Application of the Micropolar Theory to the Strength Analysis of Bioceramic Materials for Bone Reconstruction

Abstract

The application of the linear micropolar theory to the strength analysis of bioceramic materials for bone reconstruction is described. Micropolar elasticity allows better results to be obtained for microstructural and singular domains as compared to the classical theory of elasticity. The fundamental equations of the Cosserat continuum are cited. The description of FEM implementation of micropolar elasticity is given. The results of solving selected 3D test problems are presented. Comparison of classical and micropolar solutions is discussed.

On mechanically driven biological stimulus for bone remodeling as a diffusive phenomenon

“…Some continuum models have been imagined which introduce generalized structured continua, as those involving the concept of mixtures (Franciosi et al 2018;Spagnuolo et al 2017;Ambrosi et al 2010;Ateshian 2007), or micropolar kinematical descriptors (Goda et al 2014;Yoo and Jasiuk 2006;Diebels and Steeb 2003;Park and Lakes 1986), see also Eremeyev and Pietraszkiewicz 2016;Altenbach and Eremeyev 2015;Eremeyev et al 2013), or deformation energies depending on the second gradient of placement (Giorgio et al 2017a;Madeo et al 2013Madeo et al , 2012Seppecher 2000Seppecher , 1996. It is natural to imagine that their use may be required to capture the most complex aspects of growing tissue biomechanics.…”

Novel description of bone remodelling including finite memory effect, stimulation and signalling mechanisms

“…The current model will be tested in cases of analysis of the interaction between bone substitute material, living tissue, and implant. However, in order to study the behaviour of bone substitute material and implant, different constitute models should be included in our formulation, for example, models of truss and pantographic-like microstructures, see, e.g., [1,11,16,21,31,56]; models including micropolar theory, see, e.g., [2,[22][23][24]; and models including higher gradients, see, e.g., Dell'Isola et al [19,20].…”

On Finite Element Computations of Contact Problems in Micropolar Elasticity

“…Using the presented above finite element we analyzed few 3D static problems for solids with certain singularities such as notch, hole, or small contact area for the contact problem of two solids [17]. For comparison of solutions with the linear elasticity we used the fact that the micropolar elasticity provides the same solutions as classic elasticity if we assume specific form of microrotations ( = 0) or for specific set of elastic moduli that is without coupling ( = 0).…”

“…Within the Cosserat continuum model the translations and rotations determine the kinematics of the medium and the stress and couple stress tensors are introduced. The micropolar properties of material may be important near singularities or to describe observed experimentally size-effect [16][17][18][19]. Let us also note that for such complex media even more general models of continuum mechanics such as gradient elasticity may be useful; see, for example, [20][21][22][23][24].…”