title: Compatibility and the genesis of residual stress by volumetric growth.
abstract: The equations of compatibility which are pertinant for growth strain fields are collected and examples are given in simply-connected and multiply-connected regions. Compatibility conditions for infinitesimal strains are well known and the possibilities of Volterra dislocations in multiply-connected regions are enumerated. For finite growth strains in a multiply-connected regions, each case must be examined individually and no generalizations in terms of Volterra dislocations are available. Any incompatible growth strains give rise to residual stresses which are known to occur in many tissues such as the heart, arterial wall, and solid tumors.
authors.affiliation: Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, La Jolla 92093-0412, USA.
authors.forename: R
authors.initials: R
authors.lastname: Skalak
authors.forename: S
authors.initials: S
authors.lastname: Zargaryan
authors.forename: R K
authors.initials: RK
authors.lastname: Jain
authors.forename: P A
authors.initials: PA
authors.lastname: Netti
authors.forename: A
authors.initials: A
authors.lastname: Hoger
mesh_terms: D000818:Animals; D001696:Biomechanical Phenomena; D004548:Elasticity; D006128:Growth / Q000502:physiology*; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D009369:Neoplasms / Q000473:pathology / Q000503:physiopathology; D011312:Pressure