STRESS–STRAIN
BEHAVIOR
,One curve, many decisions
The stress–strain curve relates mechanical loading to the material response. Interpreting it requires
distinguishing measurements, properties, and test conditions.
Question What to examine Related decision
How much does the
Initial slope and geometry Limit displacement
component deform?
When does permanent strain
Yielding or proof stress Avoid plastic deformation
remain?
How much tension can it
Maximum stress and fracture Assess strength
withstand?
Area under the curve and
How does it absorb energy? Store or dissipate energy
recovery
The goal is to interpret the entire curve, not to select a material based on a single number.
,From specimen to material
Force and elongation describe the specimen. Normalizing by area and length allows responses to be
compared under equivalent assumptions and conditions.
Specimen measure Normalized measure Information retained
Axial force F Engineering stress σ = F/A₀ Load per initial area
Elongation ΔL Strain ε = ΔL/L₀ Relative change in length
Axial stiffness k = F/ΔL Modulus E in the linear regime Constitutive response
Mechanical work W Energy per initial volume Energy density
Normalizing geometry does not eliminate the effects of orientation, defects, temperature, loading rate, or
processing history.
, Quantities and units
Stress has dimensions of force per area. Strain is dimensionless, but its expression as a percentage must be
made explicit.
Quantity Symbol Unit or equivalence
Force F N; 1 kN = 1,000 N
Initial area A₀ mm² or m²
Stress and modulus σ; E 1 MPa = 1 N/mm²
Axial strain ε 1% = 0.01; 0.2% = 0.002
Energy per volume u 1 MPa = 1 MJ/m³
When integrating the curve, express strain as a fraction. Integrating percentage values without conversion
introduces a factor of 100.
BEHAVIOR
,One curve, many decisions
The stress–strain curve relates mechanical loading to the material response. Interpreting it requires
distinguishing measurements, properties, and test conditions.
Question What to examine Related decision
How much does the
Initial slope and geometry Limit displacement
component deform?
When does permanent strain
Yielding or proof stress Avoid plastic deformation
remain?
How much tension can it
Maximum stress and fracture Assess strength
withstand?
Area under the curve and
How does it absorb energy? Store or dissipate energy
recovery
The goal is to interpret the entire curve, not to select a material based on a single number.
,From specimen to material
Force and elongation describe the specimen. Normalizing by area and length allows responses to be
compared under equivalent assumptions and conditions.
Specimen measure Normalized measure Information retained
Axial force F Engineering stress σ = F/A₀ Load per initial area
Elongation ΔL Strain ε = ΔL/L₀ Relative change in length
Axial stiffness k = F/ΔL Modulus E in the linear regime Constitutive response
Mechanical work W Energy per initial volume Energy density
Normalizing geometry does not eliminate the effects of orientation, defects, temperature, loading rate, or
processing history.
, Quantities and units
Stress has dimensions of force per area. Strain is dimensionless, but its expression as a percentage must be
made explicit.
Quantity Symbol Unit or equivalence
Force F N; 1 kN = 1,000 N
Initial area A₀ mm² or m²
Stress and modulus σ; E 1 MPa = 1 N/mm²
Axial strain ε 1% = 0.01; 0.2% = 0.002
Energy per volume u 1 MPa = 1 MJ/m³
When integrating the curve, express strain as a fraction. Integrating percentage values without conversion
introduces a factor of 100.
