Stefan Diebels

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.

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.

The size effect in foams and its theoretical and numerical investigation

Experimental data for foams lead to different values of the elastic moduli depending on the performed test, i.e. compression and tension tests give a different set of parameters than shear and bending tests. This may be explained by the size effect, which depends on the microstructure of the foams. Thus, in this paper, the behaviour of foams is investigated on the basis of both microscopic and macroscopic mechanical models. The microscopic approach is based on a lattice beam model. The solution of this model shows that the boundary–layer effect is strongly local but allows for the explanation of the size effect. Furthermore, the size effect can be included in the macroscopic continuum model by application of a Cosserat formulation. The extended continuum model allows for the independent fit of material parameters to different load cases, i.e. to compression and shear. The solution of the macroscopic Cosserat model permits a relation of the internal length–scale to the average cell size of the microstructure.

From discrete element simulations to a continuum model

One of the essential questions in material sciences and especially in the area of granular matter is, how to obtain macroscopic quantities like velocity-field, stress or strain from “microscopic” quantities like contact-forces and deformations as well as particle-displacements and rotations in a granular assembly. We examine a two-dimensional (2D) shear-cell by means of discrete element simulations and compute kinematic quantities like the velocity field, the elastic deformation gradient and the deformation rate. Furthermore, we examine the density, the coordination number, the fabric and the stress. From some combinations of those quantities, one gets, e.g., the bulk-stiffness of the granulate and its shear modulus. The bulk modulus is a linear function of the trace of the fabric tensor which itself is proportional to the density and the coordination number. Finally, we note that the fabric, the stress and the strain tensors are not co-linear so that a more refined analysis than classical isotropic elasticity theory is required here. Another result is that the displacement rate (velocity) in the shear zone decays exponentially with the distance from the moving wall which applies the shear. Connected to the shear deformation is a rotation of the innermost layers in opposite direction, i.e., these layers roll over each other.

A Micropolar Theory of Porous Media: Constitutive Modelling

The extension of the classical mixture theory by the concept of volume fractions leads to the theory of porous media. In this article, the theory of porous media is generalised to micropolar constituents. The kinematic relations and the balance equations for a porous medium are developed without restricting the number of constituents. Based on the entropy inequality, the general form of the constitutive equations are derived for a binary medium consisting of a porous elastic skeleton saturated by a viscous pore-fluid. Both constituents are assumed to be compressible. Handling the saturation constraint by a Lagrangian multiplier leads to a compatibility of the proposed model to so-called hybrid and incompressible models.

A particle center based homogenization strategy for granular assemblies

In this paper, a new homogenization technique for the determination of dynamic and kinematic quantities of representative elementary volumes (REVs) in granular assemblies is presented. Based on the definition of volume averages, expressions for macroscopic stress, couple stress, strain and curvature tensors are derived for an arbitrary REV. Discrete element model simulations of two different test set‐ups including cohesionless and cohesive granular assemblies are used as a validation of the proposed homogenization technique. A non‐symmetric macroscopic stress tensor, as well as couple stresses are obtained following the proposed procedure, even if a single particle is described as a standard continuum on the microscopic scale.

Modelling and parameter re-identification of nanoindentation of soft polymers taking into account effects of surface roughness

In this paper the characterisation of polymers by nanoindentation is investigated numerically by the use of the inverse method. Effects of the surface roughness are explicitly considered. The boundary value problems of the nanoindentation of two polymers, PDMS and silicone rubber, are modelled with the FE code ABAQUS^(R). The model parameters are re-identified by using an evolution strategy based on the concept of the numerical optimisation. The surface roughness effects are investigated numerically by explicitly taking into account the roughness profile in the model. At first the surface roughness is chosen to have a simple representation considering only one-level of asperities described by a sine function. The influence of the surface roughness is quantified as a function of the sine parameters as well as of the indentation parameters. Moreover, it is verified that the real surface topography can be characterised by using multi-level or simple one-level of protuberance-on-protuberance sinusoidal roughness strain-energy function. profiles. The effects of the surface roughness are investigated with respect to the force-displacement data and the identified model parameters. These numerical results are expected to offer a deep insight into the influence of the real surface roughness at the results of indentation tests.

Nonlinear internal waves over variable topography

Abstract A nonlinear two-layered fluid system on a variable bottom with freely moving upper surface and abrupt density change at the interface is considered. The two stably stratified layers with constant densities are assumed to be immiscible. Starting from the continuity and the mometum equations of an incompressible inviscid fluid for each layer and associated boundary and transition conditions at the free upper surface, the interface and the bottom surface, vertically averaged equations are deduced that incorporate nonlinear advection and dispersion. The approximate equations are deduced by scaling the governing equations accordingly and by using a limit analysis for small aspect ratios (shallowness) and small amplitude disturbances. The limiting equations extend known model equations and include finite amplitude nonlinearities, dispersion and variable topography. In a second step viscous effects and wind forcing are also incorporated.

Effects of the horizontal component of the Earth's rotation on wave propagation on an f-plane

Abstract Scaling arguments are used to show that effects due to the horizontal component of the Coriolis force should be taken into account as a first correction to the traditional hydrostatic theory, before frequency dispersion due to vertical acceleration and nonlinearity are included. It is shown analytically that wave propagation of the f--plane becomes anisotropic and that amphidromic systems do not exist in their usual definition. Another important consequence is the existence of free wave solutions at subinertial frequencies.