I am trying to program a Newton-Raphson Nonlinear solver for Material nonlinearities (i.e. bilinear material) and i don't know how to define Tangential and Secant Young Moduli since the 3-node finite element doesn't have constant strain so as to find a single value fot the Tangential and Secant Moduli. Can you suggest me any references related to this?
Thanks in advance.
You can read section 6.3.3 of this book
Finite Element Procedures: K.J. Bathe
It is modeled using Fortran in this link
https://github.com/HaoguangYang/OpenSTAP
Also you can read example 4.36 in this book
Book Introduction to Nonlinear Finite Element Analysis
Hi Dimitris Dimitriou ,
I don't know what you are trying to say with "i don't know how to define Tangential and Secant Young Moduli since the 3-node finite element doesn't have constant strain". That seems to be a little bit unclear.
I assume that you are talking about plasticity. In this case the book "Computational Inelasticity" by Simo and Hughes will help you with the derivation of the Tangent Stiffness. There are a lot of other books who cover the derivation for simple cases like a bilinear material model fairly well.
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