Giulia Giantesio

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, transversely 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.

Reverse flow in magnetoconvection of two immiscible fluids in a vertical channel

This paper concerns the study of the influence of an external magnetic field on the reverse flow occurring in the steady mixed convection of two Newtonian immiscible fluids filling a vertical channel under the Oberbeck-Boussinesq approximation. The two isothermal boundaries are kept either at different or at equal temperatures. The velocity, the temperature and the induced magnetic field are obtained analytically. The results are presented graphically and discussed for various values of the parameters involved in the problem (in particular the Hartmann number and the buoyancy coefficient) and are compared with those for a single Newtonian fluid. The occurrence of the reverse flow is explained and carefully studied. Nomenclature bi constant fluid thermal diffusivity C constant such that Pi = −Cx1 + p0i, i = 1, 2 d1 +d2 channel width d = d2 d1 ratio between the channel widths Ei electric field g = ge1 gravity acceleration Hi total magnetic field hi(y) dimensionless function describing the induced magnetic field defined in (14) H0e2 external uniform magnetic field (H0 > 0) Ĥ1(x2) induced magnetic field component in the x1−direction ki constant fluid thermal conductivity k = k2 k1 ratio between the fluid thermal conductivities M i Hartmann number defined in (14) Pi difference between the hydromagnetic pressure and the hydrostatic pressure p0i arbitrary constant Ti = Ti(x2) temperature T0 reference temperature Tw1,Tw2 uniform temperatures (Tw2 ≥ Tw1) vi velocity field ui(y) dimensionless function describing the velocity defined in (14) V0 characteristic velocity yi dimensionless transverse coordinate defined in (14) Greek symbols αi thermal expansion coefficient γ constant defined in (15) ηi magnetic diffusivity θi(yi) dimensionless temperature defined in (14) λi buoyancy coefficient defined in (14) μi Newtonian viscosity coefficient (μi > 0) μ = μ2 μ1 ratio between the viscosities μe magnetic permeability ρ0i mass density at the temperature T0 σi electrical conductivity, 1 σi is called resistivity σ = σ2 σ1 ratio between the electrical conductivities

MHD mixed convection oblique stagnation-point flow on a vertical plate

Purpose This paper aims to study the problem of the steady plane oblique stagnation-point flow of an electrically conducting Newtonian fluid impinging on a heated vertical sheet. The temperature of the plate varies linearly with the distance from the stagnation point. Design/methodology/approach The governing boundary layer equations are transformed into a system of ordinary differential equations using the similarity transformations. The system is then solved numerically using the “bvp4c” function in MATLAB. Findings An exact similarity solution of the magnetohydrodynamic (MHD) Navier–Stokes equations under the Boussinesq approximation is obtained. Numerical solutions of the relevant functions and the structure of the flow field are presented and discussed for several values of the parameters which influence the motion: the Hartmann number, the parameter describing the oblique part of the motion, the Prandtl number (Pr) and the Richardson numbers. Dual solutions exist for several values of the parameters. Originality value The present results are original and new for the problem of MHD mixed convection oblique stagnation-point flow of a Newtonian fluid over a vertical flat plate, with the effect of induced magnetic field and temperature.

Loss of mass and performance in skeletal muscle tissue: A continuum model

Abstract We present a continuum hyperelastic model which describes the mechanical response of a skeletal muscle tissue when its strength and mass are reduced by aging. Such a reduction is typical of a geriatric syndrome called sarcopenia. The passive behavior of the material is described by a hyperelastic, polyconvex, transversely isotropic strain energy function, and the activation of the muscle is modeled by the so called active strain approach. The loss of ability of activating of an elder muscle is then obtained by lowering of some percentage the active part of the stress, while the loss of mass is modeled through a multiplicative decomposition of the deformation gradient. The obtained stress-strain relations are graphically represented and discussed in order to study some of the effects of sarcopenia.

Strain-dependent internal parameters in hyperelastic biological materials

Abstract 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.