Complex Modulus 

The complex modulus consists of two components, the storage and the loss moduli. The storage modulus (or Young’s modulus) describes the stiffness and the Viscous modulusThe complex modulus (viscous component), loss modulus, or G’’, is the “imaginary” part of the samples the overall complex modulus. This viscous component indicates the liquid like, or out of phase, response of the sample being measurement. loss modulus describes the damping (or viscoelastic) behavior of the corresponding sample using the method of Dynamic Mechanical Analysis (DMA). The complex modulus is the sum of the storage and loss modulus where the loss modulus is multiplied with i, the imagining unit.

The complex modulus is designated with a*.
E*= E‘+iE‘‘ and for the Shear Modulus G*G or shear modulus is defined as the ratio of shear stress and shear strain.G modulus G*= G‘+iG‘‘

The storage modulus and loss modulus for the E modulus 

The storage modulus is defined as:

The loss modulus is defined as:

tanδ is the ratio between the storage and loss modulus: