Strainrate

Strain rate refers to the rate at which deformation occurs in a material or region and is the time derivative of strain. In continuum mechanics, the rate of deformation is described by the strain rate tensor, dotε_ij = 1/2 (∂v_i/∂x_j + ∂v_j/∂x_i), where v is the velocity field. This tensor can be decomposed into a volumetric part (the trace) that represents dilation and a deviatoric part that represents distortion. In a simple uniaxial case, the scalar strain rate is dotε = dε/dt, the time derivative of the engineering strain.

Strain rate is measured in inverse seconds (s^-1). While the tensor describes deformation rates in all directions, the scalar strain rate is often used in one-dimensional problems or when strains are small and the distinction between true and engineering strains is negligible. Strain rate is a central parameter for rate-dependent phenomena, including viscosity in fluids, viscoelastic relaxation, and creep or viscoplastic behavior in solids. Material response often depends on the rate at which deformation is applied, not only on the magnitude of strain.

Measurement and estimation methods include analyzing velocity gradients or displacements using techniques such as laser Doppler vibrometry, digital image correlation, interferometry, or displacement data in laboratory tests. In geoscience, regional strain rates can be inferred from geodetic measurements (for example, GNSS) to study tectonic deformation.

Applications and significance: strain-rate sensitivity influences yield stress, ductility, and failure modes in polymers, metals, and ceramics. In geophysics, strain-rate distributions inform models of earthquake source processes and mantle dynamics. Constitutive models frequently incorporate dotε, including viscoelastic, viscoplastic, and creep formulations, to capture how materials respond to deformation over time.