Creating non-linear force

[Eugene Lin]

Hello,

I am trying to model spider threads right now, and I have come across an issue where the threads are experiencing large amounts of deformation, requiring a nonlinear stress strain curve.

Here is a sample of how a typical stress-strain curve looks like. You can see it is not exactly straight at larger loads.

I am reading the FEA module documentation and it doesn't seem like there is any information about modelling nonlinear stress strain curves in the FEA module. Is it possible to recreate a stress-strain curve to model this, maybe by adding a few functions inside the FEA module?

Thank you,

Eugene

[Mike Taylor]

Eugene,

The ANCF beam elements (ChElementBeamANCF_3243, ChElementBeamANCF_3333) in the main branch currently are only setup for a simple linear elastic/viscoelastic material model. 

Looking at your curve, I was wondering how critical it was to capture the effects of plasticity versus treating the entire curve as elastic.  If you could treat it as elastic, then potentially you could use a hyperelastic material law to approximate your curve.   It is relatively straightforward to modify these elements for hyperelastic material laws based on the principal invariants of the right Cauchy-Green deformation tensor (C).   The mathematical details for this are documented in my PhD thesis in chapters 9 & 10 (Efficient Implementation Strategies for the Absolute Nodal Coordinate Formulation with Linear and Hyperelastic Material Laws).  I have an example of a two-term Mooney-Rivlin material model for these elements in a branch of my fork of chrono (https://github.com/taylome/chrono/tree/thesis/hyperelastics) [ChElementBeamANCF_3243_MR_Damp and ChElementBeamANCF_3333_MR_Damp which both include a nonlinear Kelvin-Voight viscosity model as well].  Note that I have a couple comparison tables against results from a commercial code in chapter 10 of the thesis which shows that these beam elements are okay for axial extension but have severe locking in bending This can be somewhat addressed with selective reduced integration, but that technique over softens the elements a bit.  The hexahedral element (much more computationally expensive) performed much better for these tests [ChElementHexaANCF_3843_MR_Damp].

Alternatively, if you could define the first Piola-Kirchhoff stress tensor for your desired material law at every Gauss quadrature point in the ANCF element, then I think you could use equation 7.28 in the thesis to setup the generalized internal force vector needed in the code.  You could then implement a numeric differentiation approximation for the Jacobian of the generalized internal force to keep the implementation simpler.   There is an example of computing a numeric Jacobian in ChElementBeamANCF_3243_MR_DampNumJac.cpp

I know it is possible to model plasticity within ANCF, however I personally have not tried to do so.  If you look at the ChElementHexaANCF_3813_9 element, you'll see that this element, which is coded up differently, supports plasticity for both metals and soils.  Unfortunately, I don't know much more than that.  Looking at the code for the ChElementBeamIGA, I noticed that it also had options for plasticity, but I personally don't know anymore than that.

I hope that helps,

Mike Taylor