FEA Stress-Strain Input: Method

FEA Stress-Strain Input: What Each Package Expects, and How the Curve Is Built

Purpose

A handbook gives a material as a few numbers: the moduli E and E_c, Poisson's ratio ν, the strengths F_tu, F_ty and F_cy, the Ramberg-Osgood exponents n_t and n_c and the elongation e. A finite-element program wants the whole stress-strain curve, and every program wants it in its own form: a table against total strain or against plastic strain, in engineering or in true (logarithmic) measure, a yield stress with a tangent modulus, or the Ramberg-Osgood parameters in its own notation. Getting the form wrong is the commonest error in a nonlinear material definition: a total-strain table read as plastic strain, an engineering curve in a large-strain run, a first point that is not at yield. This tool builds the curve once and writes it the way the chosen package reads it.

What Each Package Expects

The rules below were read from the vendors' reference pages (saved with the tool's sources). Every elastic-plastic model in this list is a von Mises plasticity with a single curve for tension and compression; only Nastran's NLELAST takes two branches.

Package and option	Strain column	Stress and strain measure	First point	Beyond the last point
Nastran MATS1 PLASTIC + TABLES1, TYPSTRN 0 (MSC SOL 106 and 400, Simcenter, Femap, Inventor Nastran, OptiStruct)	total strain	engineering in a small-strain run; true stress and logarithmic strain with PARAM,LGDISP	(0, 0), then the initial yield LIMIT1 at LIMIT1/E: the first segment's slope must equal E of MAT1	linear with the last slope
Nastran MATS1 PLASTIC + TABLES1, TYPSTRN 1 (Simcenter SOL 401, 402, 601; OptiStruct)	plastic strain	true for a large-strain run	yield stress at zero plastic strain	linear with the last slope
Nastran MATS1 bilinear (LIMIT1, H)	—	either	LIMIT1 is the yield; H is the work-hardening slope, stress against plastic strain, H = E Et/(E − Et)	—
Nastran MATS1 NLELAST + TABLES1	total strain, both quadrants	engineering (small strain)	the table passes through the origin; compression branch at negative strain	linear with the last slope
MSC Nastran SOL 400 MATEP + TABLES1 (TYPE 2)	plastic strain	true stress, logarithmic strain	yield at zero plastic strain	linear with the last slope
Ansys TB,BISO and TB,BKIN	—	true with NLGEOM,ON	C1 yield stress, C2 tangent modulus of the stress–total-strain line	—
Ansys TB,PLASTIC,,,,MISO and KINH	plastic strain	true with NLGEOM,ON	yield at zero plastic strain; every segment slope between 0 and E	constant (perfectly plastic)
Ansys TB,MISO (archived command)	total strain	true with NLGEOM,ON	the yield point at strain yield/EX, so its slope is EX; the origin itself is not entered	constant
Ansys Workbench, Multilinear Isotropic or Kinematic Hardening	plastic strain	true with Large Deflection on	zero plastic strain at the yield stress	constant
Ansys Workbench, Bilinear Isotropic or Kinematic Hardening	—	true with Large Deflection on	Yield Strength and Tangent Modulus of the total-strain line	—
Abaqus *PLASTIC (also CalculiX and PrePoMax)	logarithmic plastic strain	true stress	the first row's plastic strain must be zero	constant
Abaqus *DEFORMATION PLASTICITY	—	—	E, ν, σ0, n, α with Eε = σ + α (|σ|/σ0)n−1 σ	—
LS-DYNA *MAT_024 with LCSS	effective plastic strain	effective (true) stress	yield at zero plastic strain; SIGY and ETAN are ignored when LCSS is given	linear with the last slope
LS-DYNA *MAT_024 and *MAT_003 bilinear	—	true	SIGY and ETAN, the tangent modulus of the true stress–true strain line (plastic modulus E ETAN/(E − ETAN))	—
Radioss /MAT/LAW36	plastic strain	true	the first point of each yield function at zero plastic strain	linear with the last slope
SolidWorks Simulation, plasticity von Mises curve	total strain	engineering (small strain) or Cauchy stress and logarithmic strain (Large strain option)	the yield point	linear through the last two points
SolidWorks bilinear	—	either	SIGYLD and ETAN (the solver refuses ETAN above E or below about E/100); RK = 1 isotropic, 0 kinematic	—
COMSOL Plasticity, hardening function	equivalent plastic strain	logarithmic with large plastic strain	σh(εpe) = σys − σys0 must be zero at zero plastic strain	the interpolation function's extrapolation setting
COMSOL linear isotropic hardening	—	either	σys0 and ETiso, the tangent modulus of the total-strain line	—
Code_Aster VMIS_ISOT_TRAC	total strain	engineering (PETIT) or logarithmic (GDEF_LOG)	the yield stress at strain σy/E, slope E; later slopes lower	PROL_DROITE (LINEAIRE written)
Code_Aster VMIS_ISOT_LINE	—	either	SY and D_SIGM_EPSI, the tangent modulus	—

Two distinctions run through the table. Total or plastic strain: a plastic-strain table is not the total-strain table shifted sideways; the plastic strain of every point is its total strain minus its own elastic strain σ/E, which grows along the curve. Engineering or true: a small-strain solution (Nastran SOL 106 without LGDISP, Ansys without NLGEOM, SolidWorks small strain, Code_Aster PETIT) takes the engineering curve as tested; a large-strain solution works in Cauchy (true) stress and logarithmic strain and must be given the curve converted. Abaqus, LS-DYNA, Radioss and MATEP take true values only.

