A Compendium on Linearization in Continuum Kinematics
Abstract
Abstract This work presents the linearization, about an arbitrary motion, of the main kinematical quantities in the continuum mechanics of solids and, as a novel result, of the polar decomposition of the deformation. When the polar decomposition is linearized about the identity motion (undeformed configuration), one retrieves the classical result that the multiplicative polar decomposition of the deformation gradient becomes the additive decomposition of the displacement gradient. The setting is in affine spaces, but the covariant framework allows for a relatively straightforward extension to Riemannian manifolds.
Fields of Study & Subjects
Elasticity and Material Modeling
Piezoelectric Actuators and Control
Control and Stability of Dynamical Systems
Publication details
- Journal / source
- Journal of Applied Mechanics
- Publisher
- ASME International
- Volume
- 93
- Issue
- 9
- Publication date
- 27 April 2026
- Language
- EN