Coordinate Indexing Strategies for the Laplace Stretch in Two and Three Dimensions
Abstract
A kinematic framework for finite-strain continuum mechanics invoking an upper triangular factorization of the deformation gradient is advanced. New algorithms for coordinate indexing in two and three dimensions are developed. For a given orthonormal triad, the labeling of axes, which associates Gram rotation with only pure shears, is shown to be the appropriately indexed or pivoted basis in which to construct the Laplace stretch. For transient three-dimensional problems, a single labeling is proposed to enable the greatest agreement with this properly indexed basis over the history of states, which in turn requires advanced knowledge of the deformation path. Results invoking the proposed method are obtained for a lung constitutive model in simulations of dynamic impact. Comparisons with prior results invoking dynamic indexing show that predictions of local injury are less severe when the new method is used with the same constitutive parameters. Although the previous dynamic indexing technique requires no a priori knowledge of deformation (nor is any arbitrary choice of basis required), rapid transients in continuously varying Laplace attributes may arise that accelerate damage kinetics relative to the new, more stable method.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 2022
- Accession Number
- AD1179211
Entities
People
- Alan D. Freed
- John D. Clayton
Organizations
- United States Army Research Laboratory