The Source Curve

The curve is Ramberg and Osgood's three-parameter relation with the 0.2 % offset yield, the form MIL-HDBK-5 uses: ε = σ/E + 0.002 (σ/F_y)ⁿ. It is engineering stress against engineering strain, valid to the ultimate stress; the elongation e is the engineering strain at the ultimate point and ends the curve. When no exponent is entered, n is fitted so that the curve passes through the ultimate point, n = ln[(e − F_tu/E)/0.002] / ln(F_tu/F_ty), the construction Cozzone used for his shape factor. A handbook n usually gives a plastic strain at F_tu smaller than the elongation (the specimen necks after the uniform elongation), in which case the curve reaches F_tu first and the tool adds a flat (perfectly plastic) point at the elongation, or ends at F_tu when the Curve End input says so. When the handbook n is small enough that the curve reaches the elongation below F_tu, the table ends at the elongation and the page says so.

Tension and compression. Von Mises plasticity has one yield surface: the program cannot take a tension curve and a compression curve. When a compression yield is entered the tool averages the two sets, E_b = (E + E_c)/2, F_yb = (F_ty + F_cy)/2, n_b = (n_t + n_c)/2, and writes the Ramberg-Osgood curve of the averaged properties; the ultimate point stays the tensile one, since compression has no ultimate. The Curve Basis input can force the tension or the compression curve instead. Figure 1 draws the three curves so the compromise is visible. Nastran's NLELAST, a nonlinear elastic law that unloads along the loading curve, takes the table in both quadrants and is written with the compression branch from the compression properties and the tension branch from the tension properties, no averaging; the generic CSV lists both curves.

Building the Table

Initial yield. A Ramberg-Osgood curve has no sharp yield; the plastic strain is small but not zero at every stress. Every package needs a first point with zero plastic strain, and a Nastran total-strain table needs its first segment to have the slope E exactly. The tool takes the initial yield σ₀ as the stress at a plastic strain ε_p0 = 0.01 % (the usual proportional-limit definition, adjustable), treats the material as linear below it and drops that offset from the plastic strains above it: ε_pl = 0.002 (σ/F_y)ⁿ − ε_p0, total strain σ/E + ε_pl. The table then starts at (σ₀/E, σ₀) with zero plastic strain and differs from the exact curve by 0.01 % strain. Starting the table at the 0.2 % offset yield instead, as is sometimes done, drops the knee of the curve between 0.01 % and 0.2 % plastic strain and overstates the stiffness there.

Point spacing. The plastic strains of the points are spaced geometrically from ε_p0 to the plastic strain at the end of the curve, so the points are dense around the knee, where a piecewise-linear interpolation would otherwise cut the corner, and sparse along the nearly straight hardening part. Twenty points keep the interpolated curve within a fraction of a percent of the Ramberg-Osgood curve in stress; Ansys accepts up to a hundred per temperature.

True values. Up to the ultimate point the deformation is uniform and the conversions are exact: σ_true = σ (1 + ε) and ε_true = ln(1 + ε). A large-strain program decomposes the logarithmic strain as σ_true/E + ε_pl,true, so the plastic strain written is ε_pl,true = ln(1 + ε) − σ_true/E. Near yield that expression is slightly negative, by about 1.5 (σ/E)², because ln(1 + ε) falls below ε while σ(1 + ε)/E rises above σ/E; the value at the first point (under 0.01 % strain) is subtracted from every point so the first has zero plastic strain and the sequence never decreases, and the true total strain of the table is rebuilt as σ_true/E + ε_pl,true so that the two columns agree with the program's own decomposition.

Bilinear. The yield is the 0.2 % offset yield F_yb at the strain F_yb/E_b; the tangent line runs from there to the ultimate point, (e, F_tu) in engineering measure or (ln(1 + e), F_tu(1 + e)) in true measure, unless a tangent modulus is entered. Programs differ in which slope they call the hardening input: Ansys, LS-DYNA, SolidWorks, COMSOL and Code_Aster take the tangent modulus E_t of the stress–total-strain line; Nastran's H is the plastic modulus, the slope of stress against plastic strain, H = E E_t/(E − E_t), and the two agree only when E_t is much smaller than E. Abaqus has no bilinear keyword; two *PLASTIC rows, the yield at zero plastic strain and the ultimate at its plastic strain, do the same.

Ramberg-Osgood parameters. Abaqus's deformation plasticity writes the same curve as Eε = σ + α (|σ|/σ₀)ⁿ⁻¹ σ. With σ₀ = F_yb the yield offset is α = 0.002 E_b/F_yb, because 0.002 E (σ/F_y)ⁿ = [0.002 E/F_y] (σ/F_y)ⁿ⁻¹ σ. It is a total-strain (deformation) theory meant for monotonic loading in fracture-mechanics problems and does not unload elastically.

Units

A finite-element model has no units of its own: the stress, length, force and time units must be consistent, and the density goes in as mass per volume in the same system. The Output Units input selects the set: psi with inches, lbf and seconds (density in lbf·s²/in⁴, the weight density in lb/in³ divided by g = 386.09 in/s²); ksi with inches and kips; MPa with millimetres, newtons and tonnes (density in t/mm³, the kg/m³ value times 10⁻¹²); or Pa with metres, newtons and kilograms. The file header records the choice.

Limits

The curve is monotonic and rate-independent, at the temperature of the entered properties (a saved material brings its temperature-adjusted values). Nothing is written beyond the ultimate point: the post-necking part of a true stress–strain curve, which a crash or forming model needs, must come from a test with a necking correction (Bridgman) or from an extrapolation law (Swift, Voce, Hockett-Sherby), not from handbook allowables. Kinematic and mixed hardening options are written with the same curve; the hardening rule itself is a modelling choice for reversed loading. Strain-rate, temperature-dependent and anisotropic (Hill) definitions are not produced.