Cowin S C, Luo G M, Sadegh A M, Harrigan T P
Department of Mechanical Engineering, School of Engineering, City College, City University of New York, NY 10031.
J Biomech. 1994 Feb;27(2):183-6. doi: 10.1016/0021-9290(94)90207-0.
In this technical note a sufficiency condition is established for the stability of a strain-energy-based bone remodeling theory in the special case of a beam loaded by an axial force and a bending moment. In a previous report the same condition was shown to be a necessary condition for stability in the same situation. The remodeling scheme is one characterized by a remodeling stimulus equal to the strain energy density divided by the bulk or apparent density raised to an exponent m as well an elastic modulus proportional to bulk or apparent density raised to an exponent n. In order for a remodeling scheme to be stable for an elastic beam loaded by an axial force and a bending moment, it is established that the condition that m must be greater than n is not only necessary, but also sufficient.
在本技术说明中，针对轴向力和弯矩作用下梁的特殊情况，建立了基于应变能的骨重塑理论稳定性的一个充分条件。在先前的一份报告中，已表明同一条件在相同情形下是稳定性的必要条件。该重塑方案的特点是，重塑刺激等于应变能密度除以体积密度或表观密度的m次幂，以及弹性模量与体积密度或表观密度的n次幂成正比。为使重塑方案对于轴向力和弯矩作用下的弹性梁稳定，已确定m必须大于n这一条件不仅是必要的，而且是充分的。
