Abstract
In the paper, we developed a macroscopic discrete element model of permeable fluid-saturated materials with solid skeleton characterized by viscoelastic rheological properties. The Biot’s linear model of poroelasticity was used as a mathematical basis for describing the mechanical interrelation between the solid skeleton and interstitial fluid. Using this model, we numerically studied the dependences of the effective Young’s modulus and strength of fluid-saturated viscoelastic materials on the loading rate, sample size and the mechanical parameters, which determine the relaxation time of the solid-phase skeleton and the time scale of redistribution of fluid in the pore space. We revealed two dimensionless control parameters that determine the dynamic values of the effective mechanical characteristics of the samples under compression loading. We obtained the general relations that describe the above-mentioned dependences in terms of the two proposed control parameters. These relations have a logistic nature and are described by sigmoid functions. The importance of the proposed empirical expressions is determined by the possibility of their application for predicting the mechanical response of fluid-saturated materials of different nature (bone tissue, rocks, porous materials with polymeric skeleton, including elastomers, etc.) under dynamic loading.
Highlights
The regularities of the nonlinear behavior of viscoelastic materials and the related non-stationarity of mechanical characteristics are the issues in a wide range of analytical and computational studies as these features determine the peculiarities of functioning of critical elements of various technical and natural structures including biological ones [1]-[6]
We revealed two dimensionless control parameters that determine the dynamic values of the effective mechanical characteristics of the samples under compression loading
We considered a model isotropic viscoelastic material with mechanical characteristics of the same order of magnitude as the compact bone tissue: EK=1 GPa, Е=EK+EM=11 GPa (ЕК/Е=0.1 what is a lower estimate for this class of materials), =0.3, М=10 MPa s, =2500 kg/m3, c 20 MPa and t 10 MPa ( =2 what does not go beyond the bounds of the literature data interval for compact bone tissue), 0=10%, a 0.67, b=1
Summary
The regularities of the nonlinear behavior of viscoelastic materials and the related non-stationarity of mechanical characteristics (namely, their dependence on the loading rate) are the issues in a wide range of analytical and computational studies as these features determine the peculiarities of functioning of critical elements of various technical and natural structures including biological ones [1]-[6]. A broad subgroup of materials of this class comprises materials that contain viscous soft matter phases as structural constituents. Such kind of materials is characterized by a high contrast of local mechanical properties. At higher loading rates the material response is determined by the ratio of the time of stress relaxation in the skeleton and the characteristic time of redistribution of interstitial fluid in the pore space
Sign-in/Register to view highlights & summary 
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call