Solid-fluid dynamics of yield-stress fluids

On the example of two-phase continua experiencing stress induced solid-fluid phase transitions we explore the use of the Euler structure in the formulation of the governing equations. The Euler structure guarantees that solutions of the time evolution equations possessing it are compatible with mechanics and with thermodynamics. The former compatibility means that the equations are local conservation laws of the Godunov type and the latter compatibility means that the entropy does not decrease during the time evolution. In numerical illustrations, in which the one-dimensional Riemann problem is explored, we require that the Euler structure is also preserved in the discretization.Comment: 51 pages, 7 figure

Nucleation of Cavities in Gels

University of Minnesota Ph.D. dissertation. August 2017. Major: Mathematics. Advisor: Ronald Siegel. 1 computer file (PDF); viii, 94 pages.Many implantable devices are made of synthetic polymers which upon insertion absorb water, causing the polymer to swell and form a gel (mixture of solid and fluid). Since the swelling leads to an expansion of the polymer, a gel is considered to be a compressible material. A high concentration of stress due to the swelling may lead to the nucleation and growth of cavities within the gel, which is likely to cause the debonding of the material from the support it is attached to. In this dissertation, we focus on the cavitation in a gel occupying a spherical domain, subject to either displacement boundary conditions or free swelling. We consider a total free energy of the gel accounting for the elasticity of the polymer and for the mixing between polymer and fluid, called the Flory-Huggins energy. In addition to penalizing gel deformation, the free energy represents competing effects of entropy that favours mixing, polymer-polymer and fluid-fluid interaction forces. We study the material properties necessary to allow for a nucleation of cavities and analyze radially symmetric deformations

Effect of Surface Forces on the Mechanics of Sorption-deformation in Microporous Media and Environment-assisted Crack Growth in Brittle Solids

The structurization of fluid molecules at the fluid-solid interface, known as adsorption, can create noticeable forces which are ubiquitous in material systems such as fluid-saturated porous materials and cracked solids.Adsorption alters the strain and microstructure of porous materials. However, adsorption-induced forces are routinely neglected in the continuum description of the porous media. In this thesis, a poromechanics theory is developed for deformable microporous media by thermodynamically upscaling the adsorption-induced forces from the pore-scale to the continuum scale. The capability of this model is demonstrated by quantitative comparison with experimental results using physically sound parameters. The model is further extended to incorporate detailed information of pore size distribution. A comprehensive study of the influence of pore size distribution highlights plausible causes of the distinct adsorption-deformation behaviors of various porous materials. It is found that competition between the attractive disjoining pressure and the reduction of surface energy controls the shrinkage-swelling transition of microporous media during the early stage of adsorption. On the other hand, the presence of surface-reactive species in the environment can reduce materials&rsquo; resistance to withstand fracture. It is established that the alteration of surface tension due to adsorption can qualitatively explain the reduced fracture toughness in reactive environments. However, the intricate coupling between physiochemical processes of adsorption, diffusion and fracture mechanics at the vicinity of the crack tip has never been fully resolved. A mechanistic theory is thus developed and implemented in this thesis to consider both the strong disjoining pressure between the opposing solid surfaces near the crack tip and the transport processes that control the accessibility of reactive species to the crack tip. For the first time, the classical SCG curve naturally emerges from explicit consideration of the underlying physical processes. The adoption of different fluid transport models confirms that viscous flow or surface diffusion can explain certain aspects of the transition from slow environmentally promoted crack propagation to sudden fracturing. Finally, it is shown that the complete prediction of subcritical crack propagation requires not only the knowledge of the correct fluid transport mechanisms, but also the knowledge of the interplay and transition between multiple fluid transport mechanisms.</p