A general nonlocal theory and its approximations for slowly varying acoustic waves

• Published in: International journal of mechanical sciences Vol. 130; pp. 52 - 63
• Main Author: Shaat, M.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2017
• Subjects: Acoustic waves; Couple stress; Linear elasticity; Nonlocal theory; Strain gradient; Nonlocal theory; Linear elasticity; Strain gradient; Couple stress; Acoustic waves
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/j.ijmecsci.2017.05.038

•The nonlocal theory can be reduced to the strain gradient and couple stress theories.•Strain gradient and couple stress theories reflect both softening and hardening behaviors of materials.•Real and complex length scales should be considered for the strain gradient and couple stress theories.•The nonlocal parameters and length scales are reported for diamond, graphite, Si, Ag, Au, Cu, and Pt.•Neither the strain gradient theory nor the couple stress theory can be merged with the nonlocal theory in one model.•The concept of the higher-order nonlocal strain gradient theory is not correct. In this study, the mechanics of particles, the mechanics of linear elastic continua, and the materials dispersion relations are considered in the framework of a general nonlocal theory which considers different attenuation functions for the distinct material coefficients. For slowly varying acoustic waves, i.e., weak nonlocal fields, this general nonlocal theory is reduced to the strain gradient theory and the couple stress theory. When compared to the general nonlocal theory, the nonlocal characters of the strain gradient and couple stress theories are discovered. Moreover, by fitting the experimental dispersion curves of materials, the nonlocal parameters and the material coefficients and length scales of these theories are reported for materials including diamond, graphite, silicon, silver, gold, copper, and platinum. It is revealed that, when the proper values of the material coefficients are determined, the strain gradient and the couple stress theory can capture the same phenomena as the nonlocal theory. Moreover, it is demonstrated that neither the strain gradient theory nor the couple stress theory can be merged with the nonlocal theory in a unified model. This demolishes the concept based on which the higher-order nonlocal strain gradient theory (Lim et al., 2015) was proposed. [Display omitted]