@article{bociu_guidoboni_sacco_verri_2019, title={On the role of compressibility in poroviscoelastic models}, volume={16}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2019308}, abstractNote={In this article we conduct an analytical study of a poroviscoelastic mixture model stemming from the classical Biot's consolidation model for poroelastic media, comprising a fluid component and a solid component, coupled with a viscoelastic stress-strain relationship for the total stress tensor. The poroviscoelastic mixture is studied in the one-dimensional case, corresponding to the experimental conditions of confined compression. Upon assuming (i) negligible inertial effects in the balance of linear momentum for the mixture, (ii) a Kelvin-Voigt model for the effective stress tensor and (iii) a constant hydraulic permeability, we obtain an initial value/boundary value problem of pseudo-parabolic type for the spatial displacement of the solid component of the mixture. The dimensionless form of the differential equation is characterized by the presence of two positive parameters γ and η, representing the contributions of compressibility and structural viscoelasticity, respectively. Explicit solutions are obtained for different functional forms characterizing the boundary traction. The main result of our analysis is that the compressibility of the components of a poroviscoelastic mixture does not give rise to unbounded responses to non-smooth traction data. Interestingly, compressibility allows the system to store potential energy as its components are elastically compressed, thereby providing an additional mechanism that limits the maximum of the discharge velocity when the imposed boundary traction is irregular in time.}, number={5}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Bociu, Lorena and Guidoboni, Giovanna and Sacco, Riccardo and Verri, Maurizio}, year={2019}, pages={6167–6208} }
 @article{verri_guidoboni_bociu_sacco_2018, title={THE ROLE OF STRUCTURAL VISCOELASTICITY IN DEFORMABLE POROUS MEDIA WITH INCOMPRESSIBLE CONSTITUENTS: APPLICATIONS IN BIOMECHANICS}, volume={15}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2018042}, abstractNote={The main goal of this work is to clarify and quantify, by means of mathematical analysis, the role of structural viscoelasticity in the biomechanical response of deformable porous media with incompressible constituents to sudden changes in external applied loads. Models of deformable porous media with incompressible constituents are often utilized to describe the behavior of biological tissues, such as cartilages, bones and engineered tissue scaffolds, where viscoelastic properties may change with age, disease or by design. Here, for the first time, we show that the fluid velocity within the medium could increase tremendously, even up to infinity, should the external applied load experience sudden changes in time and the structural viscoelasticity be too small. In particular, we consider a one-dimensional poro-visco-elastic model for which we derive explicit solutions in the cases where the external applied load is characterized by a step pulse or a trapezoidal pulse in time. By means of dimensional analysis, we identify some dimensionless parameters that can aid the design of structural properties and/or experimental conditions as to ensure that the fluid velocity within the medium remains bounded below a certain given threshold, thereby preventing potential tissue damage. The application to confined compression tests for biological tissues is discussed in detail. Interestingly, the loss of viscoelastic tissue properties has been associated with various disease conditions, such as atherosclerosis, Alzheimer's disease and glaucoma. Thus, the findings of this work may be relevant to many applications in biology and medicine.}, number={4}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Verri, Maurizio and Guidoboni, Giovanna and Bociu, Lorena and Sacco, Riccardo}, year={2018}, month={Aug}, pages={933–959} }