Nonlinear Classical Elasticity Model for Materials with Fluid and Matrix Phases
MetadataShow full item record
MATHEMATICAL PROBLEMS IN ENGINEERING
discern material damageWAVE SPECTROSCOPYNEWS TECHNIQUES
Muñoz, R., & Melchor, J. (2018). Nonlinear Classical Elasticity Model for Materials with Fluid and Matrix Phases. Mathematical Problems in Engineering, 2018.
SponsorshipMinistry of Education [Grant nos. DPI2014-51870-R, DPI2017-85359-R, and UNGR15-CE-3664]; Ministry of Health [DTS15/00093 and PI16/00339]; Junta de Andalucía [PIN-0030-2017 and PI0107-2017 projects]; University of Granada [PP2017- PIP2019]
Materials with fluid and matrix phases present different acoustic responses in each phase. While longitudinal waves propagate in both phases, shear waves do it only through the solid matrix. Longitudinal waves are mainly described by volumetric propagation and shear waves by deviatoric processes. In the case of nonlinear propagation cross effects occur between both components. This paper presents a new classical nonlinear model proposing a constitutive equation that separates volumetric and deviatoric effects. Four nonlinear constants of third order are defined. The formulation is compared to constitutive equations with Landau constants for weakly elasticity and both types of nonlinear constants related. Some reinterpretation of the Landau's constants arises in terms of parallel or cross nonlinear effects between volumetric and deviatoric components.