium at the point A on the effective stress strain curve, the next step may continue to flow plastically to point B or else unlaod elastically to C.

9.Clearly the to paths have very different stiffnesses.If it is known that the loads are to be reversed at the point A, the elasto platic tangent stiffness should not be used for the next increment and the elastic stiffness matrix should be used.

10.But in the absence of load reversals, it will generally be assumed that plastic flow will continue and tangent stiffness relates to AB.

11.However,even for monotonically increasing loads, certain areas of the structure can 'unload'. In such cases, it is generally left to iterative correction procedure to discover those areas that are unloading.

I shall be grateful if someone throws some insight on the termonologies used in:

Point 3: Von Misses yield criteria

Point 4:Isotropic hardening

Point 5:Plastic flow rules- what is meany by when he says-they are incremental in nature?

I'm not able to get as what he is trying to convey in point 6,8,11

Can anyone provide some insight onto this/ any web/book reference will be useful

 

Hi,

I think reading this chapter/section of A.F.Bower's book may answer some questions.

http://solidmechanics.org/text/Chapter3_7/Chapter3_7.htm#Section3_7_1

Any more suggestions?Come on all experts, help us with some funda too!

 

kajal

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