arXiv subjects

Giulia Giantesio

Publications and source records attributed to Giulia Giantesio.

4 recordsLinked to original sources

arXiv2024

Thermal convection in a higher velocity gradient and higher temperature gradient fluid

We analyse a model for thermal convection in a class of generalized Navier-Stokes equations containing fourth order spatial derivatives of the velocity and of the temperature. The work generalises the isothermal model of A. Musesti. We derive critical Rayleigh and wavenumbers for the onset of convective fluid motion paying careful attention to the variation of coefficients of the highest derivatives. In addition to linear instability theory we include an analysis of fully nonlinear stability theory. The theory analysed possesses a bi-Laplacian term for the velocity field and also for the temperature field. It was pointed out by E. Fried and M. Gurtin that higher order terms represent micro-length effects and these phenomena are very important in flows in microfluidic situations. We introduce temperature into the theory via a Boussinesq approximation where the density of the body force term is allowed to depend upon temperature to account for buoyancy effects which arise due to expansion of the fluid when this is heated. We analyse a meaningful set of boundary conditions which are introduced by Fried and Gurtin as conditions of strong adherence, and these are crucial to understand the effect of the higher order derivatives upon convective motion in a microfluidic scenario where micro-length effects are paramount. The basic steady state is the one of zero velocity, but in contrast to the classical theory the temperature field is nonlinear in the vertical coordinate. This requires care especially dealing with nonlinear theory and also leads to some novel effects.

physics.flu-dyn↗

arXiv2018

A comparison between active strain and active stress in transversely isotropic hyperelastic materials

Active materials are media for which deformations can occur in absence of loads, given an external stimulus. Two approaches to the modeling of such materials are mainly used in literature, both based on the introduction of a new tensor: an additive stress $\mathsf{P}_\text{act}$ in the active stress case and a multiplicative strain $\mathsf{F}_a$ in the active strain one. Aim of this paper is the comparison between the two approaches on simple shears. Considering an incompressible and transversely isotropic material, we design constitutive relations for $\mathsf{P}_\text{act}$ and $\mathsf{F}_a$ so that they produce the same results for a uniaxial deformation along the symmetry axis. We then study the two approaches in the case of a simple shear deformation. In a hyperelastic setting, we show that the two approaches produce different stress components along a simple shear, unless some necessary conditions on the strain energy density are fulfilled. However, such conditions are very restrictive and rule out the usual elastic strain energy functionals. Active stress and active strain therefore produce different results in shear, even if they both fit uniaxial data. Our results show that experimental data on the stress-stretch response on uniaxial deformations are not enough to establish which activation approach can capture better the mechanics of active materials. We conclude that other types of deformations, beyond the uniaxial one, should be taken into consideration in the modeling of such materials.

cond-mat.soft↗

arXiv2018

Strain-dependent internal parameters in hyperelastic biological materials

The behavior of hyperelastic energies depending on an internal parameter, which is a function of the deformation gradient, is discussed. As an example, the analysis of two models where the parameter describes the activation of a tetanized skeletal muscle tissue is presented. In those models, the activation parameter depends on the strain and it is shown the importance of considering the derivative of the parameter with respect to the strain in order to capture the proper stress-strain relations.

q-bio.TO↗

arXiv2017

A continuum model of skeletal muscle tissue with loss of activation

We present a continuum model for the mechanical behavior of the skeletal muscle tissue when its functionality is reduced due to aging. The loss of ability of activating is typical of the geriatric syndrome called sarcopenia. The material is described by a hyperelastic, polyconvex, transverse isotropic strain energy function. The three material parameters appearing in the energy are fitted by least square optimization on experimental data, while incompressibility is assumed through a Lagrange multiplier representing the hydrostatic pressure. The activation of the muscle fibers, which is related to the contraction of the sarcomere, is modeled by the so called active strain approach. The loss of performance of an elder muscle is then obtained by lowering of some percentage the active part of the stress. The model is implemented numerically and the obtained results are discussed and graphically represented.

q-bio.TO↗