Growth-induced compatible strains. (January 2017)

• Record Type: Journal Article
• Authors: Minozzi, Manuela; Nardinocchi, Paola; Teresi, Luciano; Varano, Valerio
• Is Part Of: Mathematics and mechanics of solids. Volume 22:Number 1(2017)
• Page Start: 62
• Page End: 71
• Publication Date: 2017-01
• Subjects: Growth mechanics -- Nonlinear elasticity -- Compatibility conditions; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/1081286515570510
• Languages: English
• ISSNs: 1081-2865

Abstract

We studied the time evolution problem driven by growth for a non-Euclidean ball which at its initial state is equipped with a non-compatible distortion field. The problem is set within the framework of non-linear elasticity with large growing distortions. No bulk accretive forces are considered, and growth is only driven by the stress state. We showed that, when stress-driven growth is considered, distortions can evolve along different trajectories which share a common attracting manifold; moreover, they eventually attain a steady and compatible form, to which there corresponds a stress-free state of the ball.