An engineering stress-strain curve visualizes the relationship between applied stress (MPa) and resulting strain (dimensionless) in a material under uniaxial tensile loading. The curve reveals distinct mechanical behavior regions — elastic deformation, yielding, strain hardening, and necking — culminating in fracture. It is the foundational plot for characterizing material mechanical properties and comparing material performance.
""" anyplot.ai
line-stress-strain: Engineering Stress-Strain Curve
Library: plotnine 0.15.7 | Python 3.13.14
Quality: 83/100 | Updated: 2026-06-21
"""
import os
import sys
import numpy as np
import pandas as pd
# Work around naming conflict between plotnine.py script and plotnine package
script_dir = os.path.dirname(os.path.abspath(__file__))
if script_dir in sys.path:
sys.path.remove(script_dir)
if "" in sys.path:
sys.path.remove("")
if "." in sys.path:
sys.path.remove(".")
from plotnine import (
aes,
annotate,
coord_cartesian,
element_blank,
element_line,
element_rect,
element_text,
geom_line,
geom_point,
geom_segment,
geom_text,
ggplot,
labs,
scale_color_identity,
scale_size_identity,
scale_x_continuous,
scale_y_continuous,
theme,
theme_minimal,
)
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
REGION_ALPHA = 0.18 if THEME == "light" else 0.13
# Imprint palette — position 1 is always the first categorical series
IMPRINT = ["#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD", "#954477", "#99B314"]
np.random.seed(42)
youngs_modulus = 210000 # MPa
yield_stress = 250 # MPa
uts = 400 # MPa
fracture_strain = 0.35
necking_strain = 0.22
# Elastic region
elastic_strain = np.linspace(0, yield_stress / youngs_modulus, 40)
elastic_stress = youngs_modulus * elastic_strain
# Yield plateau (part of the plastic region — not a separate band per spec)
plateau_strain = np.linspace(elastic_strain[-1], 0.025, 15)
plateau_stress = np.full_like(plateau_strain, yield_stress)
# Strain hardening (power law)
hardening_strain = np.linspace(0.025, necking_strain, 80)
hardening_stress = yield_stress + (uts - yield_stress) * ((hardening_strain - 0.025) / (necking_strain - 0.025)) ** 0.45
# Necking to fracture
necking_strain_vals = np.linspace(necking_strain, fracture_strain, 40)
necking_stress = (
uts - (uts - 320) * ((necking_strain_vals - necking_strain) / (fracture_strain - necking_strain)) ** 1.3
)
strain = np.concatenate([elastic_strain, plateau_strain[1:], hardening_strain[1:], necking_strain_vals[1:]])
stress = np.concatenate([elastic_stress, plateau_stress[1:], hardening_stress[1:], necking_stress[1:]])
df = pd.DataFrame({"strain": strain, "stress": stress})
# 0.2% offset line
offset = 0.002
elastic_end = yield_stress / youngs_modulus # ~0.00119
offset_strain_end = (yield_stress + 50) / youngs_modulus + offset
# Critical points
yield_point_strain = elastic_end + offset
yield_point_stress = yield_stress
fracture_stress_pt = float(necking_stress[-1])
df_points = pd.DataFrame(
{
"strain": [yield_point_strain, necking_strain, fracture_strain],
"stress": [yield_point_stress, uts, fracture_stress_pt],
"color": [IMPRINT[4]] * 3,
"size": [3.0, 3.0, 3.0],
}
)
# Region labels: 3 regions per spec (elastic, strain hardening, necking)
# Yield plateau is a critical point, not a separate shaded band
df_regions = pd.DataFrame(
{
"strain": [elastic_end / 2, 0.13, 0.29],
"stress": [350, 335, 385],
"label": ["Elastic", "Strain\nHardening", "Necking"],
}
)
plot = (
ggplot()
# Three region shadings: elastic, plastic (strain hardening), necking
+ annotate("rect", xmin=0, xmax=elastic_end, ymin=0, ymax=460, alpha=REGION_ALPHA, fill=IMPRINT[2])
+ annotate("rect", xmin=elastic_end, xmax=necking_strain, ymin=0, ymax=460, alpha=REGION_ALPHA, fill=IMPRINT[3])
+ annotate("rect", xmin=necking_strain, xmax=fracture_strain, ymin=0, ymax=460, alpha=REGION_ALPHA, fill=IMPRINT[4])
# Main stress-strain curve (Imprint position 1 — first categorical series)
+ geom_line(df, aes(x="strain", y="stress"), color=IMPRINT[0], size=1.0)
# 0.2% offset construction line
+ geom_segment(
aes(x=offset, xend=offset_strain_end, y=0, yend=yield_stress + 50),
color=IMPRINT[4],
size=0.6,
linetype="dashed",
)
+ annotate("text", x=0.011, y=52, label="0.2% offset", size=3.5, color=INK_SOFT, fontstyle="italic")
# Critical point markers
+ geom_point(df_points, aes(x="strain", y="stress", color="color", size="size"))
+ scale_color_identity()
+ scale_size_identity()
# Critical point labels — individual positions for clarity near y-axis
+ annotate(
"text",
x=yield_point_strain + 0.018,
y=yield_point_stress + 22,
label="Yield Point\n(0.2% offset)",
size=3.0,
color=INK,
fontweight="bold",
)
+ annotate("text", x=necking_strain, y=uts + 28, label="UTS", size=3.0, color=INK, fontweight="bold")
+ annotate(
"text",
x=fracture_strain - 0.012,
y=fracture_stress_pt + 28,
label="Fracture",
size=3.0,
color=INK,
fontweight="bold",
)
# Region labels
+ geom_text(df_regions, aes(x="strain", y="stress", label="label"), size=3.0, color=INK_SOFT, fontstyle="italic")
# Elastic modulus annotation
+ annotate(
"text", x=0.028, y=145, label=f"E = {youngs_modulus // 1000} GPa", size=3.5, color=IMPRINT[2], fontweight="bold"
)
+ labs(
x="Engineering Strain",
y="Engineering Stress (MPa)",
title="line-stress-strain · python · plotnine · anyplot.ai",
)
+ scale_x_continuous(breaks=np.arange(0, 0.40, 0.05))
+ scale_y_continuous(breaks=np.arange(0, 500, 50))
+ coord_cartesian(xlim=(0, 0.38), ylim=(0, 460))
+ theme_minimal()
+ theme(
figure_size=(8, 4.5),
text=element_text(size=7),
plot_title=element_text(size=12, weight="bold", color=INK),
axis_title=element_text(size=10, color=INK, weight="bold"),
axis_text=element_text(size=8, color=INK_SOFT),
panel_grid_major=element_line(color=INK, size=0.3, alpha=0.15),
panel_grid_major_x=element_blank(),
panel_grid_minor=element_blank(),
plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
panel_background=element_rect(fill=PAGE_BG),
panel_border=element_rect(color=INK_SOFT, fill=None),
axis_line=element_line(color=INK_SOFT),
)
)
plot.save(f"plot-{THEME}.png", dpi=400, width=8, height=4.5, units="in", verbose=False)
Part of Engineering Stress-Strain Curve on anyplot.ai.