deformim

Deformim is a hypothetical scalar quantity used in the study of continuum mechanics to quantify the local extent of deformation within a material undergoing large or small deformations. It is defined relative to a reference configuration and is intended to provide a dimensionless or dimensioned indicator of how much a point has moved and rotated as the material deforms. In many formulations, deformim is derived from the deformation gradient F, which maps reference coordinates to the current configuration. A simple interpretation is that deformim equals zero when F equals the identity (no deformation) and increases with the magnitude of the deformation, capturing both stretch and shear components.

Properties: deformim is non-negative, observer-dependent (depends on the chosen reference frame and metric), and is typically used as a visualization and debugging aid in simulations rather than as a direct physical observable. It is related to, but distinct from, classical strain measures such as Green-Lagrange strain and logarithmic strain, and from strain energy density.

Applications: used in finite element analysis, material forming simulations, and computer graphics to identify regions undergoing large deformations, guide mesh adaptation, or influence remeshing criteria. In simple shear or uniaxial tension, deformim increases with the deformation gradient components and can be calibrated to approximate other measures of deformation.

History and etymology: the term deformim is a neologism formed from deformare and the suffix -im; it is used in niche texts and online glossaries to denote a deformation indicator. Not a universally adopted standard, it coexists with established measures such as strain tensors and deformation energy.