title: Coupled electro-mechanical models of fiber-distributed active tissues.
abstract: We discuss a constitutive model for stochastically distributed fiber reinforced tissues, where the active behavior of the fibers depends on the relative orientation of the electric field. Unlike other popular approaches, based on numerical integration over the unit sphere, or on the use of second order structure tensors, for the passive behavior we adopt a second order approximation of the strain energy density of the distribution. The purely mechanical quantities result to be dependent on two (second and fourth order, respectively) averaged structure tensors. In line with the approximation used for the passive behavior, we model the active behavior accounting for the statistical fiber distribution. We extend the Helmholtz free energy density by introducing a directional active potential, dependent on a stochastic permittivity tensor associated to a particular direction, and approximate the total active potential through a second order Taylor expansion of the permittivity tensor. The approximation allows us to derive explicitly the active stress and the active constitutive tensors, which result to be dependent on the same two averaged structure tensors that characterize the passive response. Active anisotropy follows from the distribution of the fibers and inherits its stochastic parameters. Examples of passive and active behaviors predicted by the model in terms of response to biaxial testing are presented, and comparisons with passive experimental data are provided.
authors.affiliation: Politecnico di Milano, Dipartimento di Ingegneria Civile ed Ambientale, Piazza Leonardo da Vinci 32, Milano, Italy. Electronic address: anna.pandolfi@polimi.it.
authors.forename: Anna
authors.initials: A
authors.lastname: Pandolfi
authors.affiliation: Università Campus Bio-Medico di Roma, Department of Engineering, Unit of Nonlinear Physics and Mathematical Modeling, via Álvaro del Portillo 21, 00128 Rome, Italy.
authors.forename: Alessio
authors.initials: A
authors.lastname: Gizzi
authors.affiliation: Università di Chieti-Pescara, Dipartimento INGEO, Viale Pindaro 42, Pescara, Italy.
authors.forename: Marcello
authors.initials: M
authors.lastname: Vasta
mesh_terms: D016880:Anisotropy; D001696:Biomechanical Phenomena; D004560:Electricity; D006801:Humans; D055595:Mechanical Phenomena; D009132:Muscles / Q000166:cytology*; D013269:Stochastic Processes; D013314:Stress, Mechanical
keywords: Constitutive modeling; Electromechanics; Multiplicative decomposition of deformation gradient; Second order approximation; Statistical fiber distribution