A Biot–Cosserat two-dimensional elastic nonlinear model for a micromorphic medium

• Published in: Continuum mechanics and thermodynamics Vol. 32; no. 5; pp. 1357 - 1369
• Main Authors: Giorgio, Ivan, De Angelo, Michele, Turco, Emilio, Misra, Anil
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2020; Springer; Springer Nature B.V
• Subjects: Analysis; Boundary conditions; Classical and Continuum Physics; Compressibility; Computer simulation; Engineering Thermodynamics; Flux density; Heat and Mass Transfer; Mathematical analysis; Mathematical models; Numerical analysis; Original Article; Physics; Physics and Astronomy; Porosity; Static tests; Strain; Structural Materials; Theoretical and Applied Mechanics; Two dimensional models; Cosserat medium; Nonlinear elasticity; Biot poroelasticity; Variational approach
• ISSN: 0935-1175; 1432-0959
• DOI: 10.1007/s00161-019-00848-1

A possible strain energy density, incorporating Cosserat’s micro-rotations and Biot’s change in porosity conferred by the microstructure geometry, is proposed in an elastic, two-dimensional, nonlinear context. The nonlinearities are taken into account both extracting the exact macro-rotations by the polar decomposition of the standard deformation gradient F and evaluating the change in the area at the macroscopic level of observation as J - 1 . Moreover, the bulk behavior of the material is assumed to be described by a compressible neo-Hookean model. Based on a variational formulation, finite element numerical simulations of static tests in some representative examples have been performed to illustrate the main features of the proposed model and the effect of the boundary conditions.