mechanisms

model

In the case of shear, the deformation is not associated with expanding or compressing, but with laterally offsetting the faces of a cube. The shear is therefore described by the angle \gamma with which it is possible to rotate the face perpendicular to the displaced surfaces. In analogy to Hook's law for compression and expansion, we have the relationship between torsion \tau and angle \gamma:

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where G is the so-called shear modulus.

The shear modulus G is related to the modulus of elasticity E and Poisson's ratio
u by

kyon

where G is the so-called shear modulus.

In analogy to the strain energy, the shear energy is proportional to the shear angle \gamma squared, the constant being in this case the shear modulus:

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Since the strain energy is

$W=\displaystyle\frac{1}{2}VG\gamma^2$

with Hook's law for materials

$\tau=G\gamma$

is obtained:

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The ratio of energy W, volume V, modulus of elasticity E and strain \epsilon

$W=\displaystyle\frac{1}{2}VE\epsilon^2$

and the shear energy with the angle \gamma and shear modulus

$W=\displaystyle\frac{1}{2}VG\gamma^2$

can be generalized to the three-dimensional case:

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where \epsilon_i represents the deformation in each axis.

With the relationship of the energy W, the volume V, the modulus of elasticity E and deformations \epsilon_i

$W=\displaystyle\frac{1}{2}VE(\epsilon_1^2+\epsilon_2^2+\epsilon_3^2)$

and Hook's law for continuous material

$\sigma_i=E\epsilon_i$

energy can be written as a function of voltage

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where \epsilon_i represents the deformation in each axis.

Since the energy W is

equation=3766

where V is the volume, E the modulus of elasticity and \epsilon_i the strain, the energy density can be calculated

equation=3770

so we have:

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where \epsilon_i represents the deformation in each axis.

Since the energy W is

equation=3767

where V is the volume, E the modulus of elasticity and \sigma_i the tension, the energy density can be calculated

equation=3770

so we have:

kyon

where \epsilon_i represents the deformation in each axis.