Lagrange-Euler Formulierungen in der Bodenmechanik

Bodenmechanische und geotechnische Problemstellungen werden häufig durch große Materialverformungen und andere damit einhergehende Phänomene gekennzeichnet. Bei deren Modellierung stoßen die klassische Bodenmechanik und die traditionelle Finite Elemente Methode basierend auf der Lagrange Formulierung an ihre Grenzen. In dem Beitrag werden die kontinuumsmechanischen Grundlagen einer verallgemeinerten Lagrange-Euler Formulierung vorgestellt. Anschließend werden ihre unterschiedlichen Ausprägungen im Rahmen der numerischen Umsetzung anhand von Anwendungsbeispielen diskutiert sowie das Potential dieser Simulationsmethoden in der Bodenmechanik und Geotechnik aufgezeigt.DFG, 76838227, Numerische Modellierung der Herstellung von Rüttelinjektionspfähle

Contribution to the Non-Lagrangian Formulation of Geotechnical and Geomechanical Processes

Numerical simulations of geomechanical and geotechnical processes, such as vibro-injection pile installation, require suitable algorithms and sufficiently realistic models. These models have to account for large deformations, the evolution of material interfaces including free surfaces and contact interfaces, for granular material behavior in different flow regimes as well as for the interaction of the different materials and phases. Although the traditional Lagrangian formulation is well-suited to handling complex material behavior and maintaining material interfaces, it generally cannot represent large deformation, shear and vorticity. This is because in Lagrangian numerical methods the storage points (nodes resp. material points) move with the local material velocity, which may cause mesh tangling resp. clustering of points. The present contribution addresses the development of models for geotechnical and geomechanical processes by utilizing Eulerian and Arbitrary Lagrangian-Eulerian (ALE) formulations. Such non-Lagrangian viewpoints introduce additional difficulties which are discussed in detail. In particular, we investigate how to track interfaces and to model interaction of different materials with respect to an arbitrarily moving control volume, and how to validate non-Lagrangian numerical models by small-scale experimental tests

Vibro-Injection Pile Installation in Sand: Part II—Numerical and Experimental Investigation

In Part 1 of this series of papers a macroscopic two-equation (two-field) reduced model for the mechanics of the multi-material flow associated with vibro-injection pile installation in saturated sand was derived. Here we employ this model to develop a so-called multi-material arbitrary Lagrangian-Eulerian (MMALE) method. MMALE avoids the disadvantages of the classical approaches in computational continuum mechanics concerning large deformations and evolving material interfaces. The numerical implementation of this method will be outlined, and then the experimental investigations will be presented that have been carried out in order to validate the computational model. Among these investigations, small-scale model tests in chambers with observing window have been designed step-by-step to reveal penetration and vibro-injection pile installation phenomena.DFG, 76838227, Numerische Modellierung der Herstellung von Rüttelinjektionspfähle

An ALE method for penetration into sand utilizing optimization-based mesh motion

The numerical simulation of penetration into sand is one of the most challenging problems in computational geomechanics. The paper presents an arbitrary Lagrangian–Eulerian (ALE) finite element method for plane and axisymmetric quasi-static penetration into sand which overcomes the problems associated with the classical approaches. An operator-split is applied which breaks up solution of the governing equations over a time step into a Lagrangian step, a mesh motion step, and a transport step. A unique feature of the ALE method is an advanced hypoplastic rate constitutive equation to realistically predict stress and density changes within the material even at large deformations. In addition, an efficient optimization-based algorithm has been implemented to smooth out the non-convexly distorted mesh regions that occur below a penetrator. Applications to shallow penetration and pile penetration are given which make use of the developments.DFG, FOR 1136, Modellierung von geotechnischen Herstellungsvorgängen mit ganzheitlicher Erfassung des Spannungs-Verformungs-Verhaltens im Boden (GeoTech

Theory and Numerical Modeling of Geomechanical Multi-material Flow

Multi-material flow describes a situation where several distinct materials separated by sharp material interfaces undergo large deformations. The research presented in this paper addresses a particular class of multi-material flow situations encountered in geomechanics and geotechnical engineering which is characterized by a complex coupled behavior of saturated granular material as well as by a hierarchy of distinct spatial scales. Examples include geotechnical installation processes, liquefaction-induced soil failure, and debris flow. The most attractive numerical approaches to solve such problems use variants of arbitrary Lagrangian–Eulerian descriptions allowing interfaces and free surfaces to flow through the computational mesh. Mesh elements cut by interfaces (multi-material elements) necessarily arise which contain a heterogeneous mixture of two or more materials. The heterogeneous mixture is represented as an effective single-phase material using mixture theory. The paper outlines the specific three-scale mixture theory developed by the authors and the MMALE numerical method to model and simulate geomechanical multi-material flow. In contrast to traditional flow models which consider the motion of multiple single-phase materials or single multi-phase mixture, the present research succeeds in incorporating both the coupled behavior of saturated granular material and its interaction with other (pure) materials.DFG, 76838227, Numerische Modellierung der Herstellung von Rüttelinjektionspfähle

Dynamic stresses in an elastic half-space

This paper deals with the problem of time-varying point loads applied onto the surface of an elastic half-space and the stresses that such loads elicit within that medium. The emphasis is on the evaluation of the isobaric contours for all six of the stress components at various frequencies of engineering interest and for a full range of Poisson’s ratios. The extensive set of pressure bulbs presented herein may be of help in predicting the severity of dynamic effects in common practical situations in engineering—or even the lack thereof

Simple algebraic data types for C

ADT is a simple tool in the spirit of Lex and Yacc that makes algebraic data types and a restricted form of pattern matching on those data types as found in SML available in C programs. ADT adds runtime checks, which make C programs written with the aid of ADT less likely to dereference a NULL pointer. The runtime tests may consume a significant amount of CPU time; hence they can be switched off once the program is suitably debugged

A toolkit of mechanism and context independent widgets

Most human-computer interfaces are designed to run on a static platform (e.g. a workstation with a monitor) in a static environment (e.g. an office). However, with mobile devices becoming ubiquitous and capable of running applications similar to those found on static devices, it is no longer valid to design static interfaces. This paper describes a user-interface architecture which allows interactors to be flexible about the way they are presented. This flexibility is defined by the different input and output mechanisms used. An interactor may use different mechanisms depending upon their suitability in the current context, user preference and the resources available for presentation using that mechanism