Premium
On compatible strain with reference to biomechanics of soft tissues
Author(s) -
Klarbring A.,
Olsson T.
Publication year - 2005
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200410192
Subject(s) - corollary , continuum mechanics , differential geometry , biomechanics , mathematics , spheres , residual stress , residual , stress–strain curve , strain (injury) , mathematical analysis , classical mechanics , geometry , physics , pure mathematics , materials science , anatomy , composite material , algorithm , medicine , deflection (physics) , astronomy , thermodynamics
Abstract In previous studies, residual stresses and strains in soft tissues have been experimentally investigated by cutting the material into pieces that are assumed to become stress free. The present paper gives a theoretical basis for such a procedure, based on a classical theorem of continuum mechanics. As applications of the theory we study rotationally symmetric cylinders and spheres. A computer algebra system is used to state and solve differential equations that define compatible strain distributions. A mapping previously used in constructing a mathematical theory for the mechanical behavior of arteries is recovered as a corollary of the theory, but is found not to be unique. It is also found, for a certain residual strain distribution, that a sphere can be cut from pole to pole to form a stress and strain free configuration.