Dynamic strain energy release

The critical strain-energy release rate, Gp, in the specimen with notch-root radius, p, is indicated in Fig. 1.78 for both static and dynamic ceramic fracture. The linear relation of the lines in Fig. 1.78 are based on the Williams relation... 

In order to be used in a dynamic system under adhesive interaction, the rate dependence of the modulus and the work of adhesion for crack propagation need to be considered, and Dupre s work of adhesion (712) can be replaced by the strain energy release rate G. 

The dynamics of a nematic gel are assumed to be governed by the viscoelasticity of the gel, the rotational viscoelasticity of the director, and electrostatics. The governing equations for the dynamics are derived from the balance between the rates of free-energy release and viscous dissipation. In the present case, strain rates and stresses are spatially uniform because of the unconstrained geometry. Therefore, the governing equations for the dynamics of the strain and the director are obtained from the free energy as [31] ... 

When the stress is decomposed into two components the ratio of the in-phase stress to the strain amplitude (j/a, maximum strain) is called the storage modulus. This quantity is labeled G (co) in a shear deformation experiment. The ratio of the out-of-phase stress to the strain amplitude is the loss modulus G"(co). Alternatively, if the strain vector is resolved into its components, the ratio of the in-phase strain to the stress amplitude t is the storage compliance J (m), and the ratio of ihe out-of-phase strain to the stress amplitude is the loss compliance J"(wi). G (co) and J ((x>) are associated with the periodic storage and complete release of energy in the sinusoidal deformation process. Tlie loss parameters G" w) and y"(to) on the other hand reflect the nonrecoverable use of applied mechanical energy to cause flow in the specimen. At a specified frequency and temperature, the dynamic response of a polymer can be summarized by any one of the following pairs of parameters G (x>) and G" (x>), J (vd) and or Ta/yb (the absolute modulus G ) and... 

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