Vol. 12, No. 2, 2017

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12
Issue 3, 249–351
Issue 2, 147–247
Issue 1, 1–146

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 8 issues

Volume 7, 10 issues

Volume 6, 9 issues

Volume 5, 6 issues

Volume 4, 10 issues

Volume 3, 10 issues

Volume 2, 10 issues

Volume 1, 8 issues

The Journal
Cover
Editorial Board
Research Statement
Scientific Advantage
Submission Guidelines
Submission Form
Subscriptions
Author Index
To Appear
 
ISSN: 1559-3959
Conjugate stress/strain base pairs for planar analysis of biological tissues

Alan D. Freed, Veysel Erel and Michael R. Moreno

Vol. 12 (2017), No. 2, 219–247
Abstract

A theoretical framework is presented for the analysis of planar membranes based upon a triangular (as opposed to a polar) decomposition of the deformation gradient. This leads to a distillation of the deformation gradient into three distinct modes. Each mode can, in principle, be individually activated in an experiment. Measures of stress are shown to exist for each mode of strain so that the stress power can be decomposed into independent additive parts. The outcome is a set of three conjugate stress/strain base pairs (each being a pair of scalars) from which constitutive equations can be constructed for planar solids without relying on tensor invariants to cast the theory. Explicit and implicit elastic models are derived that, when convolved, produce a material model whose stress/strain response is indicative of soft biological tissues. Stress/strain curves for each conjugate pairing are constructed from published experimental data. The model describes these data.

Keywords
thermodynamic conjugate pairs, distortion, Gram–Schmidt decomposition, membrane, soft tissues
Milestones
Received: 22 July 2016
Revised: 2 October 2016
Accepted: 18 October 2016
Published: 14 December 2016
Authors
Alan D. Freed
Department of Mechanical Engineering
Texas A&M University
TAMU 3123
College Station, TX 77843
United States
Veysel Erel
Department of Mechanical Engineering
Texas A&M University
TAMU 3123
College Station, TX 77843
United States
Michael R. Moreno
Department of Mechanical Engineering
Texas A&M University
TAMU 3123
College Station, TX 77843
United States