Prof. Paolo S. VALVODepartment of Civil and Industrial EngineeringLargo Lucio Lazzarino – 56122 PISA (PI) – ItalyPhone +39 050 2218223 – Skype paolovalvoE-mail p.valvo@ing.unipi.it – Web http://www2.ing.unipi.it/paolovalvo/

Computational Mechanics

of Materials

Academic Year 2020/2021 – 2nd Semester

University of PisaMSc Degree Programme inMaterials and Nanotechnology

Learning Outcomes Knowledge

The student who successfully completes the course will learn the theoretical fundamentals of the finite element method for the analysis of both linear and non-linear behaviour of materials.

Skills

The student who successfully completes the course will be able to consciously use commercial software codes for finite element analysis. Besides, (s)he will be able to write simple software codes to implement the studied algorithms.

Behaviours

The student who successfully completes the course will be able to apply the finite element method to solve material mechanics problems. In particular, (s)he will be able to choose the most appropriate modelling approach, type of elements, level of discretisation, etc., as well as the most suitable solution methods; besides, (s)he will be able to analyse critically the obtained results.

Teaching and Assessment Methods Teaching Methods

• Face-to-face lectures;

• Computer lab classes;

• Individual study;

• Solution of homework exercises.

Assessment Methods

Oral examination with questions on taught topics, solution of simple problems, and discussion of individual exercises carried out by students during the semester.

Assessment Criteria Knowledge

The level of acquired knowledge will be assessed during the oral examination through questions on taught topics.

Skills

The possessed skills will be assessed during the oral examination through the discussion of individual exercises carried out during the semester and ex tempore demonstration with the aid of a personal computer.

Behaviours

The learned behaviours will be assessed during the oral examination through the formulation of simple problems of computational mechanics of materials and the discussion of their possible solution methods.

Syllabus Introduction to the Finite Element Method (FEM)

Introductory examples: truss structures and analogies with other fields of physics and engineering.

The displacement approach for elasticity problems: spatial discretisation, equilibrium equations, boundary conditions.

Syllabus Formulation of Elements

One-, two-, and three-dimensional elements: bar and interface elements; triangular and rectangular elements; tetrahedral and brick elements.

Mapped elements: normalised coordinates, isoparametric elements, numerical integration.

Elements for structural analysis: beams, plates, etc.

Special type elements: springs, dampers, rigid links, etc.

Syllabus Types of Analysis and Related Solution Methods

Linear and non-linear elastic analyses.

Static and dynamic analyses.

Elasto-plastic analysis.

Analysis of fracture and fatigue problems.

Syllabus Error Estimates and Convergence of Solutions

Error norms and convergence rates.

Mesh refinement and element enrichment.

Syllabus Computer Codes

Matlab.

Abaqus.

Bibliography Teacher’s notes

They will be made available on Microsoft Team.

Reference textbook

O.C. Zienkiewicz, R.L. Taylor, D.D. Fox, The Finite Element Method for Solid and Structural Mechanics – 7th ed., Elsevier, Amsterdam, 2014.

Further reading

J.C. Simo, T.J.R. Hughes, Computational Inelasticity, Springer, Berlin, 1998.

P. Wriggers, Nonlinear Finite Element Methods, Springer, Berlin, 2008.

Websites Professor’s Homepage

http://www2.ing.unipi.it/paolovalvo/index.html

Course Page on Professor’s Homepage

http://www2.ing.unipi.it/paolovalvo/cmm.html

Course Programme on esami.unipi.it

https://esami.unipi.it/programma.php?c=47981

Lesson Log

https://unimap.unipi.it/registri/dettregistriNEW.php?re=3312155::::&ri=11212

Virtual Classroom on Microsoft Teams

To be announced.