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Thermodynamic formulations of the growth of solid bodies subjected to electromechanical interactions and application to bone external and internal remodeling
Continuum Mechanics and Thermodynamics ( IF 1.9 ) Pub Date : 2021-03-21 , DOI: 10.1007/s00161-021-00986-5
J. F. Ganghoffer , X. N. Do , A. Ibrahimbegovic

The thermodynamics of open systems exchanging mass, heat, energy and entropy with their environment is examined as a convenient unifying framework to describe the evolution of growing solid bodies subjected to electromechanical stimulations in the context of volumetric growth. Extending the framework of non-equilibrium thermodynamics to open systems, the balance laws for continuum solid bodies undergoing growth phenomena incorporating mass sources and mass fluxes in the presence of electromechanical stimuli are expressed. As an alternative, general balance laws for growing solid bodies in presence of electromechanical couplings are expressed in generic format without explicit consideration of the transport phenomena and chemical reactions responsible for growth and the production of mass. The proposed formulations are next extended to the writing of flexoelectric models for growing solid bodies. Applications to electrically induced bending of thin plates and to the combine volumetric and surface growth of the diaphyseal part of the femur are provided as two illustrations of the derived state laws and kinetic equations for irreversible phenomena. The paper concludes with the elaboration of a combined internal to external surface growth model for bone remodeling describing surface apposition of mineral and local density changes, incorporating the driving effects of both electrical and mechanical signals.



中文翻译:

经受机电相互作用的固体生长的热力学公式,并应用于骨骼的外部和内部重塑

将开放系统的热力学与环境交换质量,热量,能量和熵,以此作为方便的统一框架,以描述在体积增长的情况下受到机电刺激的增长中的固体的演化。将非平衡热力学的框架扩展到开放系统,表达了连续体固体的平衡定律,该连续体在存在机电刺激的情况下结合了质量源和质量通量而经历了生长现象。作为替代,在没有机电耦合的情况下用于生长固体的一般平衡定律以通用格式表示,而没有明确考虑负责生长和质量产生的传输现象和化学反应。拟议的配方接下来将扩展到用于生长固体的柔电模型的编写。作为对不可逆现象的导出状态定律和动力学方程的两个图解,提供了对薄板的电感应弯曲以及股骨干phy部分的体积和表面结合的组合的应用。本文以结合内部到外部表面生长模型进行骨重建为结尾,描述了矿物质的表面沉积和局部密度变化,并结合了电信号和机械信号的驱动作用。作为对不可逆现象的导出状态定律和动力学方程的两个图解,提供了对薄板的电感应弯曲以及股骨干phy部分的体积和表面结合的组合的应用。本文以结合内部到外部表面生长模型进行骨重建为结尾,描述了矿物质的表面沉积和局部密度变化,并结合了电信号和机械信号的驱动作用。作为对不可逆现象的导出状态定律和动力学方程的两个图解,提供了对薄板的电感应弯曲以及股骨干phy部分的体积和表面结合的组合的应用。本文以结合内部到外部表面生长模型进行骨重建为结尾,描述了矿物质的表面沉积和局部密度变化,并结合了电信号和机械信号的驱动作用。

更新日期:2021-03-22
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