关键词: G-凸空间, 严格KKM性质, 不动点定理, 极大元, 择一定理, 极大极小不等式, wave propagation, poroelastic, wet bone, internal remodeling, magnetic field

Abstract: This paper studies the effects of the magnetic field and the porosity on a poroelastic bone model for internal remodeling. The solution of the internal bone remodeling process induced by a magnetic field is presented. The bone is treated as a poroelastic material by Biot’s formulation. Based on the theory of small strain adaptive elasticity, a theoretical approach for the internal remodeling is proposed. The components of the stresses, the displacements, and the rate of internal remodeling are obtained in analytical forms, and the numerical results are represented graphically. The results indicate that the effects of the magnetic field and the porosity on the rate of internal remodeling in bone are very pronounced.

Key words: minimax inequality, alternative theorem, G-convex space, strict KKM property, fixed point theorem, maximal element, wave propagation, poroelastic, wet bone, internal remodeling, magnetic field