Abstract
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.
Highlights
We propose a novel constitutive theory for internally stressed living matter, demonstrating how a principle of functional optimality in response to external loads allows determining the complex distribution of residual stresses
Our approach goes beyond the state of the art since it does not require any virtual state: instead, it considers that the reference configuration of the body is residually stressed, assuming that its free energy explicitly depends on the pre-existing residual stresses
We have proposed a novel constitutive theory to describe the behaviour of residually stressed elastic materials
Summary
We consider the living body as a continuous distribution of matter at the tissue scale, assuming a characteristic length larger than the cell size. Which imposes nine scalar equations involving the derivatives of the free energy with respect to the invariants All such three physical conditions result in a non trivial set of equations, as reported in the Supplementary Material, a great simplification arises if we neglect the functional dependence on J2, J3 and J4. The constitutive relation defined in Eqs (5, 6) defines a novel free energy for finite hyperelastic solids with residual stresses, which is mathematically well-posed thanks to the polyconvexity of Eq (5) It describes a residually stressed body which physically behaves as a neo-Hookean material, without requiring any guess about the virtual stress-free state, in contrast to the existing approaches based on the multiplicative decomposition. The significance of the proposed theory beyond the existing methods is exemplified in the following applications, concerning the study of the mechanical adaptation of living matter and the non-destructive determination of residual stresses by elastic wave propagation
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
