Joachim Bluhm

Effective stresses — a clarification

SummaryAlthough the phenomenon of effective stresses was known for a long time, the theoretical foundation has remained unsatisfactory until now. Due to new experimental and theoretical findings in the porous media theory, the concept of effective stresses will be reexamined. This is necessary for porous media such as concrete and rock which show at high pressure a significant deviation of the real effective stresses from those calculated with von Terzaghis concept due to the compressibility of the true material. A second feature of the present paper is the investigation of the effective stress “principle” in unsaturated porous media.

Phase transitions in gas- and liquid-saturated porous solids

Phase transitions in porous media consisting of a porous solid filled with liquid and gas constituents can occur, for example, due to freezing and drying processes. Although these phenomena are of certain relevance in soil mechanics and material sciences, a general thermo-dynamical theory is still awaited. Based on recent findings in the porous media theory, this paper is concerned with the development of thermodynamic restrictions for the constitutive relations of an elastic, incompressible porous solid, filled with an incompressible liquid and a compressible gas. The investigations show that mass conversions are related to the differences of the chemical potentials and energy transitions to the differences of temperatures. Thus, they confirm well-known results in classical thermodynamics of gases.

The influence of compressibility on the stresses of elastic porous solids—semimicroscopic investigations

Abstract In this paper the influence of the compressibility of the real material of the constituents of a porous medium on the stresses will be discussed for a simplified model of liquid-saturated porous solids. The basis of the model is the mixture theory restricted by the volume fraction condition (theory of porous media) . In comparison with the mixture theory, one additional constitutive relation for the so-called real part of the deformation of the solid phase will be formulated to close the system of equations for compressible binary porous media within the framework of the theory of porous media. The real deformation can be described by a second order tensor which results from the multiplicative decomposition of the deformation gradients of solid and liquid constituents.

Ice Formation in Porous Media

Ice formation in porous media results from coupled heat and mass transport and is accompanied by ice expansion. The volume increase in space and time corresponds to the moving freezing front inside the porous solid. In this contribution, a macroscopic model based on the Theory of Porous Media (TPM) is presented toward the description of freezing and thawing processes in saturated porous media. Therefore, a quadruple model consisting of the constituents solid, ice, liquid and gas is used. Attention is paid to the description of capillary suction, liquid- and gas pressure on the surrounding surfaces, volume deformations due to ice formation, temperature distribution as well as influence of heat of fusion under thermal loading. For detection of energetic effects regarding the control of phase transition of water and ice, a physically motivated evolution equation for the mass exchange based on the local divergence of the heat flux is used. Numerical examples are presented to the applications of the model.

Inhomogeneous Plane Waves, Mechanical Energy Flux, and Energy Dissipation in a Two-Phase Porous Medium

