M10 — Geometric and material nonlinearity · Learn to Program Ansys APDL Simulations

M09 completed the core path with verifiable automation. M10 opens the optional specializations: the same cantilever-beam family, but with a more slender variant whose response is no longer linear. You will enable NLGEOM, solve with substeps, add bilinear plasticity, and compare load–displacement curves using numerical evidence.

Your mission

You will run three progressive cases—linear, geometrically nonlinear, and elastoplastic—plot the load–response curve, read convergence in the .out file, and document the source of each deviation in CSV.

Guiding question: can you prove when the linear model stops being valid?

Objectives

After completing M10, you will be able to:

Enable NLGEOM,ON and solve with progressive ramping (KBC,0, NSUBST).
Define bilinear plasticity with TB,BISO and TBDATA.
Extract a load–displacement curve from POST1 with OUTRES,ALL,ALL.
Check convergence (n_sets = n_substeps) and global equilibrium.
Quantify geom_dev_ratio and plastic_dev_ratio against the baseline.
Distinguish static load factor, substep, and equilibrium iteration.

Prerequisites and downloads

M07: linear validation with passes=1.
M06: substeps and the meaning of TIME as a load factor.
Optional M07 extension: curve with POST26.

10_start.mac — starting point.
10_static_nonlinear.mac — audited deliverable.
10_bug_hunt.mac — five faults.
10_challenge.mac — verifiable challenge.
10_expected_results.csv — numerical contract.
load-displacement-linear-vs-nl.svg — curves.
convergence-substeps.svg — substeps.

How to use this lesson

Path	Duration	Coverage
First win	20–25 min	Linear baseline + NLGEOM with ramping and first CSV.
Complete	70–75 min	Plasticity, full curve, debugging, challenge, and mastery.

Session map

Mission: objectives, downloads, and prediction.
Mental model: linear versus geometric versus material.
Demonstration: baseline, NLGEOM, curve, and plasticity.
Debugging: five common faults.
Challenge: modify the load and explain the curve.
Mastery: final M10 test.

Prediction — When does nonlinearity matter?

Slender variant: L = 0.5 m, h = 0.04 m, b = 0.05 m, F = −10000 N, E = 210 GPa.

I = b·h³/12
uy_ref = F·L³/(3·E·I)

Quantity	Value	Interpretation
`uy_ref`	−7.44047619E−3 m	Euler–Bernoulli reference
`\|uy_ref\|/h`	≈ 18.6%	Large displacements likely
Theoretical `σ_max`	≈ 450 MPa	Above Sy = 250 MPa → yielding
Topology	312 nodes / 150 elems	Mesh consistent with `mesh_h = 0.02 m`

Prediction: with NLGEOM,ON, the final deflection will differ from the linear result by at least 0.05% (a small geometric effect in bending). With plasticity, the deviation will be much larger (~24%).

Mental model — Linear versus nonlinear

Linear, geometrically nonlinear, and elastoplastic curves — Figure 1. Three branches on the same geometry: linear, elastic NLGEOM, and elastoplastic.

Geometric: NLGEOM,ON updates stiffness with the deformed configuration.
Material: TB,BISO allows yielding beyond Sy.
Numerical: substeps + iterations; convergence ≠ automatic physical validity.
TIME: load factor in static analysis; do not confuse it with M14 transient time.

Step 1 — Reproducible linear baseline

/CLEAR,START
/FILNAME,m10_nonlinear,1
/UNITS,SI
beam_l=0.5
beam_h=0.04
tip_force=-10000
...
ANTYPE,STATIC
NLGEOM,OFF
KBC,1
NSUBST,1
OUTRES,ALL,LAST
SOLVE

Check equilibrium (force_error and moment_error < 0.5%), topology 312/150, and uy_linear close to uy_ref.

Linear baseline deformed shape with NLGEOM OFF for a slender beam — Figure 3. Linear baseline deformed shape (`NLGEOM OFF`). Slender geometry `L=0.5 m`.

Step 2 — Enable NLGEOM and substeps

Substeps and convergence iterations — Figure 2. Ramp with 10 substeps; each may require several equilibrium iterations.

