Open Source Mechanics

20260320 - Implicit u-p Solver, first tests
#FEM #Forging #Implicit #Quad #2D

I’ve recently integrated remeshing into my Updated Lagrangian U–P SRI (Selective Reduced Integration) formulation with Picard iteration for viscoplastic flow governed by a Hollomon hardening law.

This marks a significant step in the development of my implicit FEM solver, especially for large deformation problems such as forging simulations.

After implementing the remeshing pipeline, I ran a series of benchmark comparisons against industrial-grade software. The results are encouraging:

The load–displacement curves match very closely with reference solutions

The deformation patterns and field distributions are in strong agreement

The overall numerical behavior remains stable through large strains

The remeshing does not introduce noticeable artifacts in the solution when properly transferred

The remeshing strategy allows the solver to maintain mesh quality during severe deformation, which is essential for robustness in Updated Lagrangian formulations. Combined with the U–P approach and SRI, this helps mitigate volumetric locking while preserving accuracy in nearly incompressible regimes.

From a practical standpoint, this improves the solver’s capability to handle realistic forming processes where mesh distortion would otherwise lead to divergence or loss of accuracy.

This implementation is still based on a Picard iteration framework, which is simpler but less efficient than a full Newton–Raphson scheme. However, the current results confirm that the overall numerical formulation is consistent and physically reliable, which is a key milestone before moving toward a more robust nonlinear solver.

Next steps include:

Improving convergence behavior of the nonlinear iterations

Transitioning from Picard to a Newton-based + Line Search implicit scheme

Further validation against a broader set of industrial benchmarks

Enhancing the remeshing transfer accuracy for internal variables

Add Norton-Hoff & Johnson Cook material models

This work is part of the broader OpenSource Mechanics effort focused on building and understanding industrial-grade finite element solvers from the ground up.

If you’re interested in FEM development, solver architecture, or large deformation mechanics, this series will continue to dive deeper into the implementation details.

Skip the Carousel

1 2 3

4 days ago | [YT] | 8

Open Source Mechanics

HUGE News!! Implicit u-p Solver is working!!

#FEM #Forging #Implicit #Quad #2D

The implicit mixed u–p Selective Reduced Interation quasi-static formulation with contact is now operational in 2D axisymmetric form. This completes the implementation of both the explicit and implicit computational frameworks for this class of problems.

The implicit approach is commonly used in industrial forming software such as DEFORM and Forge. In this implementation, it provides a complementary methodology to the explicit solver, particularly for:
Load and deformation verification.

Quasi-static analyses where explicit time integration becomes computationally expensive.

At this stage, the nonlinear system is solved using a successive iteration scheme.
As a next step, a Newton–Raphson procedure will be introduced to improve convergence behavior, while preserving the current formulation as the baseline implementation.
Some limitations were observed in the friction model due to a simplification in the contact formulation (see figure).
The same issue was previously encountered in the explicit solver and was resolved by incorporating the history of tangential displacements.

1 week ago | [YT] | 4

Open Source Mechanics

Remap Improvement Goodbye Numerical drifting!!!

#FEM #Forging #Explicit #Quad #2D #Remapping #Martins #Remeshing

Up until now, remapping of element fields was performed using the nearest element.
With this approximation, numerical drifting could be observed. For example, in a plane strain compression test, the maximum values gradually moved upward in the domain.
This effect was not observed in 3D because the MMG remesher preserves the mesh for a relatively long time.
In contrast, the custom 2D remesher starts from a structured mesh generated from the bottom up, which caused this drifting.
This issue has now been fixed by including neighboring elements in the remapping procedure.

2 weeks ago | [YT] | 4

Open Source Mechanics

WeldFormFEM First Load Test cases!
Comparison against industrial tools.

Skip the Carousel

1 2 3 4

2 weeks ago | [YT] | 6

Open Source Mechanics

20260218 - Quad Remeshing extremely improved !!!
#FEM #Forging #Explicit #Quad #2D #Contact #Martins #Remeshing
News!Remeshing algorithm i widely fixed, not only for 2D but also for original 3D.
Now can be reached extreme strains. Remeshing library has its own repo!

Check
opensourcemech.com/

4 weeks ago (edited) | [YT] | 8

Open Source Mechanics

Quad remeshing is finally working on WeldFormFEM!

Ok, I have tested first version of Paulo Martin's Style UP implicit solver and is working smoothly!
It is a simple fixed point iteration Picard style, which will be the first iterations starter before switching to NR (which is already coded).
This is a Mixed VP formulation, rigid viscoplastic flow formulation, with quasi-static regime, updated lagrangian, with Norton-Hoff Material.
The pressure is obtaining by divergence penalization, and hence no stabilization (like PSPG) is needed.
Q1-P0 element is used, with selective integration.
I have migrated to C++ and is ready to add contact feature!



Check latest news:
opensourcemech.com/

Skip the Carousel

1 2 3

4 weeks ago (edited) | [YT] | 15

Open Source Mechanics

Quad Remeshing is almost done!

Skip the Carousel

1 2

4 weeks ago | [YT] | 10

Open Source Mechanics

2D Quad Contact is ready!
Next step is own remeshing algorithm.
Check mi page!

4 weeks ago | [YT] | 6

Open Source Mechanics

I built a 2D quad remesher in python based on Petersen-Martins (2000). It combines grid based, projection, delaunay, collapsing tris to quads, subdivide fallback quads, and smart iteration to make the mesh conforming!
This will be soon included in the 2D solver as built tin remeshing algorithm!!

Skip the Carousel

1 2 3 4 5 6 7 8

1 month ago | [YT] | 6

Open Source Mechanics

WeldFormFEM News!
Both explicit & Implicit FEM solvers are gettin' bigger & robust!
Explicit FEM version now accept:
- Elasto Visco Plastic (Perzyna Style) plastic models, to work with Hollomon, Johnson Cook, Norton Hoff, GMT among others. This is a lot more stable than conventional plastic radial return with hardening like Simo & Huges style, wich is more suited for non rate dependent models.
- Rigid Visco Plastic Norton-Hoff style (WIP)
- The main focus is on remeshing, up until now was periodic, but now has a lot of new controls based on :
- distortions
- normalized jacobians
- bad count element percentage
which trigger both delta time reduction & remeshing.

Keep on track! Follow me!
opensourcemech.com/subscribe

3 months ago | [YT] | 12