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Earlier modeling approaches in the field of mixtures assumed the solid phase of the mixture was the predominant constituent and simplified the constitutive laws for the fluid phase. In the field of mixtures, it has been argued that methods such as the theory of poroelasticity are incapable of accurately capturing mass exchange between phases and stress and strain fields. Mass exchange between phases and accurate stress and strain variations of each phase are indispensable to many fields of study, such as bone remodeling, fault movement in rocks, and shock waves in soils. This study presents an alternative method for capturing the stress and strain fields of mixtures, focusing on the advection term in the balance of linear momentum and mass exchange for each phase. In addition, this extended theory has the potential for measuring the shear stress field of a viscous fluid component, considering complex boundary conditions, and modeling chemical reactions between mixture phases. The capability of the model has been evaluated by analyzing 2D and 3D examples, including a realistic bone remodeling scenario. Calculations have shown a maximum difference of 20% in the displacement fields. Thus, results clearly demonstrate the importance of considering the advection term and mass exchange between phases, as its application causes significant variations in the displacement and stress fields of the mixture. The developed model of this study can be considered as a general theory, which yields the classic poroelastic model with certain manipulations. [ABSTRACT FROM AUTHOR]

Abstract: Bone is maintained through a coupled process of bone resorption and bone formation, in a continuous process called bone remodeling. An imbalance in this process caused by disease, abnormal mechanical demands, or fatigue may predispose bone to fracture injuries. The remodeling process is generally viewed as a material response to functional demands. Here, we propose a new set of constitutive equations for the bone remodeling process and contains the specific surface, instead of volume fraction, and the degree of microcracking in the constitutive equations. The rate of remodeling is related to mechanical stimuli, free surface density and a microcrack factor. In this approach, the effect of mechanical stimuli, rate of mechanical stimuli, and integration of mechanical stimuli on bone remodeling can be evaluated simultaneously in the remodeling equation. Specific examples are given for illustration of the model. [Copyright &y& Elsevier]