Linear vs Nonlinear FEA: Stress-Strain Curve Guide

Linear and nonlinear choices in FEA are decisions about assumptions and data, not settings. Linear holds while stiffness stays proportional, and constraints do not switch state. Once yielding, large deflection, or contact changes the load path, you neea d nonlinear model. This guide gives solver-ready inputs and review-grade checks.

Difference In FEA

Linear analysis assumes constant stiffness, so results scale proportionally with load.

Nonlinear analysis updates stiffness during the step, so load history and state changes matter.

• Use nonlinear when yielding starts, deflection changes the load path, or contact status changes. (Control.com)

What actually makes it nonlinear

Linear Analysis Validity

Linear analysis is a strong tool when assumptions match physics. It is fastest for stiffness screening, baseline load paths, and early design reviews. It becomes risky when you unknowingly cross the proportional limit, because the plot can still look clean while the physics is already wrong. (Control.com)

From a review standpoint, treat linear as acceptable when all of these remain true: elastic behavior everywhere, small enough deflection that geometry does not alter the load path, and boundary conditions that do not change status during loading. When any one of those fails, use linear only as a baseline, not as a sign-off model. (goengineer.com)

Nonlinear Setup Controls

Nonlinear runs fail less from “hard math” and more from unmanaged transitions. Your job is to control when the model changes stiffness, and to help the solver follow that path without taking steps that are too large.

The controls that matter most

Automatic time stepping reduces load increment when the response becomes stiff or unstable, and it can recover from failed convergence by stepping back and retrying smaller increments. ANSYS documentation describes this bisection style recovery as a core mechanism for nonlinear robustness. (ansyshelp.ansys.com)

Line search improves Newton updates when the first correction overshoots, which is common in contact and plasticity. Nonlinear stabilization can help with locally unstable behavior and contact chatter, but you must check that stabilization energy is not dominating the real strain energy. Arc length is the right tool when a structure follows an unstable equilibrium path, including snap-through type problems. ANSYS explicitly groups these as standard nonlinear diagnostics and solution aids. (ansyshelp.ansys.com)

Common divergence patterns

The decision flow you can defend in review

If yielding is plausible anywhere, plan nonlinear with a solver-ready curve. If the contact status can change, plan nonlinear contact. If deflection can change the load path, enable geometric nonlinearity. This is the same practical framing you see repeated in strong engineering explainers and vendor guidance, because it matches real failure modes. (Control.com)

Stress Strain Curve Data Pack For Solvers

Most competitors explain the curve. To win trust, you need an input artifact that engineers can copy into a workflow.

Engineering to true conversion

True strain and true stress are commonly derived from engineering measures using:

• ε_true = ln(1 + ε_eng)

• σ_true = σ_eng (1 + ε_eng) (Innovation Space)

Bold warning: This conversion is valid only up to uniform elongation, which occurs up to the onset of necking. Beyond necking, strain is nonuniform in the gauge length, and computing a true stress-strain curve by simple conversion is not meaningful. (Innovation Space)

If you truly need post-UTS behavior, do not pretend a converted uniaxial curve is the truth. Use an approach designed for it. AHSS Guidelines explicitly note bulge testing as a way to determine stress-strain beyond uniform elongation. (AHSS Guidelines)

Abaqus plasticity input rule 

The first plasticity data pair defines the initial yield stress, and the initial plastic strain must be zero. (WUSTL Engineering Classes)

TECHNIA’s Abaqus focused guide also states that plasticity points past yield must be entered as true stress and logarithmic plastic strain, and the yield point is entered with logarithmic plastic strain equal to zero. (blog.technia.com)

Example input table 

This is a format example only, not material data. Units and strain definition must match your solver settings and your test basis.

Row 1 is yielded with plastic strain set to zero. That is the rule. (WUSTL Engineering Classes)

Units trap

Most solver failures I review trace back to one of these:

• Stress is entered in MPa while the model is in Pa, so the material becomes 10⁶ times softer or stronger than intended.

• Strain entered as a percent instead of a decimal, so plastic strain is off by 100.

• Engineering strain is fed where log plastic strain is expected, especially in Abaqus-style plasticity tables. (blog.technia.com)

What to request from the test lab

Ask for raw force extension, specimen geometry, gauge length, strain measurement method, yield definition used, and the uniform elongation point. If you expect to use the curve past uniform elongation, state that early and request an appropriate characterization approach, such as bulge testing, rather than forcing a conversion beyond necking. (AHSS Guidelines)

Micro Case Studies

Bracket with a clearance gap

Linear predicts a smooth load transfer because it assumes the interface is always engaged. Nonlinear shows contact turns on late, stiffness jumps, and peak stress relocates to the real bearing zone. (WorQuick)

Thin plate where deflection changes the load path

Linear predicts bending only. Nonlinear shows membrane action as deflection grows, which increases stiffness and shifts peak stress. (Control.com)

Yielding near a notch

Linear keeps scaling peak stress with load. Nonlinear shows stress redistributes after yield, while plastic strain becomes the design driver. (WUSTL Engineering Classes)

FAQ 

1) When is linear analysis acceptable in FEA

When the part stays elastic everywhere, deflections do not change load path, and constraints do not switch state. If yield, contact switching, or large deflection is plausible, linear is only a baseline. (goengineer.com)

2) Difference between linear and non-linear analysis in fea

Linear uses constant stiffness, so results scale with load. Nonlinear updates stiffness during the step, so yielding, large deflection, and contact changes are handled realistically. (Control.com)

3) What is the first plasticity data pair in Abaqus

Yield stress paired with plastic strain equal to zero. That first row sets the start of plastic flow. (WUSTL Engineering Classes)

4) Why does non-linear analysis fail to converge

Because constraints are incomplete, contact stiffness is too aggressive, increments are too large, or the material curve is wrong in units or strain type. Automatic time stepping and proper diagnostics fix many cases, but unstable equilibrium paths require arc length. (ansyshelp.ansys.com)

5) When do I need a true stress-strain curve

When you model plasticity or large-strain behavior. Conversions from engineering to true are valid only up to uniform elongation. Beyond necking, simple conversion is not meaningful, and you need a method designed for post-necking characterization if that range matters. (Innovation Space)

References

• Control.com, linear vs nonlinear FEA overview and nonlinearity drivers. (Control.com)

• Worquick, linear vs nonlinear decision framing with practical examples. (WorQuick)

• WUSTL Abaqus docs, the first data pair yields with plastic strain zero. (WUSTL Engineering Classes)

• TECHNIA, Abaqus plasticity input uses true stress and logarithmic plastic strain. (blog.technia.com)

• ANSYS Innovation Space PDF, conversion valid only up to necking; beyond necking, not meaningful. (Innovation Space)

• AHSS Guidelines, true stress strain is valid only through uniform elongation and bulge testing beyond. (AHSS Guidelines)

• ANSYS Help, nonlinear diagnostics including automatic time stepping, line search, stabilization, arc length. (ansyshelp.ansys.com)