Assessment of a Log Stretch-Quaternion Decomposition of the Deformation Gradient to Reduce Advection Error
Abstract
Alternative decompositions of the deformation gradient into distortion and rotation components are examined to determine whether advection error can be reduced. The distortion is described either by the right stretch tensor or logarithm of the right stretch tensor. The rotation is represented as quaternions, following earlier research. Accuracy of the decomposition schemes is assessed by using closed-form expressions for deformation fields that are spatially shifted to be consistent with the advected material motion. The results support prior findings where accuracy was improved by representing the deformation gradient as a stretch and quaternions. The results further suggest that additional benefit can be gained by using the log of the stretch. The improvement is credited to two factors: the diagonal and off-diagonal components are of similar magnitude for the log stretch, and the log volume strain is advected accurately.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 2018
- Accession Number
- AD1063519
Entities
People
- Richard Becker
- Travis Wagner
Organizations
- United States Army Research Laboratory