Energy Dissipation in Structural Materials - Civil Engineering (CE) PDF Download

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 m³ 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

whereJ₁, J₂ 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

s₁, s₂, s₃ are the principal stress amplitudes. λ₁, 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