Abstract
We demonstrate that for a rigid and incompressible network in mechanical equilibrium, the microscopic stress and strain follows a simple relation, σ=pE, where σ is the deviatoric stress, E is a mean-field strain tensor, and p is the hydrostatic pressure. This relationship arises as the natural consequence of energy minimization or equivalently, mechanical equilibration. The result suggests not only that the microscopic stress and strain are aligned in the principal directions, but also microscopic deformations are predominantly affine. The relationship holds true regardless of the different (foam or tissue) energy model considered, and directly leads to a simple prediction for the shear modulus, μ=⟨p⟩/2, where ⟨p⟩ is the mean pressure of the tessellation, for general randomized lattices.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
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.