Wolfgang Ehlers

Foundations of multiphasic and porous materials

Miscible multiphasic materials like classical mixtures as well as immiscible materials like saturated and partially saturated porous media can be successfully described on the common basis of the well-founded Theory of Mixtures (TM) or the Theory of Porous Media (TPM). In particular, both the TM and the TPM provide an excellent frame for a macroscopic description of a broad variety of engineering applications and further problems in applied natural sciences. The present article portrays both the standard and the micropolar approaches to multiphasic materials reflecting their mechanical and their thermodynamical frameworks. Including some constitutive models and various illustrative numerical examples, the article can be understood as a reference paper to all the following articles of this volume on theoretical, experimental and numerical investigations in the Theory of Porous Media.

Constitutive Equations for Granular Materials in Geomechanical Context

This lecture outlines the possibilities of porous media theories in describing granular materials in geomechanical context as, for example, saturated or unsaturated soils or granular rocks, etc. In the present investigations, porous media theories are referred to as classical mixture theories extended by the concept of volume fractions. This approach, assuming statistically distributed and superimposed continua with internal interactions, implies the diverse field functions of both the porous solid matrix and the respective pore contents to be represented by average functions of the macroscale.

The development of the concept of effective stresses

SummaryIn the theory of saturated porous media and especially in soil mechanics, the concept of effective stresses (total stresses minus poreliquid pressure) plays an important role. The historical review of the development of this concept and its foundation via the modern mixture theory extended by the concept of volume fractions, will reveal some interesting new aspects.

Continuous and discontinuous modelling of cohesive-frictional materials

Computational models for failure in cohesive-frictional materials with stochastically distributed imperfections.- Modeling of localized damage and fracture in quasibrittle materials.- Microplane modelling and particle modelling of cohesive-frictional materials.- Short-term creep of shotcrete - thermochemoplastic material modelling and nonlinear analysis of a laboratory test and of a NATM excavation by the Finite Element Method.- Thermo-poro-mechanics of rapid fault shearing.- A view on the variational setting of micropolar continua.- Macromodelling of softening in non-cohesive soils.- An experimental investigation of the relationships between grain size distribution and shear banding in sand.- Micromechanics of the elastic behaviour of granular materials.- On sticky-sphere assemblies.- Cohesive granular texture.- Micro-mechanisms of deformation in granular materials: experiments and numerical results.- Scaling properties of granular materials.- Discrete and continuum modelling of granular materials.- Difficulties and limitation of statistical homogenization in granular materials.- From discontinuous models towards a continuum description.- From solids to granulates - Discrete element simulations of fracture and fragmentation processes in geomaterials.- Microscopic modelling of granular materials taking into account particle rotations.- Microstructured materials: local constitutive equation with internal lenght, theoretical and numerical studies.- Damage in a composite material under combined mechanical and hygral load.

DYNAMIC ANALYSIS OF A FULLY SATURATED POROUS MEDIUM ACCOUNTING FOR GEOMETRICAL AND MATERIAL NON-LINEARITIES

Based on the theory of porous media (mixture theories extended by the concept of volume fractions), a model describing the dynamical behaviour of a saturated binary porous medium is presented including both geometrical and material non-linearities. Transformed toward a weak formulation, the model equations are solved by use of the finite element method. Applications of the model range from one-dimensional linear problems to two-dimensional problems including the full dynamics and non-linearities.

One-dimensional transient wave propagation in fluid-saturated incompressible porous media

SummaryIn this investigation, the general formalism for the field equations governing the dynamic response of fluid-saturated porous media is analyzed and employed for the study of transient wave motion. The two constituents are assumed to be incompressible. A one-dimensional analytical solution is derived by means of Laplace transform technique which, as a result of the incompressibility constraint, exhibits only one independent dilatational wave propagating in the solid and the fluid phases, respectively. The fluid-saturated porous material is supplied with characteristics similar to those occuring in viscoelastic solids. This work can provide the further understanding of the characteristics of wave propagation in porous materials and may be taken for a quantitative comparision to various numerical solutions.ÜbersichIn dieser Arbeit wird der allgemeine Formalismus für die Feldgleichungen, die das dynamische Verhalten der fluidsaturierten Medien bestimmen, analysiert und für die Untersuchung der transienten Wellenbewegung ausgewertet. Es wird angenommen, daß beide Konstituierenden inkompressibel sind. Mit Hilfe der Laplacetransformation wird eine eindimensionale analytische Lösung abgeleitet, die als ein Resultat der Inkompressibilitätsbedingung nur eine unabhängige dilatante Wellenfortplanzung zeigt. Das fluidsaturierte poröse Material ist mit Charakteristiken versehen, die denen viskoelastischer Festkörper ähnlich sind. Diese Arbeit soll das weitere Verstehen der charakteristischen Eigenschaften der Wellenfortpflanzung in porösen Materialien erleichtern. Die Ergebnisse können zum quantitativen Vergleich mit verschiedenen numerischen Lösungen verwendet werden.

