On residual stresses and homeostasis: an elastic theory of functional adaptation in living matter.
Living matter can functionally adapt to external physical factors by developing internal tensions, easily revealed by cutting experiments. Nonetheless, residual stresses intrinsically have a complex spatial distribution, and destructive techniques cannot be used to identify a natural stress-free configuration. This work proposes a novel elastic theory of pre-stressed materials. Imposing physical compatibility and symmetry arguments, we define a new class of free energies explicitly depending on the internal stresses. This theory is finally applied to the study of arterial remodelling, proving its potential for the non-destructive determination of the residual tensions within biological materials.
Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190, Institut Jean Le Rond d'Alembert, F-75005 Paris, France.|MOX and Fondazione CEN, Politecnico di Milano, P.za Leonardo da Vinci 32, 20133 Milano, Italy.
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P
Ciarletta
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland Galway, University Road, Galway, Ireland.
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M
Destrade
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland Galway, University Road, Galway, Ireland.|School of Mathematics, University of Manchester, Oxford road, Manchester, M13 9PL, UK.
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Gower
D000818:Animals; D001696:Biomechanical Phenomena; D004548:Elasticity; D006801:Humans; D008962:Models, Theoretical; D010944:Plants; D013314:Stress, Mechanical