# Continuum Mechanics

CurriculumHYRIS

Term: 1st year, 1st Semester

Syllabus

CFU: 6

SSD: CEAR-01/A

Duration and Scheduleavailable here

Office hours: upon request by email

OBJECTIVES

The course will provide the fundamental theoretical concepts and mathematical tools for the formalization, analysis and solution of relevant problems in the field of material continuum mechanics.

The fundamental mathematical relations for the analysis of stress and deformation at material point are introduced first; then, the mathematical formulation of the conservation principles is carried out leading to the governing equations of material continua; finally, the linear constitutive equations are introduced bringing to the mathematical formulation of the dynamic problem of solid and fluid continua.

These topics, whose understanding is strengthened through the computer analysis and solution of applied engineering problems of practical interest, will provide the basis for the analysis and mitigation of natural hazards, such as flooding, and landslide induced risk.

DESCRIPTION

Fundamentals of vector, tensor and matrix algebra. The continuum postulate.

Analysis of stress: Cauchy stress principle; stress tensor. Mohr’s circle representation.

Local deformation and strain: small deformation theory; Saint-Venant’s compatibility equations.

Lagrangian and Eulerian description of flow; material derivative.

Reynolds transport theorem. Conservation principles and the fundamental laws of Continuum Mechanics.

Constitutive equations: generalized Hooke’s law; Newtonian fluid, Stokes assumption.

Navier-Stokes equation; Euler and Bernoulli equations; Laplace equation.

Applications and problems.

REQUIREMENTS

Basic concepts of integral and differential calculus; fundamentals of mechanical physics.

REFERENCES

1. Aris R. “Vectors, tensors, and the basic equations of fluid mechanics” 1990 Dover pub ISBN-10: 0486661105.
2. Chou P.C. & Pagano N.J. “Elasticity, tensor, dyadic, and engineering approaches” 1992 Dover pub ISBN-13: 978-0486669588.
3. Mase G.E. “Theory and problems of Continuum Mechanics” Schaum’s Outline Series – McGraw Hill 1970.
4. Prager W. “Introduction to Mechanics of Continua” Ginn and Co. 1961.
5. Lecture notes and course exercises available at https://elearning.unipv.it/.+

ASSESSMENT

The final examination consists of an oral discussion during which the student must demonstrate acquired capacity to describe the problems developed during the course, describing their mathematical formulation and solution method. Critical analysis of results allows testing the comprehension of the basic theoretical aspects.

Instructor: Sauro Manenti: official webpage and CV

Institution: DICAR (UNIPV)

E-mailsauro.manenti@unipv.it

Voice:  +39 0382 985321

Fax:     +39 0382 985589

Bio: Sauro Manenti is currently Associate Professor at the Department of Civil Engineering and Architecture from the University of Pavia. He obtained his Ph.D. in Hydraulic Engineering in 2008 at the University of Rome “Sapienza”. Between 2007 and 2010 he was appointed Adjunct Professor on Maritime Constructions, Port and Coastal Engineering, Maritime Engineering and Coast Protection at the University of Rome “Sapienza”. Involved in several scientific activities and research projects with role of both coordinator and component. Research interests: development and application of Lagrangian Meshfree Particle models for the analysis of multi-phase non-Newtonian rapidly-varied flows with interaction phenomena; post-failure analysis of rainfall-induced shallow landslides; fast landslides and impulsive waves generation; ocean wind waves generation, interaction with floating body and propagation nearshore; filtration flow in porous media; river hydraulics and inundation; sediment transport; water flow in natural and anthropic environments under uncertainty.