Tensor Notation and Analysis
Biomaterials and Biomechanics
Introduction
We are going to look at tensor notation and
how to use vectors and rotate and translate
them.
This notation is the mathematical language
that we will use this semester.
Vectors
Wha

Materials Basics Structure
Processing
Properties
Performance
3
SP
What are Materials?
What are Materials?
Early materials used to
build tools
Clay
Stone
Wood
Skins
Early humans had
limited selection
https:/commons.wikimedia.org/wiki/File:JomonPottery.JP

Problem set 4 Intro Biomaterials Spring 2016
NAME:.
Due at lecture Thursday March 10th
Q1. Find two independent definitions and combine them for these terms (give references for the sources).
a) Define what opsonins are:
See definitions on line or in text

Viscoelasticity-Part 2
Biomaterials and Biomechanics
Tissue Modeling: Overview
Originally we looked at a general technique to
characterize the response of a time-dependent
material
To discover the viscoelastic characteristics of the
material, the materi

Viscoelasticity-Part 3
Biomaterials and Biomechanics
Viscoelasticity
We have looked at the most basic lumped
parameter models
Maxwell fluid and Kelvin solid
When it comes to modeling tissue behavior,
they each have positives and negatives
Viscoelastici

Viscoelasticity-Part 1
Biomaterials and Biomechanics
Viscoelasticity
Viscoelasticity describes the mechanical
response of tissues that both store and
dissipate energy
We can describe materials as linear
viscoelastic or non-linear viscoelastic, with
many

Principal Stress
Biomechanics and Biomaterials
What is Principal Stress
Stresses, normal and shear, vary smoothly as
you rotate an object, the stresses are found
using our coordinate transformation
equations (bij).
What is Principal Stress
What do we me

Introductory Lecture
Biomaterials and Biomechanics
Objective
The objective of this class is for you to
understand the principles that underlay
complex problems in continuum mechanics,
with an emphasis on biomechanics problems
What do you need to know?
V

Constitutive Equations
Biomaterials and Biomechanics
Constitutive Equations
What is a constitutive equation?
It is an equation that describes a property of a
material
In these equations we are looking at one
tensorial quantity (like stress) and relatin

Strain
Biomaterials and Biomechanics
Statics vs. Deformable Bodies
We have used statics to solve problems
We have assumed that the structural elements
behave as rigid bodies
Statics vs. Deformable Bodies
In statics, forces do not have a consequence
on

Analysis of Stress
Biomechanics and Biomaterials
Stress Notation
2 pieces of information that are important for
identifying stresses
Orientation
Surface
Stress Notation
Take a cube with stresses applied to each face
For the diagram shown here:
The s

Velocity Fields and Compatibility
Conditions
Biomaterials and Biomechanics
Velocity Fields
We have 2 points in a velocity field .
Velocity Fields
When we look at fluid flow we are usually
concerned with the velocity of every particle
in the fluid
Veloc

Microstructure 1
Microstructure depends on processing, properties depend on the microstructure
Microstructure is:
Defects in crystals - point, line and planar
Phases - distribution
Thermodynamics - this deals with equilibrium
Kinetics - deals with changes