Modelling virus contact mechanics under atomic force imaging conditions. Issue 11 (24th July 2022)

• Record Type: Journal Article
• Authors: Piersanti, Paolo; White, Kristen; Dragnea, Bogdan; Temam, Roger
• Is Part Of: Applicable analysis. Volume 101:Issue 11(2022)
• Page Start: 3947
• Page End: 3957
• Publication Date: 2022-07-24
• Subjects: Elliptic variational inequalities -- contact mechanics -- biological systems; 74M15 -- 35Q92 -- 35J86 -- 92B05; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2022.2044027
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we present a discrete model governing the deformation of a convex regular polygon subjected not to cross a given flat rigid surface, on which it initially lies in correspondence of one point only. First, we set up the model in the form of a set of variational inequalities posed over a non-empty, closed and convex subset of a suitable Euclidean space. Second, we show the existence and uniqueness of the solution. The model provides a simplified illustration of processes involved in virus imaging by atomic force microscopy: adhesion to a surface, distributed strain, relaxation to a shape that balances adhesion and elastic forces. The analysis of numerical simulations results based on this model opens a new way of estimating the contact area and elastic parameters in virus contact mechanics studies.