TAGGED: fem, materialnonlinearity, newtonraphsonresiduals


August 7, 2024 at 9:42 amC DehoSubscriberÂ
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Hello everyone,
I am working on implementing a nonlinear finite element analysis (FEA) code in MATLAB. I have verified that my linear analysis results are accurate and that the initial displacement values match perfectly with those from ANSYS. However, when I proceed to compute internal forces and perform iterations for the nonlinear analysis, I am encountering issues where the residuals do not decrease and the iteration process diverges.
Here's a summary of my approach and where I suspect the issue might be:
Nonlinear Analysis Process:
 In each iteration, I update the global stiffness matrix by adding the stress stiffness matrix $S_{i}$.
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 I compute $S_{i}$ using the Cauchy stress tensor Â in the global cartesian system and then use it to determine the local coordinate system's Cauchy stress vector.( By mltiplying Rotation matrix/ value doesn't changed a lot)
 The straindisplacement matrix$B$ is used for linear stiffness matrix calculations, which I believe is correctly implemented as it matches with linear analysis results.
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$Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â$
$Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â$
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The issue is that the newton raphson restoring force(internal force) $F_{nr}$ become excessively large, causing the iterations to diverge.
I have ensured that the straindisplacement matrix $B$ is used correctly and consistently, as it is crucial for calculating the linear stiffness matrix.
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When computing the internal forces, I average the strains at Gaussian points and multiply them by theÂ $D to get cauchy stress tensor.$Since the only new value I am calculating is the Cauchy stress tensor, I suspect that this might be the source of the problem.Â Â
Given the above, is there a common pitfall or error in the approach of incorporating the stress stiffness matrix $S_{i}$ into the global stiffness matrix that could cause divergence?
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Any insights or suggestions to help resolve this issue would be greatly appreciated.
Thank you in advance for your assistance

August 12, 2024 at 11:07 amAkshay ManiyarAnsys Employee
Hi,
Please check the below Ansys video on the NewtonRaphson method.
Newton Raphson Method  Ansys Innovation Courses
Also, you can check the forum question mentioned below:
What does Stress Stiffening means and why does it happen if Large Deflection = ON? (ansys.com)
Thanks,
Akshay Maniyar

August 15, 2024 at 8:51 amC DehoSubscriber
Thank you for your response.
I appreciate the information provided, but the links you shared only cover the process of NewtonRaphson method and do not address how to calculate internal forces.
Upon review, it seems that the issue may lie in the process of calculating element cauchy stresses, as other matrices appear to be functioning correctly.
Could you please provide details on how to accurately compute internal forces from the element stresses?
Any related resources or references would be greatly appreciated.
Thank you!


August 16, 2024 at 12:30 pmAkshay ManiyarAnsys Employee
Hi,
Please check the below link to a forum question and see if it helps.
Calculation of displacement from nodes on the interface of two materials (ansys.com)
Thanks,
Akshay Maniyar

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