Ing - Civ (Mag.)(ord. 270) - MI (489) INGEGNERIA PER L'AMBIENTE E IL TERRITORIO - ENVIRONMENTAL AND LAND PLANNING ENGINEERING
057938 - COMPUTATIONAL MECHANICS FOR GEOMATERIALS
Ing Ind - Inf (Mag.)(ord. 270) - MI (487) MATHEMATICAL ENGINEERING - INGEGNERIA MATEMATICA
058207 - COMPUTATIONAL MECHANICS FOR GEOMATERIALS
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.
Integrated course topics: (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)
1. Elastic problem for a single-phase continuum Three-dimensional, plane and axial-symmetric elastic problems. Isotropic and anisotropic elastic constitutive model.
2. 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.
3. 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.
4. 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.
5. Introduction to the mechanics of materials Mechanical behavior of materials: elastic, visco-elastic, elastic-plastic, visco-plastic
6. 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
7. 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.
8. Applications of the finite element method to geotechnical engineering problems Examples of finite element analyses for non-linear problems. Soil-structure interaction problems. Unconfined seepage in unsaturated levees. Excavation and construction procedures. Slope stability problems.
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.
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