3rd Euroconference
MATHEMATICAL FOUNDATIONS OF GEOMECHANICS
GeoMath 3
EU contract No. HPCF-CT-1999-00046
Place
The Greek village Horton, situated on the bay of Volos. Some photographic impressions of a previous conference held in Horton can be viewed.
We recommend to fly to Saloniki. We will organize a coach transfer from Saloniki to Horton (ca. 3 hours drive). Car-drivers can take the ferryboat from Italy (there are many new ferries departing from Ancona or Venice or Trieste) and come either to Igoumenitsa or Patras. The subsequent drives to Horton (both ca. 5 hours) are picturesque.
Date
| day | activity |
| Monday 1.7.2002 | arriving and settling |
| Tuesday 2.7.2002 | conference |
| Wednesday 3.7.2002 | conference |
| Thursday 4.7.2002 | boat excursion |
| Friday 5.7.2002 | conference |
| Saturday 6.7.2002 | departure |
To obtain a reduced air ticket, we recommend to depart on Sunday 7th July.
Accompanying persons are welcome. Upon request (email to Christine.Neuwirt@uibk.ac.at ) we will provide support.
Programme
This programme is tentative. Small changes referring to the sequence of presentations can still be provided.
The duration of each presentation is ca 45 minutes followed by 15 minutes of discussion.
Tuesday, 2.7.02:
09.00 - 09.10: D. Kolymbas: Opening
09.10 - 10.10: I. Herle: ''Numerical predictions and reality'' (3.3 MB)
10.10 - 10.30: BREAK
10.30 - 11.30: P. Vermeer: ''Possibilities and limitations of numerical analysis''
11.30 - 12.00: BREAK
12.00 - 13.00: A. Puzrin: ''Elasticity in constitutive modelling of soils''
13.00 - 15.30: LUNCH + BREAK
15.30 - 16.30: M. Brokate: ''Rate independent constitutive equations with internal variables''
16.30 - 17.00: BREAK
17.00 - 18.00: W. Fellin, A. Ostermann: ''Numerical implementation of a consistent stress update algorithm for constitutive rate equations''
Lecture W. Fellin (0.8 MB)
Video 1 (0.9 MB), Video 2 (2.7 MB), PowerFLiC for watching the videos
Lecture A. Ostermann (0.2 MB)
Wednesday, 3.7.02:
10.00 - 10.30: BREAK
10.30 - 11.30: G. Houlsby: ''Mathematics for plasticity theory in geomechanics'' (0.3 MB)
11.30 - 12.00: BREAK
12.00 - 13.00: N. Aravas: ''Continuum Gradient Theories: Constitutive equations and computational issues''
13.00 - 15.30: LUNCH + BREAK
15.30 - 16.30: I. Vardoulakis (et al.): ''Mechanical behavior of Dionysos-Pentelikon marble'' (20.5 MB)
16.30 - 17.00: BREAK
17.00 - 18.00: P. Krejcí: ''Wave propagation in hysteretic media''
Thursday, 4.7.02: EXCURSION
Friday, 5.7.02:
09.00 - 10.00: K. Hutter: ''Rapid flows of geomaterials''
10.00 - 10.30: BREAK
10.30 - 11.30: L. Lliboutry: ''Creep and recrystallization of glacier ice, a metamorphic rock'' (0.8 MB)
11.30 - 12.00: BREAK
13.00 - 15.30: LUNCH + BREAK
15.30 - 16.30: Y.F. Dafalias: ''Mathematical Treatement of Inherent and Evolving Soil Fabric Anisotropy''
16.30 - 17.00: BREAK
17.00 - 18.00: D. Kolymbas: ''Similarity in soil and rock mechanics'' (5.1 MB)
Accompanying persons are welcome. Upon request (email to Christine.Neuwirt@uibk.ac.at ) we will provide support.
Topics
Geotechnical Engineering and Geomechanics comprise a wealth of mathematical problems such as highly non-linear constitutive models, numerical simulations, ill posedness, regularization, handling with discontinuities and shocks, inverse problems, similarity, fractals etc. Recently, numerical simulation in soil mechanics and rock mechanics faces some criticism:
- FEM-performance of nonlinear problems with discontinuities in time and space and geometrical and/or material instabilities leads to 'computer games'. (Belytschko, T., 1996. On difficulty levels in non linear finite element analysis of solids. IACM Expressions, No.2 , 6-8.)
