R. De Boer

Uplift, friction and capillarity: Three fundamental effects for liquid-saturated porous solids

Abstract In the present paper, the effects of uplift, friction and capillarity for liquid-saturated porous solids are discussed by use of general porous media theories (mixture theories extended by the volume fraction concept). Preceded by several historical remarks on former approaches to a.m. effects, the present investigation is based on a macroscopic binary model of incompressible constituents where, in the constitutive range, use is made of the second-grade character of general heterogeneous media. As a direct consequence of this procedure, the magnitudes of uplift, friction and capillarity effects are easily determined, thus solving an old problem in applied engineering.

Theory of Porous Media — Past and Present

Porous solids filled with liquid or gas play an important role in engineering, e.g., in material science, petroleum industry, chemical engineering, and soil mechanics as well as in biomechanics. Although porous media are of considerable practical significance the description of their mechanical and thermodynamical behavior has been unsatisfactory for a long time. The theory to describe the complex thermodynamical behavior of such saturated porous solids has come to certain well-founded conclusions only recently. It is the goal of this paper to show the historical development of the porous media theory, which already started in the eighteenth century, formed in some areas by polemic disputes and tragic events in the lifes of the scientists involved. Furthermore, the current state of the research into this subject is discussed, whereby the state of the development of the material independent basic equations and the constitutive theory is illustrated. For a certain class of models general theorems, such as minimum and maximum problems, are derived and the uniqueness of solutions of boundary value problems is proved.

On the problem of fluid- and gas-filled elasto-plastic solids

Abstract In the frame of continuum mechanics elasto-plastic porous solids with their intercommunicating void spaces filled with a viscous fluid and gas can be described as multicomponent models. For such models constitutive equations are developed, making full use of the thermodynamical restrictions. These constitutive equations are suitable to describe continua with idealplastic properties as well as brittle continua.

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.

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.

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.

Kinematic hardening of granular materials

SummarySome recently developed constitutive equations (yield function, loading criteria, flow rule) for kinematic hardening of granular materials are discussed and some relevant material dependent parameters are determined on the basis of test results.ÜbersichtEinige in jüngster Zeit entwickelte konstitutive Beziehungen (Fließbedingung, Belastungsbedingung und Fließregel) für kinematisch verfestigende granulare Stoffe werden diskutiert und einige relevante materialabhängige Parameter werden auf der Grundlage experimenteller Ergebnisse bestimmt.

On non-isothermal elastic-plastic and elastic-viscoplastic deformations

Abstract Starting with the equations of balance of energy and the Clausius-Duhem inequality the non-isothermal behavior of elastic-plastic materials without and with viscous properties is described. All quantities in the equations of balance of energy and in the Clausius-Duhem inequality are expanded in series. This procedure leads to the development of restrictions and stress-strain-relations, which contain as special cases the constitutive equations of classical plasticity and viscoplasticity.

Extremum principles in the theory of plasticity for fluid-saturated porous media

SummaryFor ideal plastic deformed porous solids filled up with fluid, extremum principles are formulated: a minimum principle for the velocities and a maximum principle for the stresses. These principles enable to restrict the exact solution of boundary-value problems. This is shown in an example.ÜbersichtFür ideal plastisch deformierte poröse Körper, die mit Flüssigkeit gefüllt sind, werden Extremalaussagen formuliert: ein Minimalprinzip für die Geschwindigkeiten und ein Maximalprinzip für die Spannungen. Sie gestatten die Einschränkung der exakten Lösung eines Randwertproblems. Dies wird an einem Beispiel gezeigt.