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Finite strain and stability · VNV-TET4-TL-STRESS-001

TET4 affine finite-strain patch

An affine deformation checks Green–Lagrange strain, PK2 and Cauchy stress transformations, strain energy and positive Jacobian behavior.

Internal review accepted with recommendationsCampaign version 0.2.0
Read the recorded results← All calculation cases
Affine finite-strain patch errors across four TET4 meshes. Curves sit near floating point precision; the acceptance limit is 10⁻¹¹.
Patch error traces for Green–Lagrange strain, PK2 stress, Cauchy stress, energy and deformation determinant.

Affine finite-strain patch errors across four TET4 meshes. Curves sit near floating point precision; the acceptance limit is 10⁻¹¹.

Recorded values

Main observables and references

Values come from the linked campaign record. Acceptance thresholds are shown separately from observed results.

Observed patch error≈ 10⁻¹⁵Floating point scale shown in the source plotAcceptance threshold ≤ 10⁻¹¹ acceptance threshold
Refinement levels12 / 96 / 768 / 2,592 elementsTET4 meshes
Model and execution

What was calculated?

  • The St. Venant–Kirchhoff material law is evaluated under a prescribed affine finite deformation.
  • Four TET4 meshes contain 12, 96, 768 and 2,592 elements.
  • The exact affine field provides the patch reference without a support singularity.
How to read the evidence

What the results say

  • The plotted errors are around floating point precision, approximately 10⁻¹⁵.
  • The acceptance threshold is 10⁻¹¹. It is a gate, not the measured error.
  • The check verifies stress transformations and energy for this affine path.

Additional figures from this calculation

Select a figure to inspect it at full size. Captions state the quantity, comparison and any display amplification available in the source.

Cauchy von Mises stress field for the affine patch case, which avoids a singular support.
TET4 finite-strain model showing the Cauchy von Mises field on the deformed shape.

Cauchy von Mises stress field for the affine patch case, which avoids a singular support.

Scope boundary

Where this case stops

  • The patch does not establish peak stress convergence at an encastrement, contact qualification or finite-strain plasticity.
  • The source reports a combined maximum across Green–Lagrange strain, PK2 stress, Cauchy stress, energy and det(F).

Open the calculation method

These white box sheets explain the element, constitutive law or numerical method used by this case.

White box sheetTET4 element formulationWhite box sheetSt. Venant–Kirchhoff lawWhite box sheetLinear static assembly

Reproduce and inspect the source

The source paths below are pinned to one repository commit. Opening the current site does not rerun the original calculation.

Controlled V&V reviewdocs/verification/tet4_total_lagrangian_structural_v2.mdPatch and stress campaign scriptscripts/run_tet4_tl_stress_vnv.py

Figure and source snapshot e367fe58b2b9ebb4aef321424ca775e80e82d9ca. Campaign execution version: 0.2.0. Current site release and original calculation version identify different events.

Related cases

Other recorded calculations in this family.

TET4 linearized buckling refinementTET4 imperfect postbuckling paths
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