In dieser Arbeit werden inhomogene ebene Wellen, Energieflus und Energiedissipation in einem mit Flussigkeit gefullten porosen Medium untersucht. Die beiden Phasen des porosen Mediums werden als inkompressibel angesehen, d. h., die mikroskopischen Dichten der realen Materialien sind konstant. Die entsprechenden makroskopischen Dichten konnen sich im Verhaltnis zu den Volumenanteilen andern. Unter der Voraussetzung, das sich das Festkorperskelett linear elastisch verhalt, konnen sich in diesem Medium eine gekoppelte P-Typ-Welle und eine gekoppelte S-Typ-Welle ausbreiten. Die Struktur der ebenen inhomogenen Wellen wird ausfuhrlich diskutiert. Das Verschiebungsfeld fur jede Welle ist durch einen komplexen Amplitudenvektor und einen komplexen Wellenvektor charakterisiert. Der komplexe Wellenvektor umfast einen realen Ausbreitungsvektor sowie einen realen Dampfungsvektor. Es wird gezeigt, das jede gekoppelte Welle inhomogen ist, da die Ebenen der konstanten Phasen im allgemeinen nicht parallel zu den Ebenen der konstanten Amplituden sind. Dieser Effekt basiert auf dem Dissipationsmechanismus des Modells. Die Spur des bewegten Teilchens fur jede Wellenart ist elliptisch polarisiert in Verbindung mit dem entsprechenden komplexen Amplitudenvektor. Die Energiebilanz fur das gesamte porose Medium wird ohne Berucksichtigung des thermischen Austauschs entwickelt. Der Energieflusvektor und die Energiedissipationsrate werden somit in der allgemeinen Form definiert. Die expliziten Ausdrucke des durchschnittlichen Energieflusvektors und der durchschnittlichen Energiedissipationsrate werden uber eine komplette Periode fur jede Art der inhomogenen Welle angegeben. In this paper inhomogeneous plane waves, energy flux, and energy dissipation in a liquid-saturated porous medium are investigated. The two-phase porous medium is described by an incompressible porous media model in which the microscopic density of each real material is assumed unchangeable whereas the respective macroscopic density may change in relation with the volume fractions. Within the context of a linearly elastic solid skeleton a coupled longitudinal (P-type) wave and a coupled transversal (S-type) wave may propagate in the medium and the structure of plane inhomogeneous waves is intensively discussed. The displacement field for each type of waves is characterized in terms of a complex-valued amplitude vector and a complex-valued wave vector which includes a real-valued propagation vector and a real-valued attenuation vector. It is shown that each coupled wave is inhomogeneous as the planes of constant phase are in general not parallel to the planes of constant amplitude due to the dissipative property of the porous medium. The trace of the particle motion for each type of waves is of elliptical polarization associated with the complex-valued amplitude vector. The energy conservative equation for the entire porous medium is developed without considering the thermal exchange. The energy flux vector and the energy dissipation rate are thus defined in the general form. The explicit expressions of the mean energy flux vector and the mean energy dissipation rate are given over a complete period for each type of the inhomogeneous waves.

Continuum Mechanical Description of an Extrinsic and Autonomous Self-Healing Material Based on the Theory of Porous Media

Polymers and polymeric composites are used in many engineering applications, but these materials can spontaneously lose structural integrity as a result of microdamage caused by stress peaks during service. This internal microdamage is hard to detect and nearly impossible to repair. To extend the lifetime of such materials and save maintenance costs, self-healing mechanisms can be applied that are able to repair internal microdamage during the usual service load. This can be realized, for example, by incorporating microcapsules filled with monomer and dispersed catalysts into the polymeric matrix material. If a crack occurs, the monomer flows into the crack, reacts with the catalysts, and closes the crack.

Modeling of Ice Formation in Porous Media

A simplified quintuple model for the description of freezing and thawing processes in gas and liquid saturated porous materials is investigated by using a continuum mechanical approach based on the Theory of Porous Media (TPM). The porous solid consists of two phases, namely a granular or structured porous matrix and an ice phase. The liquid phase is divided in bulk water in the macro pores and gel water in the micro pores. In contrast to the bulk water the gel water is substantially affected by the surface of the solid. This phenomenon is already apparent by the fact that this water is frozen by homogeneous nucleation.

Modeling of liquid and gas saturated porous solids under freezing and thawing cycles

In many branches of engineering, e.g. material science, soil constructions, and geotechnics, freezing and thawing processes of fluid filled porous media play an important role. The coupled fluid-ice-solid behavior is strongly influenced by phase transition, heat and mass transport as well as interactions of fluid-solid/ice pressure depending on the entropy of fusion, and is accompanied by a volume expansion. In this contribution, a macroscopic model based on the Theory of Porous Media (TPM) is presented toward the description of freezing and thawing processes/ freeze-thaw cycles in fluid filled porous media. Therefore, a quadruple model consisting of the constituents solid, ice, liquid and gas is used. Attention is paid to the description of capillary effects, especially, the frost suction, the distribution of fluid and ice pressure as well as solid deformation before, during and after the ice formation in consideration of energetic effects under cycling thermal loading. Numerical examples are presented to demonstrate the usefulness of the model.

The Thermodynamic Structure of a Ternary Model of Porous Compressible Materials

In the present paper a consistent model for porous media consisting of three compressible phases (S = solid, L = liquid, G = gas) is developed, whereby any thermal effects and phase transitions are neglected. The model is based on the assumption that the volume fraction condition is treated as a constraint restricting the motion of the constituents. The above assumption implies the necessity of the formulation of additional field equations. In the present model these equations are constitutive relations with respect to the deformation parts of the true (realistic) materials following from a multiplicative decomposition of the deformation gradients of the constituents.