Rate-independent soft crawlers. Issue 4 (3rd August 2018)

• Record Type: Journal Article
• Authors: Gidoni, Paolo
• Is Part Of: Quarterly journal of mechanics and applied mathematics. Volume 71:Issue 4(2018:Nov.)
• Page Start: 369
• Page End: 409
• Publication Date: 2018-08-03
• Subjects: Mechanics -- Mathematics -- Periodicals; Applied mathematics -- Periodicals; 530.1
• DOI: 10.1093/qjmam/hby010
• Languages: English
• ISSNs: 0033-5614

Abstract

Summary: This article applies the theory of rate-independent systems to model the locomotion of bio-mimetic soft crawlers. We prove the well-posedness of the approach and illustrate how the various strategies adopted by crawlers to achieve locomotion, such as friction anisotropy, complex shape changes and control on the friction coefficients, can be effectively described in terms of stasis domains. Compared to other rate-independent systems, locomotion models do not present any Dirichlet boundary condition, so that all rigid translations are admissible displacements, resulting in a non-coercivity of the energy term. We prove that existence and uniqueness of solution are guaranteed under suitable assumptions on the dissipation potential. Such results are then extended to the case of time-dependent dissipation potential.