Peer-Reviewed Journal Details
Mandatory Fields
Gower, AL, Ciarletta, P, Destrade, M
2015
November
Proceedings Of The Royal Society A-Mathematical Physical And Engineering Sciences
Initial stress symmetry and its applications in elasticity
Published
()
Optional Fields
biomechanics mechanics applied mathematics RESIDUAL-STRESS STRAIN DEFORMATION ELLIPTICITY PRESSURE GROWTH SOLIDS WAVES AORTA
471
An initial stress within a solid can arise to support external loads or from processes such as thermal expansion in inert matter or growth and remodelling in living materials. For this reason, it is useful to develop a mechanical framework of initially stressed solids irrespective of how this stress formed. An ideal way to do this is to write the free energy density psi in terms of initial stress tau and the elastic deformation gradient F, so we write psi = psi(F, tau). In this paper, we present a new constitutive condition for initially stressed materials, which we call the initial stress symmetry (ISS). We focus on two consequences of this condition. First, we examine how ISS restricts the possible choices of free energy densities psi = psi (F, tau) and present two examples of psi that satisfy the ISS. Second, we show that the initial stress can be derived from the Cauchy stress and the elastic deformation gradient. To illustrate, we take an example from biomechanics and calculate the optimal Cauchy stress within an artery subjected to internal pressure. We then use ISS to derive the optimal target residual stress for the material to achieve after remodelling, which links nicely with the notion of homeostasis.
10.1098/rspa.2015.0448
Grant Details
Irish Research Council (IRC)
IRC postgraduate scholarship
Publication Themes
Biomedical Science and Engineering, Informatics, Physical and Computational Sciences