Mechanics of biological structures (prima parte) - Prof. Vena

Name: Mechanics of biological structures (prima parte) - Prof. Vena
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Esame Mechanics of Biological Structures

Facoltà Ingegneria dei sistemi

Dal corso del Prof. Vena Pasquale

Università Politecnico di Milano

A.A. 2016-2017

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Mechanics of biological structures lecture 2 – 10-10-2016

Introduction

The topics of this course are divided into two main groups: hard tissues and soft tissues. If we want to model the mechanical behavior of these tissues, we need a specific mathematical framework. While if we want to model the mechanical behavior of soft tissues, we need another mathematical framework. The first part of the course is on hard tissue. However, there are some properties which are common to both soft and hard tissues.

Hierarchical architecture

In particular, one of the most important functions of biological tissues is that they always exhibit a sort of hierarchical architecture. This means that we can observe our biological tissue by using different magnification lenses. If we use the magnification lens, we see a specific structure, and going on, we can see other substructures at each level.

We start from the macroscopic level and then we go down and down with a magnification lens until the primary structure, characterized by the components of our material. The idea is that all tissues exhibit hierarchical levels of microstructures, and the geometrical arrangement of the constituents at each level and the mechanical properties of the single constituent at each level define the mechanical properties that we observe at the macroscopic level.

Anisotropic and non-linear properties

All biological tissues exhibit anisotropic mechanical properties. This means that the stress-strain response of the material will depend on the direction of loading with respect to the direction of the microstructure of the tissue that we have in our material.

They are also non-linear. In general, the bone can be approximated as a linear material for a very small strain, but in any case, all the other biological materials (in particular, soft biological materials) exhibit a non-linear stress-strain relationship. This means that when we take a little piece of the biological tissue and we put it under a tensile test equipment, the relationship between forces and displacement is always non-linear, and therefore the relationship between stress and strain is non-linear. Non-linearity is again given by the hierarchical arrangement of the constituent at the microscopic levels.

Residual stress

Another important feature is the residual stress. This means that in these tissues, there is a pre-existing state of stress even if no external loading is applied. The most important example is the vascular vessels. There is an internal pressure inside the vessels, but the idea is that if we have an artery with no blood pressure inside it, some stresses are acting into the material, and we can visualize this stress by taking a knife and cutting the arterial wall longitudinally.

This is not typical for any engineering structure. In fact, if we take an engineering structure and we have no load applied, there is no stress and so no strain.

No Load → No Stress → No Strain

The topics of this course are divided into two main groups: hard tissues and soft tissues. If we want to model the mechanical behavior of these tissues, we need a specific mathematical framework. While if we want to model the mechanical behavior of soft tissues, we need another mathematical framework. The first part of the course is on hard tissue. However, there are some properties which are common to both soft and hard tissues.

In particular, one of the most important functions of biological tissues is that they always exhibit a sort of hierarchical architecture. This means that we can observe our biological tissue by using different magnification lenses. If we use the magnification lens, we see a specific structure, and going on, we can see other substructures at each level.

All biological tissues exhibit anisotropic mechanical properties. This means that the stress-strain response of the material will depend on the direction of loading with respect to the direction of the microstructure of the tissue that we have in our material.

Another important feature is the residual stress. This means that in these tissues, there is a pre-existing state of stress even if no external loading is applied. The most important example is the vascular vessels. There is an internal pressure inside the vessels, but the idea is that if we have an artery with no blood pressure inside it, some stresses are acting into the material.

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