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In this article we propose a novel mathematical description of biomass growth that combines poroelastic theory of mixtures and cellular population models. The formulation, potentially applicable to general mechanobiological processes, is here used to study the engineered cultivation in bioreactors of articular chondrocytes, a process of Regenerative Medicine characterized by a complex interaction...
We aim at coupling the theory of swelling, describing the effects of solvent uptake in polymeric solids, with that of growing, describing the change of the relaxed state in a continuum body. Basing on the hypotheses underlying the two theories, and using some key principles of continuum mechanics, we develop a chemo-mechanical model which describes the combined effects of swelling and growing in solids.
We present a constitutive model for stochastically distributed fiber reinforced visco-active tissues, where the behavior of the reinforcement depends on the relative orientation of the electric field. Following our previous works, for the passive behaviors we adopt a second order approximation of the strain energy density associated to the parameters of the fiber distribution. Consistently, we also...
A new mathematical model for the macroscopic behavior of a material composed of a poroelastic solid embedding a Newtonian fluid network phase (also referred to as vascularized poroelastic material), with fluid transport between them, is derived via asymptotic homogenization. The typical distance between the vessels/channels (microscale) is much smaller than the average size of a whole domain (macroscale...
Morphogenesis in living tissues is the paramount example of a time- and space-dependent orchestration of living matter where shape and order emerge from undifferentiated initial conditions. The genes encode the protein expression that eventually drives the emergence of the phenotype, while energy supply and cell-to-cell communication mechanisms are necessary to such a process. The overall control...
A viscoelastic constitutive law is developed for a hydrogel to encompass deviatoric deformations where the viscosity of the solvent contributes to the deviatoric stress of the system. The law is obtained in Kelvin–Voigt form by adding together the stress in the polymer network, the osmotic and solvent pressures and the viscous stress induced in the solvent. Transient behavior of the hydrogel is presented...
Many models of the mechanical response of arteries assume a reinforcement with two families of helically wound fibres of collagen of opposite pitch. Motivated by experimental observations, the consequences for the internal pressurisation of arteries of a slight asymmetry in the winding angles is investigated here. It is shown that a torsional shear stress is generated as a result of this flaw, with...
We study the onset of delamination blisters in a growing elastic sheet adhered to a flat stiff substrate. When the ends of the sheet are kept fixed, its growth causes residual stresses that lead to delamination. This instability can be viewed as a discontinuous buckling between the complete adhered solution and the buckled solution. We provide an analytic expression for the critical deformation at...
We present a rigorous derivation of dimensionally reduced theories for thin sheets of nematic elastomers, in the finite bending regime. Focusing on the case of twist nematic texture, we obtain 2D and 1D models for wide and narrow ribbons exhibiting spontaneous flexure and torsion. We also discuss some variants to the case of twist nematic texture, which lead to 2D models with different target curvature...
Brittle materials fail catastrophically. In consequence of their limited flaw-tolerance, failure occurs by localized fracture and is typically a dynamic process. Recently, experiments on epithelial cell monolayers have revealed that this scenario can be significantly modified when the material susceptible to cracking is adhered to a hydrogel substrate. Thanks to the hydraulic coupling between the...
Cell mechanical recognition of extracellular matrix determines the cell activities and functions. Focal adhesions are part of the cell mechanosensing machinery and, operating at the very dynamic interface between cell and extracellular matrix, can operate this recognition and trigger conformational, functional and behavioral modification of the cell. To investigate how the dynamic of assembly and...
Under suitable conditions, the motion of a fluid in a porous medium can be studied by assuming the validity of Darcy’s law. Since many biological tissues can be thought of as porous media, Darcy’s law is invoked in several biomechanical contexts, like the transport of the chemical species needed for the metabolism of tissue cells. Although Darcy’s law supplies physically sound results in many circumstances,...
We provide a quantitative description of the helicoid-to-spiral transition in thin ribbons of nematic elastomers using an elementary calculation based on a Koiter-type plate with incompatible reference configuration. Our calculation confirms that such transition is ruled by the competition between stretching energy and bending energy.
A classical problem in structural mechanics is the evaluation of beam stretching and curvature in slender bilayered beams, due to mechanical actions, thermal distortions, differential growth, and more recently, to swelling. We investigate the non-monotonic changes in the curvature of swollen bilayer beams due to mismatches in physical properties of the two layers starting from a simple structural...
Based on the framework of sliding-filament theory and on the cross-bridges dynamics, a mathematical model for the simulation of the force response and length change of individual myofibril is presented. The myofibril is modeled as a group of segments placed in series, each segment represents a half-sarcomere with active and elastic properties. A multiple-state cross-bridge formalism relates the half...
In this paper we investigate different strategies to overcome the scallop theorem. We will show how to obtain a net motion exploiting the fluid’s type change during a periodic deformation. We are interested in two different models: in the first one that change is linked to the magnitude of the opening and closing velocity. Instead, in the second one it is related to the sign of the above velocity...
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