Lecturer: Ferdinando Auricchio  

Course name: Constitutive modeling of materials
Course code: 502862
Degree course: Bioingegneria
Disciplinary field of science: ING-IND/34
University credits: CFU 6
Course website: http://www-2.unipv.it/compmech/teaching_av.html

Specific course objectives

The course wishes to introduce the attending student to analytical and numerical mathematical models for the description of material costitutive behavior.
Starting from a general theory for deformable bodies, we will discuss elastic and inelastic relations (presenting visco-elastic, visco-plastic and plastic models, possibly with some comments on damage and fatigue), for isotropic and non-isotropic materials, giving also some hints on their numerical solutions.
We will also discuss the extension of some specific models to the finite strain regime

Course programme

• Tensor algebra review
• Fundamentals of mechanics for deformable bodies under the assumption of finite-strain. Change of configuration. Equilibrium. Specialization to the small-strain situation.
• Fundamental principles for the development of constitutive models: observer invariance and material symmetry
• Small-strain elastic model: Cauchy and Green elasticity. Model developments for different material symmetries: isotropic materials, one-fiber materials, two-fiber materials. Extension to the finite-strain case.
• Development of a computer code (in Matlab or Sage) for the simulation of strain and/or stress control loading histories.
• Application to some specific classes of materials (i.e. polymers, composites, soft tissues). Comparison with experimental data and development of a computer code for the automatic computation of constitutive parameters.
• Inelastic model under small-strain: visco-elasticity, visco-plasticity, classical plasticity, plasticity with isotropric and kinematic hardening.
• Numerical integration schemes and development of a computer code (in Matlab or Sage) for the simulation of strain and/or stress control loading histories.
• Application to some specific classes of inelastic materials (i.e. metals, concrete, etc. ). Comparison with experimental data.
• Possible discussion on damage and fatigue issues.

Course entry requirements

Intermediate knowledge of algebra, mechanics of solids (introductory concepts on strain and stress), numerical analysis.

Course structure and teaching

Lectures (hours/year in lecture theatre): 36
Practical class (hours/year in lecture theatre): 20
Practicals / Workshops (hours/year in lecture theatre): 0

Suggested reading materials

Notes prepared by the teacher

Extra material for further studies:

• Besson, J. et al. (2010) Non-linear mechanics of materials. Springer
• Bonet, J. and R. Wood (1997). Nonlinear Continuum Mechanics for finite element analysis. Cambridge University Press.
• Hjelmstad, K. (1997). Fundamentals of Structural Mechanics. Prentice Hall.
• Holzapfel, G. (2000). Nonlinear solid mechanics: a continuum approach for engineering. John Wiley & Sons.
• Lemaitre, J. and J. Chaboche (1990). Mechanics of solid materials. Cambridge University Press.
• Lubliner, J. (1990). Plasticity theory. Macmillan.
• Sacco, E. (1997). Argomenti di Scienza delle Costruzioni. (in italiano).
• Simo, J. (1999). Topics on the numerical analysis and simulation of plasticity. Handbook of numerical analysis, Volume III. Elsevier Science Publisher B.V.
• Simo, J. and T. Hughes (1998). Computational inelasticity. Springer-Verlag.
• Zienkiewicz, O. and R. Taylor (1991). The finite element method (fourth ed.), Volume II. New York: McGraw Hill.

Testing and exams

Written and oral final exam, with discussion of the proposed homeworks suggested during the course and eventually of a either theoretical or numerical final project.