CONSTITUTIVE MODELING OF MATERIALS
Stampa
Enrollment year
2021/2022
2021/2022
Regulations
DM270
ING-IND/34 (INDUSTRIAL BIOENGINEERING)
Department
DEPARTMENT OF ELECTRICAL,COMPUTER AND BIOMEDICAL ENGINEERING
Course
BIOENGINEERING
Curriculum
Cellule, tessuti e dispositivi
Year of study
Period
1st semester (27/09/2021 - 21/01/2022)
ECTS
6
Lesson hours
57 lesson hours
Language
Italian
Activity type
WRITTEN AND ORAL TEST
Teacher
AURICCHIO FERDINANDO (titolare) - 3 ECTS
ALAIMO GIANLUCA - 1 ECTS
CONTI MICHELE - 2 ECTS
Prerequisites

Basic knowledge of algebra, solid mechanics (concepts
introduction of deformation and tension), of numerical calculation.
Learning outcomes

The module aims to introduce the student to the study and use of
analytical and numerical mathematical models for the description of the
constitutive behavior of materials.
Starting from a general framework of the theory of bodies
deformable, the development of elastic and inelastic models will be addressed
(discussing visco-elasticity models, visco-plasticity, plasticity, with
possible extensions to the case of damage and fatigue), for isotropic and non-isotropic materials,
also giving hints to the problems for their solution in
numerical area.
The mechanical tests to be performed for the calibration of the models will also be discussed.
Course contents

The module aims to introduce the student to the study and use of
analytical and numerical mathematical models for the description of the
constitutive behavior of materials.
Starting from a general framework of the theory of bodies
deformable, the development of elastic and inelastic models will be addressed
(discussing visco-elasticity models, visco-plasticity, plasticity, with
possible extensions to the case of damage and fatigue), for isotropic and non isotropic materials,
also giving hints to the problems for their solution in
numerical area.
Mechanical tests will be discussed.
Review of tensor algebra
Fundamentals of deformable bodies kinematics. Deformation analysis. Equilibrium. Specialization in the case of small displacement gradients.
Fundamental principles for the development of constitutive models: invariance
of the observer and material symmetry
Elastic models in small deformations: Cauchy elasticity and Green elasticity. Development of models for different material symmetries:
isotropic materials, materials with one family of fibers, materials with two families of fibers.
Extension to the case of large deformations.
Development of a calculation program (for example in matlab) for the
simulation of strain and / or stress control stories.
Application to the case of particular classes of materials (for example,
polymers, composite materials, soft biological tissues, etc.).
Comparison with
experimental data and development of a determination program
automatic constitutive parameters.
Inelastic models in small deformations: visco-elasticity, visco-plasticity,
classical plasticity, plasticity with isotropic hardening e
kinematic.
Integration schemes numerical solution and program development
of calculation (for example, in matlab) for the simulation of stories to control of
deformation and / or tension.
Application to the case of particular classes of inelastic materials (for
example, metallic materials, concrete, etc.). Comparison with data experimental.
Basic knowledge of damage and fatigue of materials will be provided as well.
Teaching methods

Taught lesson; when required, the implementation of the proposed models will be performed using computer.

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.
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.
Assessment methods

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.
Further information