A single-surface yield function for geomaterials

SummaryThe article outlines a seven-parametric yield function for geomaterials such as soils and rocks. Proceeding from a geometric representation in the principal stress space, the yield surface exhibits a closed shape, thus reflecting the sensitivity of the plastic response of this type of media to hydrostatic stresses. The yield function is able to describe the effects of primary yielding, as well as of isotropic and kinematic hardening. In addition the failure envelope contains an open cone when the number of material parameters is reduced from seven to five.

On theoretical and numerical methods in the theory of porous media based on polar and non-polar elasto-plastic solid materials

The consideration of saturated and non-saturated porous solid materials as for instance soil, concrete, sinter materials, polymeric and metallic foams, temperate ice, living tissues, etc. naturally falls into the category of multiphase materials, which can be described by use of a macroscopic continuum mechanical approach within the well-founded framework of the Theory of Porous Media (TPM) . In the present contribution, granular elasto-plastic porous solid skeletons ( frictional materials) are taken into consideration, where, regardless of whether or not the solid is fluid-saturated or empty, localization phenomena can occur as a result of local concentrations of plastic strains. As a consequence of localization phenomena, the numerical solution of the governing equations generally reveals an ill-posed problem. In particular, the shear band width strongly depends on the mesh size of the finite element discretization by the fact that each mesh refinement leads to a decrease of the shear band width until one obtains a singular surface. In the present article, it is shown that the inclusion of fluid-viscosity in the saturated case and the inclusion of micropolar grain rotations both in the saturated and in the non-saturated case leads to a regularization of the shear band problem. On the other hand, the inclusion of micropolar degrees of freedom in the sense of the Cosserat brothers additionally allows for the determination of the local average grain rotations. The numerical examples are solved by use of finite element discretization techniques, where, in particular, the computation of shear band localization phenomena is carried out by the example of the well-known geotechnical slope failure problem and two additional academic problems, which clearly demonstrate the efficiency of the proposed procedure.

A Linear Viscoelastic Biphasic Model for Soft Tissues Based on the Theory of Porous Media

Based on the Theory of Porous Media (mixture theories extended by the concept of volume fractions), a model describing the mechanical behavior of hydrated soft tissues such as articular cartilage is presented. As usual, the tissue will be modeled as a materially incompressible binary medium of one linear viscoelastic porous solid skeleton saturated by a single viscous pore-fluid. The contribution of this paper is to combine a descriptive representation of the linear viscoelasticity law for the organic solid matrix with an efficient numerical treatment of the strongly coupled solid-fluid problem. Furthermore, deformation-dependent permeability effects are considered. Within the finite element method (FEM), the weak forms of the governing model equations are set up in a system of differential algebraic equations (DAE) in time. Thus, appropriate embedded error-controlled time integration methods can be applied that allow for a reliable and efficient numerical treatment of complex initial boundary-value problems. The applicability and the efficiency of the presented model are demonstrated within canonical, numerical examples, which reveal the influence of the intrinsic dissipation on the general behavior of hydrated soft tissues, exemplarily on articular cartilage.

From particle ensembles to Cosserat continua: homogenization of contact forces towards stresses and couple stresses

In the present contribution, a transition from the dynamics of single particles to a Cosserat continuum is discussed. Based on the definition of volume averages, expressions for the macroscopic stress tensors and for the couple stress tensors are derived. It is found that an ensemble of particles allows for a non-symmetric macroscopic stress tensor and, thus, for the existence of couple stresses, even if the single particles are considered as standard continua. Discrete element method simulations of a biaxial box are used for the validation of the proposed homogenization technique.