Viscous interfaces as source of material creep : new, micromechanics-based, perspectives on liquid crystal physics, rheology, and thixotropy

Abstract

It is well accepted that absorption of water (or other fluids) at interfaces within the microstructures and nano-structures of hydrated biomaterials or geomaterials are a very probably origin of their macroscopic creep and relaxation behavior; which has been studied particularly intensively for, e.g., concrete or bone. At the same time, the macroscopic creep behavior is standardly given in terms of classical rheological models (Kelvin-Voigt, Maxwell, Zener, chain models) with a number of regression parameters obtained from some fitting algorithms, while the actual micromechanical origin of the creep process remains fully unconsidered. The present thesis aims at delivering a first remedy to this somehow unsatisfactory situation. It is divided into five chapters, relating to articles published or prepared for publication in scientific journals, documenting the development of a new theoretical approach for the upscaling of interface viscosities to bulk material creep properties - and its first confrontation to experimental results as well. Chapter 1 introduces the novel theoretical concept: Interfaces are perceived as zero-thickness limit cases of spheroidal, eigenstressed inclusions in an elastic matrix, and the limit case-driven eigentractions are inserted into viscosity laws, relating them to interface dislocation rates. In this way, the rich theoretical heritage of continuum micromechanics based on Eshelby problems and their derivatives for cracks, as developed over the last decades, can be triggered, so as to mathematically derive compact analytical formulae showing how macroscopic creep rates depend on interface density, size, and viscosity. Chapter 2 extends the discussion to the case of more than one interface characteristic, i.e. to interfaces differing in size, density, and/or viscosity. The mathematical expenditures increase significantly, however, an elegant combination of advanced solution methods of differential equations, such as Laplace transforms, elimination schemes, and non-dimensionalization, do finally allow for the arrival at very elegant analytical formulae for the relaxation function of materials embedding differing interfaces - showing clearly the mutual interaction of these interfaces when governing macroscopic relaxation times or capacities. Chapter 3 provides a link between the novel micromechanics-derived creep and relaxation functions, and those obtained from classical rheological models. Based on the structure of the underlying differential equation, a full analogy between matrix-interface composites with only one interface type and classical Kelvin-Voigt and Maxwell models is developed, and independently proven by the dissipation expressions for both the micromechanical and the rheological systems. Chapter 4 extends this analogy to the case of arbitrarily many (countable) interface types. Particularly, the Kelvin-Voigt parameters can be easily linked to interface and matrix properties. Chapter 5 finally uses the newly developed methods in the light of real materials. A carefully experimentally validated hierarchical micromechanics model for bone viscoelasticity is complemented by an additional homogenization step, downscaling from the mineral clusters found in the extrafibrillar space, to the interfaces probably present within these clusters. The downscaled interface viscosity is (surprisingly) 14 orders of magnitude larger than that obtained from molecular dynamics. On a second glance, this huge discrepancy can be traced back to the 16 orders of magnitude difference between dislocation rates appearing during bone creep, and those used (for computational reasons) in molecular dynamics simulations. Glassy water in inter-crystalline interfaces in bone obviously show very pronounced thixotropy, i.e. viscosity decrease with increasing shear rate.