Università di Pavia - Offerta formativa

CONSTITUTIVE MODELING OF MATERIALS

Enrollment year

2021/2022

Academic year

2021/2022

Regulations

DM270

Academic discipline

ING-IND/34 (INDUSTRIAL BIOENGINEERING)

Department

DEPARTMENT OF ELECTRICAL,COMPUTER AND BIOMEDICAL ENGINEERING

Course

BIOENGINEERING

Curriculum

Cellule, tessuti e dispositivi

Year of study

1°

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

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.

Reccomended or required readings

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

useful links:

http://www-2.unipv.it/compmech/teaching_av.html

http://www-2.unipv.it/compmech/mate-lab.html

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