ANTYPE,STATIC
NLGEOM,ON
KBC,0
NSUBST,10,10,10
NEQIT,50
OUTRES,ALL,ALL
TIME,1
SOLVE

After solving, verify in POST1: *GET,n_sets,ACTIVE,0,SET,NSET must equal 10. Look in the .out file for completed convergence messages without aborts.

Deformed shape with NLGEOM ON under the same load as the linear baseline — Figure 4. `NLGEOM ON` deformed shape (same load). Compare it with the preceding figure, not only with the CSV.

Step 3 — Load–displacement curve

/POST1
*DO,i,1,n_sets_geom
  SET,1,1,,,i
  *GET,load_factor,ACTIVE,0,SET,TIME
  *GET,uy_step,NODE,corner_node,U,Y
  ! write row to m10_load_curve.csv
*ENDDO

Calculate geom_dev_ratio = |uy_geom − uy_linear| / |uy_linear|. It must be ≥ 0.05%. Plasticity must produce plastic_dev_ratio ≥ 5% relative to the elastic geometric case.

POST26 load–displacement curve for the NLGEOM branch — Figure 5. Load–displacement curve for the `NLGEOM` branch (`POST26`). All three complete branches are in `m10_load_curve.csv`.

Step 4 — Controlled plasticity

TB,BISO,1,1
TBDATA,1,250E6,0    ! Sy = 250 MPa, tangent = 0 (perfectly plastic)

Repeat the ramp with NLGEOM,ON. Compare uy_plastic against uy_geom: plastic_dev_ratio must be ≥ 5%. Document whether yielding amplifies deflection beyond the geometric effect alone.

Equivalent von Mises stress contour for the elastoplastic case — Figure 6. Equivalent stress in the elastoplastic case (`PLNSOL,S,EQV`).

Step 5 — Read convergence in .out

Minimum checks before accepting results:

n_converged = n_substeps in POST1.
No unresolved “Solution not converged” lines.
Global equilibrium < 0.5% in all three cases.
Curve with 10 points in m10_load_curve.csv.

Bug hunt

#	Fault	Symptom	Correction
1	`NLGEOM,OFF`	Curve matches linear case	`NLGEOM,ON`
2	No `TB,BISO`	Plastic = geometric	Define table and `TBDATA`
3	`NSUBST,1`	Does not converge or underestimates	Ramp with 10 substeps
4	`OUTRES,LAST`	Only one set	`OUTRES,ALL,ALL`
5	Not reading `.out`	False `passes=1`	Verify `n_sets`

Verifiable challenge

Change tip_force=-12000 N while keeping the geometry. Predict whether geom_dev_ratio increases. Run from two clean directories and document uy_linear, uy_geom, and the physical explanation (greater load → greater geometric deviation and potentially earlier yielding).

uy_ref = -8.92857143E-3 m   (F = -12000 N)

Self-assessment

What does TIME represent in a static ramp?

The load factor applied in that substep, not physical transient time.

Does convergence imply a physically valid solution?

Not necessarily. You must still check equilibrium, boundary conditions, a reasonable deformed shape, and comparison with the baseline.

Why use OUTRES,ALL,ALL with a ramp?

Because OUTRES,LAST discards intermediate substeps needed for the load–displacement curve.

When should TB,BISO be enabled?

When stress exceeds Sy and you need to capture yielding in addition to NLGEOM.

Learning evidence

m10_nonlinear_audit.csv — three cases with passes=1.
m10_load_curve.csv — 10 points from the geometric case.
m10_summary.csv — ratios and study_passes=1.
Excerpt from the .out file showing substep convergence.
Brief note explaining the source of geom_dev_ratio and plastic_dev_ratio.

Exit checklist

Linear baseline with equilibrium < 0.5%.
NLGEOM ON with n_sets = 10.
geom_dev_ratio ≥ 0.05%.
Plasticity with plastic_dev_ratio ≥ 5%.
Challenge with F = −12000 N documented.
study_passes=1 in a clean run.

Technical traceability

Commands: NLGEOM, TB,BISO, TBDATA, NSUBST, NEQIT, KBC, OUTRES, SET, *GET. References: Structural Analysis Guide; Material Reference. Inherited from: M07 (KEYOPT(2)=3, equilibrium). Next: M11 contact.

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Geometric and material nonlinearity