Basics of Solid Mechanics

Jiangting Wang

jiangtin@deakin.edu.au

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Week 02, Trimester 1, 2013

SEM712 CAE and Finite Element Analysis

Contents

Introduction Strain Stress Stiffness Tensor Material Failure Reading for this topic:

Appendix B in Hutton’s book Section 2.1 – 2.3 (P12-22) in Liu’s book (The finite element method: a practical course, 2003)

Online resources:

Deformation: http://en.wikipedia.org/wiki/Deformation_%28mechanics%29 Stress: http://en.wikipedia.org/wiki/Stress_%28mechanics%29 School of Engineering 2 Week 02, Trimester 1, 2013

SEM712 CAE and Finite Element Analysis

Introduction

Experiment Theory

����, ������ �� < ���� �� �� = � ���� ( ⋅ ��)�� , ������ �� ≥ ���� ����

Predict Generalize

Finite Element Analysis

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SEM712 CAE and Finite Element Analysis

Introduction

Solid mechanics - is the branch of mechanics, physics, and mathematics that concerns the mechanical behaviour of solid matter under external stimuli.

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Week 02, Trimester 1, 2013

SEM712 CAE and Finite Element Analysis

Introduction

Deformation

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Introduction

Applications of solid mechanics in engineering:

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Mechanical engineering

e.g. designing load bearing components for vehicles e.g. designing metal and polymer forming processes; machining e.g. designing composites; alloy microstructures, thin films. e.g. the shape of planets; tectonics; and earthquake prediction; e.g. such as designing foundations or structures e.g. designing failure resistant interconnects and packaging e.g. stress driven self-assembly on surfaces, atomic-force microscope/sample interactions.

Manufacturing engineering Materials Science Geomechanics Civil engineering Microelectronics Nanotechnology

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SEM712 CAE and Finite Element Analysis

Introduction

A list of things that can be calculated accurately using solid mechanics: • Deformed shape of a structure or component subjected to mechanical, thermal, or electrical loading; • Internal stresses in a structure or component; • Forces required to cause a particular shape change, or critical forces that lead to failure by structural instability (buckling) • Stiffness of a structure or component, and natural frequencies of vibration for a structure or component.

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Week 02, Trimester 1, 2013

SEM712 CAE and Finite Element Analysis

Introduction

Solid mechanics can be also used to model a variety of failure mechanisms: • Critical loads causing fracture • Fatigue life of a component under cyclic loading; • Creep life of a component • Wear rate of a surface under contact loading;

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Week 02, Trimester 1, 2013

SEM712 CAE and Finite Element Analysis

Introduction

General steps in solving a problem in solid mechanics:

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Decide what you want to calculate Identify the geometry of the solid to be modeled (CAD) Determine the external loading applied Decide what physics must be included in the model Choose (and calibrate) a constitutive relation to describe the behavior of the material Choose a method of analysis Solve the problem

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Week 02, Trimester 1, 2013

SEM712 CAE and Finite Element Analysis

Strain

• Definition

������������ ���� ������������ ������������ = ���������������� ������������ Sign convention: + : tensile - : compressive

–

–

Engineering strain ��2 − ��1 ���� = ��1 ���� ���� = �� ��2

Logarithmic strain (True strain) ��2 1 �� = � ���� = ln ��1 �� ��1

= ln(1 + ���� )

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SEM712 CAE and...