Stressstrain

Stress-strain is a fundamental concept in materials science and continuum mechanics that describes how a material deforms under applied loads. Stress is the internal force per unit area within a material, while strain is the relative deformation resulting from the load.

There are different ways to quantify stress and strain. In a uniaxial test, engineering (nominal) stress is sigma = F/A0 and engineering strain is epsilon = Delta L / L0, using the original cross-sectional area A0 and length L0. True stress uses the actual area and length during deformation: sigma_true = F/A and epsilon_true = ln(L/L0). Strains can be tensile (positive) or compressive (negative), and shear stress and shear strain describe deformation due to tangential forces.

In many materials, the initial portion of the stress-strain curve is linear, described by Hooke’s law: sigma = E * epsilon, where E is Young’s modulus. This elastic region is reversible. Beyond the elastic limit, permanent (plastic) deformation occurs. The yield strength marks the onset of plasticity, and the ultimate tensile strength is the maximum stress the material can sustain before necking and fracture. The area under the curve up to fracture represents toughness, or the energy required to fail the material.

Additional considerations include rate, temperature, and time-dependent behavior. Cyclic loading can cause fatigue failure; viscoelastic materials show time-dependent responses such as creep and stress relaxation. Designers use concepts like allowable stress and factors of safety to ensure performance under multiaxial states of stress, accounting for material properties such as Poisson’s ratio, shear modulus, and bulk modulus.