INVESTIGATING VISCOELASTIC PROBLEMS: AN INNOVATIVE ENERGY BALANCE APPROACH
Abstract
Energy dissipation in solids involves various mechanisms, leading to the conversion of mechanical energy into heat. Two primary dissipative processes, namely 'static hysteresis' and viscosity properties, contribute to this energy loss. Static hysteresis is characterized by frequency-independent energy loss per cycle, attributed to the non-linear stress-strain behavior of materials. On the other hand, viscosity properties cause losses related to velocity gradients induced by vibrations, and the forces producing these losses exhibit a viscous nature, with mechanical behavior dependent on the rate of strain. Linear viscoelasticity is the field that addresses this issue.
When energy is applied to a viscoelastic body, a portion dissipates as heat due to the material's viscosity, while the remainder is stored as reversible energy known as potential energy. Understanding the total energy of deformation, energy storage, and dissipation is of interest when investigating viscoelastic materials. The total deformational energy can be expressed as the sum of stored energy and dissipated energy. This energy relationship applies generally and can be represented in terms of unit volume.
Viscoelastic materials are defined based on this energy relationship, wherein the applied energy is either stored elastically or dissipated as heat. Equation (1) captures this relationship, which is applicable beyond linear behavior and mechanical models. Sufficient information on applied deformation and energy rate is necessary for energy analysis.
In addition to potential energy, there is also residual energy, associated with inertial energy storage encountered in fast loading experiments or high-frequency wave propagation. Although linear viscoelasticity theory neglects the role of inertial energy storage, it may be of interest to calculate it. Deformation of these structures involves the exchange of residual energy and various internal elastic energies, achieved through the coupling of internal elastic variables and induced elastic stress, as determined by Hamilton's principle.
This paper presents a novel perspective on energy components and their balance, defining and calculating residual energy and non-inertial energy. The approach is applied to different basic linear viscoelasticity models, and the results are discussed. The analysis of equation (1) and the study of body's residual energy, as well as energy dissipation and storage, are essential for a comprehensive understanding of viscoelastic behavior.