- 'The progress in information technology has induced a devastating intellectual decadence in simulation science.' ... 'as far as physical content is concerned, structural finite element models are subject to a constant erosion and devaluation given that most of the available computing horsepower is being invested simply in increasing model size.' (Marczyk, J., 1999. Recent trends in FEM. Proc. NAFEMS World Congress, Rhode Island)
- 'Computer-Aided Engineering is experiencing a period of crisis.'... 'Excess of computer power has induced, in the CAE community, the belief that, due to some divine interposition, we have now automatically entered the realm of virtual prototyping.' (Marczyk, J., 2000. Uncertainty management and knowledge generation in CAE. Europ. Congress on Computational Methods in Applied Sciences and Engineering, Barcelona, 11-14)
Information on the last Euroconference on Mathematical Foundations of Geomechanics can be obtained from http://sg1-c813.uibk.ac.at/cgi-bin/GeoMath2/main
Speakers/Lectures
- N. Aravas:
- ''Continuum Gradient Theories: Constitutive equations and computational issues''
A review of elastic and elastoplastic continuum gradient theories is presented. Issues related to the required additional boundary conditions and their physical interpretation, and the numerical implementation of such theories are discussed. Traditional finite element procedures require C1 displacement continuity with all the complications associated with it. An alternative "mixed" formulation is discussed, in which both displacement and displacement gradients are used as independent nodal unknowns and their relationship is enforced in an "integral sense". Several applications in the areas of metal forming and fracture mechanics are presented. - M. Brokate:
- ''Rate independent constitutive equations with internal variables''
Rate independent constitutive laws with internal variables can be treated in different ways. We outline some approaches and discuss their consequences from the standpoint of mathematics. Particular emphasis is given to models for elastoplasticity. - Y.F. Dafalias:
- ''Mathematical Treatement of Inherent and Evolving Soil Fabric Anisotropy''
Soil fabric anisotropy, inherent and/or evolving, plays a very significant role in soil plasticity constitutive modelling. Yet, it is often omitted or, if considered, it ends up with unnecessarily complex and difficult to use relations. It is shown that some simplest expressions of tensor invariant theory, if used within a proper constitutive platform, can lead to simple constitutive laws with surprisingly extensive simulative capabilities of anisotropic soil response, as comparison of data with model results show. - W. Fellin, A. Ostermann:
- ''Numerical implementation of a consistent stress update algorithm for constitutive rate equations''
A general approach for error controlled time integration of constitutive laws in rate form is presented. In order to achieve quadratic convergence in the finite element equilibrium iteration, the knowledge of the consistent tangent operator is essential. This operator is assembled from the material Jacobian matrices, which on the other hand are obtained from a numerical approximation of the variational equations of the underlying constitutive law. Several examples with a hypoplastic constitutive law and various numerical integrators are given. Implementation details of the corresponding FORTRAN subroutine are explained and quadratic convergence of the equilibrium iteration is shown. - I. Herle:
- ''Numerical predictions and reality''
Numerical predictions belong to common tasks in engineering. Powerfull computers and numerical techniques evoke an impression of the ability to reliably forecast the behaviour of materials and structures. Several examples illustrate critically this matter and pose questions on limitations of our models. - G. Houlsby::
- ''Mathematics for plasticity theory in geomechanics''
The purpose of this talk will be to demonstrate how certain advanced mathematical techniques can be used to gain new insights into constitutive modelling of soils. A brief introduction will be made into some branches of mathematics, illustrating the benefits these can bring to an understanding the mechanics of geotechnical materials. Topics will include the Legendre transform (and the relationships between yield and dissipation), use of energy functionals and Frechet derivatives (applied to modelling of nonlinearity at small strain) and convex analysis, including the Legendre-Fenchel transform (with applications in plasticity and damage mechanics). - K. Hutter:
- ''Rapid flows of geomaterials''
Order and disorder in geophysical flows. A review is given about granular flow in avalanching context using examples from geology. Then mathematical modelling is discussed. - D. Kolymbas:
- ''Similarity in soil and rock mechanics''
Mechanical similarity allows to transfer results obtained with small scale test to reality. It also helps to simplify mathematical expressions. Aspects of similarity and self-similarity of geomaterials and their mathematical implications will be presented. - P. Krejcí:
- ''Wave propagation in hysteretic media''
