Computation of the effective mechanical response of biological networks accounting for large configuration changes

Abstract : The asymptotic homogenization technique is involved to derive the effective elastic response of biological membranes viewed as repetitive beam networks. Thereby, a systematic methodology is established, allowing the prediction of the overall mechanical properties of biological membranes in the nonlinear regime, reflecting the influence of the geometrical and mechanical micro-parameters of the network structure on the overall response of the equivalent continuum. Biomembranes networks are classified based on nodal connectivity, so that we analyze in this work 3, 4 and 6-connectivity networks, which are representative of most biological networks. The individual filaments of the network are described as undulated beams prone to entropic elasticity, with tensile moduli determined from their persistence length. The effective micropolar continuum evaluated as a continuum substitute of the biological network has a kinematics reflecting the discrete network deformation modes, involving a nodal displacement and a microrotation. The statics involves the classical Cauchy stress and internal moments encapsulated into couple stresses, which develop internal work in duality to microcurvatures reflecting local network undulations. The relative ratio of the characteristic bending length of the effective micropolar continuum to the unit cell size determines the relevant choice of the equivalent medium. In most cases, the Cauchy continuum is sufficient to model biomembranes. The peptidoglycan network may exhibit a re-entrant hexagonal configuration due to thermal or pressure fluctuations, for which micropolar effects become important. The homogenized responses are in good agreement with \FE\ simulations performed over the whole network. The predictive nature of the employed homogenization technique allows the identification of a strain energy density of a hyperelastic model, for the purpose of performing structural calculations of the shape evolutions of biomembranes.
Keywords : Biomembranes
Type de document :
Article dans une revue
Journal of mechanical behavior of biomedical materials, Elsevier, 2016, 58, pp.28 - 44. 〈10.1016/j.jmbbm.2015.09.009〉
Liste complète des métadonnées

https://hal.univ-lorraine.fr/hal-01417904
Contributeur : Lemta Ul <>
Soumis le : vendredi 16 décembre 2016 - 10:53:23
Dernière modification le : jeudi 11 janvier 2018 - 06:27:33

Identifiants

Collections

Citation

Khaled El Nady, Jean-François Ganghoffer. Computation of the effective mechanical response of biological networks accounting for large configuration changes. Journal of mechanical behavior of biomedical materials, Elsevier, 2016, 58, pp.28 - 44. 〈10.1016/j.jmbbm.2015.09.009〉. 〈hal-01417904〉

Partager

Métriques

Consultations de la notice

24