Intermezzo

In light of the lengthy and rigorous derivation of the fundamental equations of Continuum Mechanics in the preceding chapter, the reader may be at a loss as to what are the most important ones to remember.

Hence, since the complexity of some of the derivation may have eclipsed the final results, this handout seeks to summarize the most fundamental relations which you should always remember.

Stress Vector/Tensor Strain Tensor

Engineering Strain Equilibrium Boundary Conditions Energy Potential Hooke's Law ti Tij nj E „ = 1 I dm +

duj duk duk ell l.

2 Y12

e22 2 Y 23

2 Y13

2 Y23

Tij dEij

Plane Stress Plane Strain

£xx

£yy

£ zz

=

Ixy

Yyz

Yxz

0

0

0

0

®xx

0

0

0

ayy

0

0

0

<

&zz

1 G

0

0

Txy

0

1 G

0

Tyz

0

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G .

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Part II

ELASTICITY/SOLID MECHANICS

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