Ing - Civ (Mag.)(ord. 270) - MI (489) INGEGNERIA PER L'AMBIENTE E IL TERRITORIO - ENVIRONMENTAL AND LAND PLANNING ENGINEERING

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057938 - COMPUTATIONAL MECHANICS FOR GEOMATERIALS

Ing Ind - Inf (Mag.)(ord. 270) - MI (487) MATHEMATICAL ENGINEERING - INGEGNERIA MATEMATICA

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058207 - COMPUTATIONAL MECHANICS FOR GEOMATERIALS

Obiettivi dell'insegnamento

The integrated course Computational Mechanics for Geomaterials consists in two strictly integrated modules:

the Computational Mechanics module (5 CFU) aims to introduce the theoretical and operational aspects of the finite element method for the solution of elastic and elasto-plastic problems and to present the main classes of constitutive laws in the non-linear field

the Geomaterials module (5 CFU) aims to present some aspects of the behaviour of soils, as two-phase materials characterized by a non-linear mechanical response, in geotechnical problems where close interactions between various physical processes may occur. These problems are typical of environmental engineering and geosciences and require, to obtain an accurate solution, the use of computational methods.

Risultati di apprendimento attesi

After lectures and teaching workshops attendance and exam passing, the student:

will master the main constitutive laws employed to describe the behavior of different classes of material, with particular emphasis on geotechnical materials, and will understand their field of application;

will master the equations governing the elastic and elasto-plastic problems for single-phase solids and for saturated soils and will be able to describe them clearly and effectively;

will be able to apply the above knowledge to solve simplified problems;

will master the displacement formulation of the finite element method, in the linear and non-linear regime, even in presence of saturated porous materials;

will be able to independently solve typical problems of geotechnical engineering through the conscious use of a multi-purpose finite element code;

will be able to draw up a report on the obtained results, with clarity and language skills.

Argomenti trattati

Contents of the integrated course:

(the part related to the Computational Mechanics module, points 1,3,5,6, is written in normal font, the part relating to the Geomaterials module, points 2,4,7,8 is written in italics)

Elastic problem for a single-phase continuum

Three-dimensional, plane and axial-symmetric elastic problems. Isotropic and anisotropic elastic constitutive model.

Hydro-mechanical problem for a saturated porous continuum

Equations of equilibrium, compatibility and mass conservation for the saturated porous medium. Seepage analysis for a porous medium with rigid skeleton. Displacements analysis with uncoupled approach. The hydro-mechanical coupled problem in a deformable medium with elastic behaviour.

Fundamentals of the finite element method

Weak formulation of the elastic problem. General aspects of the displacement formulation of the finite element method. Finite element formulation for plane problems. Isoparametric elements.

The finite element method for geomaterials

Formulation of the finite element method for the hydro-mechanical coupled problem of a saturated porous medium. Fundamental characteristics and procedures of the finite element analysis in a geotechnical engineering problem. Analysis of soil response under various working conditions. Analysis of serviceability and ultimate state. Examples of finite element solutions for linear elastic problems.

Introduction to the mechanics of materials

Mechanical behavior of materials: elastic, visco-elastic, elastic-plastic, visco-plastic

Elasto-plastic constitutive models

Yield functions, hardening laws, associated and non-associated sliding laws, examples. Hints on the integration methods of nonlinear constitutive models. The finite element method for elastoplastic problems

Elasto-plastic models for geomaterials

Mechanical behaviour of soil, rock and discontinuities. Elasto-plasticity, softening and rheological models. Constitutive parameters and their calibration. Soil behaviour in partially saturated conditions.

Applications of the finite element method to geotechnical engineering problems

Examples of finite element analyses for non-linear problems. Soil-structure interaction problemes. Unconfined seepage in unsaturated levees. Excavation and construction procedures. Slope stability problems.

Prerequisiti

Basic knowledges of Solid Mechanics and Soil Mechanics, such as those that can be acquired in the courses of Solid Mechanics and Geotechnics.

Modalità di valutazione

The evaluation is based on an oral discussion and a written report to be prepared during the semester.

The written report focuses on the case-studies analyzed during computer laboratories through a commercial software.

The students (possibly in pairs) re-elaborate the topic covered during the course in a personal and autonomous way and draw up a technical report, structured as if it were addressed to an external client. The written report must clearly describe the examined problem and comment the obtained results in a complete and critical way.

Bibliografia

Corigliano A., Taliercio A., Meccanica computazionale. Soluzione del problema elastico lineare, Editore: Esculapio, Progetto Leonardo, Bologna, Anno edizione: 2005, ISBN: 88-7488-188-6 Note:

Testo di riferimento per gli argomenti 1 e 3

Lemaitre J., Chaboche J.-L., Mechanics of solid materials , Editore: Cambridge Univ. Press., Anno edizione: 1990 Note:

Testo di riferimento per le parti 5 e 6

Potts D.M., Zdravkovic L., Finite element analysis in geotechnical engineering: Theory, Editore: Thomas Telford, Anno edizione: 1999 e.book Politecnico Note:

(Modulo Geomateriali)

Potts D.M., Zdravkovic L., Finite element analysis in geotechnical engineering: Applications, Editore: Thomas Telford, Anno edizione: 2001 e.book Politecnico Note:

(Modulo Geomateriali)

Additional textbooks may be suggested during the year and notes on specific topics, prepared by the teachers, will be available on WeBeep.

Software utilizzato

Nessun software richiesto

Forme didattiche

Tipo Forma Didattica

Ore di attività svolte in aula

(hh:mm)

Ore di studio autonome

(hh:mm)

Lezione

32:30

48:45

Esercitazione

17:30

26:15

Laboratorio Informatico

0:00

0:00

Laboratorio Sperimentale

0:00

0:00

Laboratorio Di Progetto

0:00

0:00

Totale

50:00

75:00

Informazioni in lingua inglese a supporto dell'internazionalizzazione

Insegnamento erogato in lingua
Inglese

Disponibilità di materiale didattico/slides in lingua inglese

Disponibilità di libri di testo/bibliografia in lingua inglese

Possibilità di sostenere l'esame in lingua inglese

Disponibilità di supporto didattico in lingua inglese