(U,W) Strain energy density has units : [J/m3] =[Pa.m3/m3]=[Pa]
All the strain energy functions are expressed uniquely in terms of the principal stretches or in terms of the invariants of the left Cauchy–Green deformation tensor which are in both cases dimensionless. That’s important because any coefficient multiplying dimensionless elements is responsible to carry the final units of the equation.
For example Mooney-Rivlin according to the manual :
[Pa]=[C10]*[.]+ [C01] * [.] + [1/D] * [.]
All them, C10 , C01 and 1/D must have Strain energy density units [Pa] in SI.
Not that bad considering the fact that hyperelastic constants are obtained here by just deriving them from linear elastic data, without any calibration with test results. Maybe it’s just a matter of refining the mesh and using different boundary conditions.
i quick viewing the shell models only, it may need to be refined the quadratic mesh of mid nodes to fit on curved geometry. another improvement is layering shell element trough the thickness. theoretically this approach will lead to better results at most cases…
Me neither. I’m just reading this afternoon about hyperelasticity.
Well, in fact, stresses and energy density ENER should be the same as the field is conservative. ¿isn’t it? U is its potential energy function.
You can impose displacements to one face and go to the same final position through different routes.
Final energy should be the same. It’s kind of elasticity, but with nonlinear stress strain curves if I’m not wrong.
I have tried with tension and some bending and energy is the same at the end of the process.
This do not necessarily happen with plasticity as part of the energy is lost (hardening work,….).
Please someone correct me if I’m saying something brutal.
For Arruda-Boyce model , lambda_m parameter is not factorizable so must be dimensionless like I1. (A typical value of lambda_m is 7)
Mu is the one that carry the strain energy density units ([Pa] in SI units) for consistency. (Value related with the shear modulus)
In the same way, as J is dimensionless, [1/D] must have strain energy density units ([Pa] in SI units) for consistency. (1/D is related with the bulk modulus k)
In the Ogden strain energy potential, alpha_i could a priori have units but it doesn’t because it also is at the power term of lambda_i.
Once again, alpha_i are weighting coefficients between the different dimensionless stretching ratios.
mu_i is the responsible of carry the strain energy density units ([Pa] in SI units).
[1/D] is like previous models and has strain energy density units ([Pa] in SI units).
Hope this helps to find the units of the different coeficients shown in the hyperelastic models.
Abaqus itself doesn’t use units but the 3DExperience platform utilizing Abaqus as a solver does. To sum up and make it 100% clear, here are the standard units for different hyperelastic models:
I also have another question; hyper elastic materials usually follow a linear pattern and then shift to behaving differently as shown in @fgr’s post. The tube will definitely buckle after a certain point which is when the pressure is increased to like 400 Pa. This case diverges, I assume because it undergoes buckling.
Is there a way for me to model that part without divergence or would the only way be to add a perturbation and switch the cross section to an ellipse to see exact deformation patterns?
If you are concerned about buckling, you could add some geometrical imperfections to perform a nonlinear buckling analysis. Recently we had a long discussion about this topic here: Nonlinear buckling of a cylindrical shell
That’s just linear buckling analysis, it assumes linear elastic behavior. It can help you generate imperfections but what you need is nonlinear buckling analysis like the one described in the thread linked above.
In my experience, the eigen solver struggles to find eigen factors smaller than 1.
I recommend you start way below the expected load (1 Pa) to be sure you don’t skip the first buckling factor and request min 3 modes .
If result is close to 1, recalculate with even lower load.
NOTE: As Calc_em says, that’s Linear Buckling but your material is nonlinear. You should go to nonlinear buckling analysis with material nonlinearities.
