24 research outputs found
Analytical and numerical analyses of the micromechanics of soft fibrous connective tissues
State of the art research and treatment of biological tissues require
accurate and efficient methods for describing their mechanical properties.
Indeed, micromechanics motivated approaches provide a systematic method for
elevating relevant data from the microscopic level to the macroscopic one. In
this work the mechanical responses of hyperelastic tissues with one and two
families of collagen fibers are analyzed by application of a new variational
estimate accounting for their histology and the behaviors of their
constituents. The resulting, close form expressions, are used to determine the
overall response of the wall of a healthy human coronary artery. To demonstrate
the accuracy of the proposed method these predictions are compared with
corresponding 3-D finite element simulations of a periodic unit cell of the
tissue with two families of fibers. Throughout, the analytical predictions for
the highly nonlinear and anisotropic tissue are in agreement with the numerical
simulations
Some aspects of the Liouville equation in mathematical physics and statistical mechanics
This paper presents some mathematical aspects of Classical Liouville theorem
and we have noted some mathematical theorems about its initial value problem.
Furthermore, we have implied on the formal frame work of Stochastic Liouville
equation (SLE)
Multiscale instabilities in soft heterogeneous dielectric elastomers
The development of instabilities in soft heterogeneous dielectric elastomers is investigated. Motivated by experiments and possible applications, we use in our analysis the physically relevant referential electric field instead of electric displacement. In terms of this variable, a closed form solution is derived for the class of layered neo-Hookean dielectrics. A criterion for the onset of electromechanical multiscale instabilities for the layered composites with anisotropic phases is formulated. A general condition for the onset of the macroscopic instability in soft multiphase dielectrics is introduced. In the example of the layered dielectrics, the essential influence of the microstructure on the onset of instabilities is revealed. We found that: (i) macroscopic instabilities dominate at moderate volume fractions of the stiffer phase, (ii) interface instabilities appear at small volume fractions of the stiffer phase and (iii) instabilities of a finite scale, comparable to the microstructure size, occur at large volume fractions of the stiffer phase. The latest new type of instabilities does not appear in the purely mechanical case and dominates in the region of large volume fractions of the stiff phase