Abstract
The purpose of this brief note is to develop fully Eulerian, implicit constitutive equations for the mechanical response of a class of materials that do not dissipate mechanical work in any process. We show that such materials can be modelled by obtaining a form for the Helmholtz potential as a function of the current mass density, the Cauchy stress and certain other parameters that capture anisotropic response. The resulting constitutive equations are of the form , where and are functions of the state variables of the system. The class of materials that can be obtained from such a constitutive relation is considerably more general than conventional Green-elastic hyperelastic materials. Such response functions may be suitable for the modelling of biological tissue where, due to the constant remodelling that takes place, there may be no physical meaning to a ‘reference configuration’.
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 callMore From: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Disclaimer: 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.
