Boundary Integral Method in the Theory of Bone Thermoporoelasticity
The concept of porous media is used in many areas of engineering and applied science (e.g., biology, biophysics, biomechanics). The double porosity model would consider the bone fluid pressure in the vascular porosityand the bone fluid pressure in the lacunar-canalicular porosity. It is an effective and useful model for deformation-driven bone fluid movement in bone tissue.
In the present paper, we shall consider the linear theory of bone thermoelasticity. The system of equations of this theory is first set up starting from the equations of the theory of thermoelasticity for solids with double porosity, and the following results are obtained: the fundamental solution of equations of steady vibrations is constructed by means of elementary functions and its basic properties are established, the GreenвЂ™s formulas and Somigliana-type integral representation of regular vector and classical solution of equations of steady vibrations are obtained, the uniqueness theorems for the internal and external boundary value problems (BVPs) of steady vibrations are proved, the basic properties of surface and volume potentials are established, and finally, the existence of classical solutions of the BVPs by means of the boundary integral method and the theory of singular integral equations are proved.
The journal Biomath Communications is an open access journal. All published articles are immeditely available online and the respective DOI link activated. All articles can be access for free and no reader registration of any sort is required. No fees are charged to authors for article submission or processing. Online publications are funded through volunteer work, donations and grants.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).