This course aims at providing students with the basic knowledge of mechanics of materials allowing for the micro-structural architectures and the constituents' properties. So the main objectives of the course will be the mechanics of composite materials. A second part of the course will be focused on the mechanics of thin films, and mechanical characterization testing at small length scale.

The lectures will focus mainly on the mathematical modeling of the mechanical behavior of the materials as well as to the mechanical experimental characterization techniques. To this purpose a brief summary on solid mechanics will be provided at the beginning of the course.

Applications to specific material systems will be treated in the practical lectures.

Two short visits at the Laboratory of Biological Structure Mechanics of Politecnico di Milano are planned with illustration of practical cases of the nanoindentation technique and of the micro-tensile testing.

The students will learn the modeling approaches for the basic mechanical response of micro and nanocomposite materials on the basis of the mechanical properties of the constituents. The student should be able to effectively describe theoretical and numerical approaches. Furthermore, the student should be able to effectively discuss literature papers describing theoretical and numerical approaches to micromechanics of materials and thin layers systems. The student may also show their level of comprehension of the subjects by showing their capability to implement simple micromechanics problems using numerical codes or MATLAB environment.  

Basic equation of continuum mechanics (a brief summary)

Mechanics of composite materials, homogenization of elastic properties:

Concept of inclusions and inhomogeneities

                Concept of eigenstrain

                Definition of effective elastic properties

                Bounds on effective moduli

Brief introduction to non linear homogenization approaches.

Mechanics of thin films

                Motivation for thin films mechanics

                Mechanical issues in thin films

                Residual stresses in 1D and 2D problems

                Curvature induced by residual stresses

                Stress state at the interfaces

                Experimental techniques for the Study of Mechanical Properties of Thin Films;

Practical lectures:

Applications to specific material systems: ceramic/ceramic composites; metal/ceramic composites; biological tissues (with specific reference to the bone tissue);

Nanoindentation experimental technique; Micro-tensile testing (an in-situ testing).

Solid mechanics

Each student will be called to make a critical review on literature papers focusing on a selected topic previously agreed with the lecturer. An oral presentation of such review with a deep discussion on the topic will constitute the oral exam.

As an alternative, the students may develop a simple project in which they implement a specific micromechanics problems using numerical codes or MATLAB environment.  

The above mentioned examination modes will aim at: 

1. showing his/her level of knowledge and comprehension of basic micromechanics.

2. showing his/her capability to apply basic micromechanics concepts to specific problems;

3. showing capability of critically review the works of others in the field of micromechanics;

4. showing his/her skill of communication. 

Lecture notes