undeformed

Undeformed is an adjective used in physics, engineering, materials science, and related disciplines to describe an object in its original configuration, before forces or processes have caused any change in shape, size, or internal structure. The undeformed state is the reference configuration against which deformations, strains, or displacements are defined. When external loads are applied, the body may become deformed and adopt a deformed configuration that differs from the undeformed one.

In continuum mechanics, points of a body in the undeformed configuration are labeled by material coordinates X, while those in the current, deformed configuration are labeled by spatial coordinates x. The deformation gradient F = ∂x/∂X maps X to x and encodes stretch and rotation. Strain measures (such as the Green-Lagrange strain E = (F^T F − I)/2) are defined relative to the undeformed configuration. In small-strain theory, linearized strains ε ≈ (∇u + ∇u^T)/2 rely on the displacement field u relative to the undeformed state. The term undeformed is also used to denote a material or structure in its stress-free state, if such a state exists.

In computer graphics and manufacturing, the term describes a base geometry or pose prior to any articulation, animation, or forming operations. Reverting to the undeformed state is common in testing, reverse engineering, or comparative analysis to assess the effects of loading, processing history, or treatment. The distinction between undeformed and deformed states is essential for defining boundary conditions, constitutive laws, and material behavior.