Wave equations with hysteretic constitutive laws describing the propagation of mechanical or electromagnetic waves in elastoplastic or ferromagnetic media exhibit some particular features. They share with systems of conservation laws the property of bounded speed of propagation, but the hysteresis energy dissipation prevents the system from shock formation. The lecture will give an overwiew of results on properties and approximation of solutions, and homogenization. - L. Lliboutry:
- ''Glacier sliding''
Taking into account field observations about subglacial hydraulics a new theory for sliding of glaciers is derived where the sliding law is replaced by four coupled equations. - A. Puzrin:
- ''Elasticity in constitutive modelling of soils''
Elasticity, the oldest and the best developed among the constitutive models, still raises a lot of questions when it comes to its applicability to soils. Is there any purely elastic region of soil behaviour (some experimentalists claim there is)? But if there is not, and plastic strains develop immediately, is there any elastic component at all in total strain (hypoplasticity claims there is not)? But if this component exists, should this component satisfy energy conservation (hypoelasticity claims it is not necessary)? But if energy conservation is not satisfied, how does this affect the constitutive behavior and solutions of boundary value problems? And if it is satisfied, how to make it properly to avoid inconsistencies, which have been encountered in some recent publications? - I. Vardoulakis (et al.):
- ''Mechanical behavior of Dionysos-Pentelikon marble''
The pre-failure uniaxial stress strain curve of marble reveals a significant scale effect. In the post failure regime the direct tension experiment is discussed within a simple continuum elastic damage model. Strain localization under tension is described by means of a linear stability analysis of the underlying dynamic equations in the softening regime. A strain assisted damage diffusion model explains the observed stress-displacement post-failure response. The model introduces an internal length that correlates with the boundary displacement. - P. Vermeer:
- ''Possibilities and limitations of numerical analysis''
Numerical simulations (mainly with finite elements) are widely used. The results are, however, sensitive especially when dealing with discontinuities, softening material and other instabilities. Strategies for the evaluation of quality of numerical results and also to overcome present limitations will be discussed. - C. Wieners (et al.):
- '' Parallel 3-d simulations for porous media models in soil mechanics''
Numerical simulations in 3-d for porous media models in soil mechanics is a difficult task for the engineering modelling as well as for the numerical realization. Here, we present a general numerical scheme for the simulation of two-phase models in combination with an abstract material model via the stress response with a specialized parallel saddle point solver. A brief introduction into the theoretical background of the Theory of Porous Media will be given. The governing equations are transfered to a weak formulation suitable for the application of the finite element method. We define a clear interface between the assembling process and the parallel solver modules. We demonstrate the efficiency of this approach by challenging numerical experiments realized on the Linux Cluster in Chemnitz. - K. Wilmanski:
- ''Microworld and macroworld - multiscaling problems in modelling of geophysics'' Multiscaling refers to
- different scales of time, e.g. BBGKY hierarchy following from the Liouville equation for particles, and the hierarchy of extended thermodynamics of gases.
- different scales of space due to order of gradients included in the constitutive relations or due to various microstructural properties, e.g. pores, dislocations, damage, phase transformations.
- different scales of time and space refering to ranges of observation. Consequently, the same class of phenomena may be modeled by propagation of waves or by diffusive propagation with infinite speed.
Registration
By email to Christine.Neuwirt@uibk.ac.at
Please add:
- Name, birthday, sex, citizenship
- affiliation, education, academic titles
- email, telephone, mobile, address
- scientific interests and present work
In case of too many registrations we will have to select according to scientific interest and priority of registration.
Deadline for registration: 2nd April 2002Financial organization
- Speakers
- will be reimbursed their travel and accommodation expenses.
- Other participants:
- They have to pay a registration fee of 150 EURO. Provided they are citizen of a EU or associated country (Bulgaria, Cyprus, Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, Slovakia, Slovenia, Iceland, Liechtenstein, Norway, Israel) they will be reimboursed the registration fee and a part of their travel and accommodation expenses. This part will be as large as possible and depends on the final breakdown. All payments can be done in Horton in cash or with credit card.
Non-reimbursed participants have to count with ca. 75 EURO per day (for accommodation, breakfast, lunch and dinner).
We presuppose the use of economic travels. In case we succeed organizing group travel, we will expect to use it (if suitable).