Growing Membranes

  • Alain Goriely
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 45)


In the previous chapter we gave a theory of axisymmetric elastic shells and membranes. Biological membranes have the additional ability to change their internal configuration to grow and remodel. Since we are considering biological membranes, we are mostly interested in systems in which the membrane is under pressure. At the mechanical level when an elastic shell in its reference configuration is pressurized it will expand until a new stress equilibrium is achieved in its current configuration. During the course of this deformation the initially uniformly distributed material points will become redistributed, typically separated under expansion, as a manifestation of the new strained configuration. Furthermore, the shell expansion leads to a reduction in the shell wall thickness—although this may not be uniform around the shell.

Copyright information

© Springer Science+Business Media LLC 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OxfordOxfordUK

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