Mechanics of soft composites under axial, torsional, shear and dilatational loadings - Wang, Dong (2015)
The mechanics of soft matter has stimulated much interest due to diverse applications of soft materials in medicine and engineering. A critical issue is the nonlinear mechanical behavior of composites under different loadings. This research focuses on characterizing the nonlinear phenomena of multilayered soft materials under dilatation, axial loading, torsion, shear and combined loadings. The constitutive equations are those of second-order elasticity and the governing equations are Lagrangian equilibrium equations in terms of the first Piola-Kirchhoff stresses. First, the problem of soft bilayered spherical and multilayered cylindrical hydrogels subjected to various dilatation profiles is studied. The results show that: (1) elastic nonlinearity and inhomogeneity play a crucial role in the mechanical state, (2) a wide range of mechanical states can be designed for specific applications by manipulating the layer elasticity, interface positions and dilatation profile, and (3) the displacement and stresses can be characterized by a reduced set of geometric-elastic constants. Second, analytical solutions are obtained for homogeneous and bilayered cylinders under torsion, axial and combined loadings. Explicit parameters are given for judging the sign of the Poynting effect, in which a cylinder elongates or contracts axially under torsion. It is found that the effect in a soft composite may be significantly amplified over that in homogeneous materials and that it is strongly influenced by the interface position and by the material configuration in the composite. A coupled axial force-twist effect under combined loading, i.e., the twist of a torsionally loaded cylinder can be affected by the axial loading, is also found. Comparison of the predictions with the torque-tension-twist data for cardiac papillary muscles shows reasonable agreement. The solutions also provide the basis for a mechanistic method of determining third-order elastic constants. Third, the problems of the shear of homogenenous and bilayered blocks are treated in terms of a generalized shear displacement. In this generalization, the applied shear displacement is neither uniform nor is the shear displacement of the block assumed a priori to be a linear function of the height. The shear displacement solutions are characterized by the product of sine and hyperbolic sine functions of the height and depth variables, respectively. The height dependence of the shear displacement is a combination of linear and sinusoidal functions, and is verified against the test data of homogeneous and bilayered agar-gelatin cuboidal blocks. The calculation of stresses reveals the presence of not only negative normal stresses but also sinusoidally varying shear stresses on the lateral planes tending to distort the block about the height direction. These results can be of great importance in tissue/cell mechanics.