Thermodynamic formulations of the growth of solid bodies subjected to electromechanical interactions and application to bone external and internal remodeling

Abstract

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.