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The main goal of this work is to clarify and quantify, by means ofmathematical analysis, the role of structural viscoelasticity in thebiomechanical response of deformable porous media with incompressibleconstituents to sudden changes in external applied loads. Models of deformableporous media with incompressible constituents are often utilized to describethe behavior of biological tissues, such as cartilages, bones and engineeredtissue scaffolds, where viscoelastic properties may change with age, disease orby design. Here, for the first time, we show that the fluid velocity within themedium could increase tremendously, even up to infinity, should the externalapplied load experience sudden changes in time and the structuralviscoelasticity be too small. In particular, we consider a one-dimensionalporo-visco-elastic model for which we derive explicit solutions in the caseswhere the external applied load is characterized by a step pulse or atrapezoidal pulse in time. By means of dimensional analysis, we identify somedimensionless parameters that can aid the design of structural propertiesand/or experimental conditions as to ensure that the fluid velocity within themedium remains bounded below a certain given threshold, thereby preventingpotential tissue damage. The application to confined compression tests forbiological tissues is discussed in detail. Interestingly, the loss ofviscoelastic tissue properties has been associated with various diseaseconditions, such as atherosclerosis, Alzheimer's disease and glaucoma. Thus,the findings of this work may be relevant to many applications in biology andmedicine.

The role of structural viscoelasticity in deformable porous media with incompressible constituents: applications in biomechanics