A stress–strain curve shows how a material deforms as load is applied to it, and it is one of the most fundamental tools used in mechanics of materials and engineering design.
Sliders update the graph immediately. Number edits apply when you press Enter or leave the field. Expand Curve shape to adjust the position of the maximum stress and the stress decrease before fracture.
Basic properties
Curve shape
What the parameters mean
- Young’s Modulus (E): the ratio of stress to strain in the elastic region, representing how stiff the material is. A larger E means more stress for the same strain, so the initial slope of the curve becomes steeper.
- Yield Strength: the stress at which the elastic region ends and permanent (plastic) deformation begins. Beyond this point, the material no longer returns to its original shape once the load is removed.
- Ultimate Tensile Strength (UTS): the maximum engineering stress. In ductile metals, necking reduces engineering stress after maximum load; not every material follows that sequence.
- Fracture Strain: the strain at the moment the material breaks, indicating how ductile the material is.
- Strain at UTS: the position of the maximum stress. This demo calculates yield strain as σy / E and constrains UTS strain between yield and fracture.
- Fracture strength (% UTS): stress immediately before fracture as a percentage of UTS. A UTS of 400 MPa and a ratio of 85% give a fracture stress of 340 MPa.
- Strain hardening shape: Gentle, Normal and Strong change the stress rise within the hardening region while keeping the yield and UTS points fixed.
About this demo
This demo does not implement a precise constitutive model for any real material. Instead, it uses a simplified curve — a straight line for the elastic region and a smooth curve for the plastic region — so that the effect of each parameter is easy to understand for educational purposes. Internal constraints prevent physically impossible combinations of values (for example, a yield strength greater than the UTS).
Keep in mind that the behavior of real materials is far more complex, depending on factors such as strain hardening, temperature, and strain rate.
The steel example separates yielding, hardening and necking. PP illustrates post-yield softening, plastic drawing and orientation hardening. Its yield strain also uses the simplified σy / E relation, so it does not predict measured nonlinear yield strain. Alumina and CFRP illustrate linear elasticity followed by fracture, without yield or necking settings. Their fracture strain is calculated from UTS / E and the UTS and fracture markers coincide. CFRP also depends on fiber direction and layup.
Choosing a material applies all settings; subsequent edits retain that curve type. Reset restores the default curve and settings. Hover or tap the graph to inspect regions and stress/strain values, or explore with the arrow keys, Home and End.
References: Plastometrex — Necking and fracture during tensile testing, DoITPoMS — Polymer stress–strain curves.