01. Introduction to continuum mechanics applied to living and inert solids PDF

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01. Introduction...

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Theme 1. Introduction to continuum mechanics applied to living and inert solids

CONTINUUM BIOMECHANICS I Academic Year 2017/18

Theme 1

Introduction to continuum mechanics applied to living and inert solids J. A. Rodríguez-Martínez Department of Continuum Mechanics and Structural Analysis

Theme 1. Introduction to continuum mechanics applied to living and inert solids

INDEX

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Objectives Continuum theory Continuum mechanics Continuum biomechanics

Theme 1. Introduction to continuum mechanics applied to living and inert solids

INDEX

• • • •

Objectives Continuum theory Continuum mechanics Continuum biomechanics

Theme 1. Introduction to continuum mechanics applied to living and inert solids

OBJECTIVES

Relying on the continuum theory the continuum biomechanics framework is developed

Theme 1. Introduction to continuum mechanics applied to living and inert solids

INDEX

• • • •

Objectives Continuum theory Continuum mechanics Continuum biomechanics

Theme 1. Introduction to continuum mechanics applied to living and inert solids

INDEX

• • • •

Objectives Continuum theory Continuum mechanics Continuum biomechanics

Theme 1. Introduction to continuum mechanics applied to living and inert solids

Continuum theory Matter is composed of discrete units called molecules, which consist of atoms and subatomic particles … Thus matter is not continuous

In principle, we could describe the macroscopic behaviour of materials based on detailed knowledge of the microscopic behaviour using statistical mechanics,

though even the simplest of problems can be mathematically intractable

Theme 1. Introduction to continuum mechanics applied to living and inert solids

Continuum theory However, and fortunately, many aspects of daily life can be described or

predicted with theories that pay no attention to the molecular structure of materials (e. g., bone deformation, blood flow)

Continuum theory describes relationships between phenomena by paying no attention to the molecular structure of materials

It regards matter as indefinitely divisible, an assumption that is justified only so far as it can adequately capture experimental observations

Theme 1. Introduction to continuum mechanics applied to living and inert solids

INDEX

• • • •

Objectives Continuum theory Continuum mechanics Continuum biomechanics

Theme 1. Introduction to continuum mechanics applied to living and inert solids

INDEX

• • • •

Objectives Continuum theory Continuum mechanics Continuum biomechanics

Theme 1. Introduction to continuum mechanics applied to living and inert solids

Continuum mechanics Mechanics is the branch of physics relating applied forces to motion Continuum mechanics studies the response of materials, both solids and fluids, at the macroscopic level when subjected to different loading conditions

While rigid body motion is included in this theory as a special reduction,

deformation of materials under applied loads is its most important common application The subject of continuum mechanics can be subdivided into two primary parts:

general principles (i. e. governing equations) and constitutive relationships

Theme 1. Introduction to continuum mechanics applied to living and inert solids

Continuum mechanics General principles

General principles are common to all materials (e. g. conservation of mass and energy, principle of linear momentum and angular momentum, principle of entropy)

These governing equations can take two different, yet equivalent, forms One is an integral formulation over a finite volume

The second is field equation for a particle or differential material volume at every point

Theme 1. Introduction to continuum mechanics applied to living and inert solids

Continuum mechanics Constitutive relationships

Constitutive relationships are equations defining idealized materials. Some examples are an elastic body (deformation → 0 as load → 0), linearly elastic solid (stress linearly related to strain), and linearly viscous luid (stress linearly related to strain rate)

In general, constitutive equations vary from material to material and, for a given material, may vary depending on the loading conditions

Theme 1. Introduction to continuum mechanics applied to living and inert solids

Continuum mechanics The elegance of continuum mechanics is its mathematical framework that yields concise treatment of the governing equations and constitutive relationships

In continuum mechanics two aspects of investigation can be considered One is the formulation of constitutive equations appropriate for describing behaviours of particular classes of materials under certain loading conditions The second is solving the governing equations, in combination with the constitutive equations under circumstances of interest to scientist and engineers

Theme 1. Introduction to continuum mechanics applied to living and inert solids

INDEX

• • • •

Objectives Continuum theory Continuum mechanics Continuum biomechanics

Theme 1. Introduction to continuum mechanics applied to living and inert solids

INDEX

• • • •

Objectives Continuum theory Continuum mechanics Continuum biomechanics

Theme 1. Introduction to continuum mechanics applied to living and inert solids

Continuum biomechanics Biomechanics is the application of engineering mechanics to biological systems

It is important to keep in mind that the majority of equations

and problem solving techniques that will be studied in this course are applicable to a large range of engineering materials and not just to human locomotion or to tissues and cells within the body...