Mechanics constitutive models for viscoelastic solid materials: Development and a critical review

Mathematical constitutive models are crucially important for the real viscoelastic solid materials in academic investigation and engineering application. The viscoelastic solid materials and their composites are extensively applied in practice engineering, including biomechanics, aviation, aerospace, and geology, and it has captured more and more attention in recent years. Proper application and selection for the constitutive models of the solid viscoelastic materials will be directly influenced by the investigation accuracy in analysis. The aim of this monograph is to essentially describe the development and evolution of the constitutive equations for viscoelastic solid materials in terms of their mechanics and physical behaviors. For isotropic viscoelastic material, its physical behaviors and mechanical properties are influenced by the environmental effects and external exaction factors. In this report, more than 14 classical and fundamental types/categories of the constitutive models for the real viscoelastic solid material are discussed and reviewed. Physical and mechanics behaviors in the time-, temperature-, moisture-, and frequency-domain are provided. Moreover, the development of the time-temperature-, frequency-temperature-, temperature-moisture-, and pressure-time-dependent constitutive models are also presented. We intend to illustrate and emphasize the mathematical and graphical aspects related to the constitutive models for the real viscoelastic solid material, serving as a foundation reference in future academic investigation and practical application.