The document Energy Dissipation in Structural Materials Civil Engineering (CE) Notes | EduRev is a part of Civil Engineering (CE) category.

All you need of Civil Engineering (CE) at this link: Civil Engineering (CE)

**Introduction **

• Selection of structural materials corresponding to high inherent energy dissipation or damping depends on three factors

- material properties
- geometric property of the structural member and
- type of loading

• Material properties are connected with the system parameters as follows:

• Damping capacity of structural materials may depend on the following mechanisms

**dislocation movement:**this occurs due to the presence of slip planes in crystalline materials;**grain boundary slip:**movement of one grain over the other causes energy dissipation;**magnetoelastic effect:**due to interaction between magnetization and strain of a magnetic material;**thermoelastic effect:**due to interaction between thermal and mechanical deformation;**localized plastic strain -**presence of defects like shear bands can entangle dislocations preventing the crystal from sliding. This may also create energy dissipation.

**Stress Dependence of Energy Dissipation **

The stress-strain plot of a structural material (metals and metallic alloys are considered here) under harmonic loading and low stress level may be plotted as

Figure 9.1: Stress strain plot

• The energy dissipated per unit volume of a structural material per unit cycle is given by the area of the hysteresis loop (also known as mechanical hysteresis loop).

• This is generally denoted as D_{m} (dissipated energy per m^{3} per cycle)

• The energy dissipated per unit volume per cycle, D_{m} is related to the applied stress as

where J is the damping constant and n the damping index.

• At a very low stress level, n=2 and the stress diagram becomes elliptic instead of showing pointed tip

Figure 9.2 : Energy dissipation at different stress level

Generally n varies from 2 to 3. For, higher values of n a modified relationship is used as follows

whereJ_{1}, J_{2} are the damping constants.

For multi axial loading of a structural member, The D_{m} is given by

Note that the uniaxial stress σ is replaced by equivalent stress, .

is denoted as

s_{1}, s_{2}, s_{3} are the principal stress amplitudes. λ_{1}, usually is very small.

The material loss factor η_{m} could be expressed in terms of D_{m} as

The total loss factor of a composite specimen η_{s} can be obtained as

where

b_{i} - width of the i-th layer

t_{i} - thickness of i-th layer

Table below shows the list of density, Young's modulus, and the order of loss factor of a few common structural materials.

**Table 9.1: Mechanical properties of important structural materials**

Offer running on EduRev: __Apply code STAYHOME200__ to get INR 200 off on our premium plan EduRev Infinity!