On strength analysis of highly porous materials within the framework of the micropolar elasticity

We discuss the finite element approach to modelling of static deformations of porous materials such as foams, beam lattices, and others within the linear micropolar elasticity. It is known that the micropolar elasticity may be used for microstructured solids and fluids since it can forecast size-effect near geometrical singularities such as holes, notches, small contact areas of two solids. Within the micropolar elasticity the translational and rotational interactions of the material particles can be taken into account. Here we present the recent developments in the theory of finite elements calculations for micropolar solids in order to capture the stress behaviour in the vicinity of geometric singularities such as holes, notches, imperfections or contact areas. The fundamental equations of the micropolar continuum are presented. The FEM implementation in micropolar elasticity is given. The new 8-node hybrid micropolar isoparametric element and its implementation in ABAQUS are introduced. The solutions of few 3D benchmark problems of the micropolar elasticity are given. Among them are analysis of stresses and couple stresses near notches and holes, contact problem of parabolic stamp and half space. The main attention is paid to modelling of interaction between a biodegradable porous implant and a trabecular bone. Comparison of classical and micropolar solutions is carefully discussed. Comparison of classical and micropolar solutions is discussed. Numerical tests have shown that couple stress appears almost in the vicinity of geometrical singularities. It is shown that micropolar elasticity allows to obtain better results for domains with microstructures and singularities than classical theory of elasticity

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

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.The research received funding from the People Program (Marie Curie ITN transfer) of the European Union’s Seventh Framework Programme for research, technological development and demonstration under grant agreement No. PITN-GA-2013- 606878

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

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

Wpływ lokalizacji śruby na dokręcanie na odpowiedź korową podczas szybkiego rozszerzania się szczęki

Rapid maxillary expansion is employed for the treatment of cross-bite and deficiency of transversal dimension of the maxilla in patients with and without cleft of palate and lip. The aim of this study is the finite-element analysis of stresses and displacements of skull, with and without unilateral cleft, after application of the HYRAX orthodontic device. Three different constructions of the orthodontic Hyrax device with different positions of the screw - in the occlusal horizontal plane, near occlusal horizontal plane and near the palate - are considered. Application of the orthodontic device corresponds to the rotation of the screw on one-quarter turn. It is established that the screw position significantly affects the stress patterns in skull and displacements of the cranium with and without unilateral palate cleft. Depending on the construction of the orthodontic appliance, the maxilla halves in the transversal plane are unfolded or the whole skull is entirely rotated in the sagittal plane. The obtained results can be used for designing of orthodontic appliances with the Hyrax screw, as well as for planning of osteotomies during the surgical assistance of the rapid maxillary expansion.Do leczenia przekrwienia i niedoboru wymiarów przekroju poprzecznego szczęki u chorych z rozszczepem lub bez rozszczepu podniebienia i wargi stosowana jest szybka ekspandacja szczęki. Celem tego badania jest analiza naprężeń oraz przemieszczeń czaszki, z/bez jednostronnego rozszczepu, po zastosowaniu urządzenia ortodontycznego HYRAX. Uwzględniane są trzy różne konstrukcje przyrządu HYRAX z różnymi pozycjami śruby - w płaszczyźnie poziomej zgryzu, w pobliżu płaszczyzny poziomej okluzji i pod podniebieniem. Ustalono, że pozycja śruby w znaczący sposób wpływa na rozkłady przemieszczeń i naprężeń w czaszce z/bez jednostronnego rozszczepu podniebienia. W zależności od konstrukcji urządzenia ortodontycznego przemieszczane są połówki szczęki w płaszczyźnie poprzecznej lub cała czaszka jest całkowicie obracana w płaszczyźnie strzałkowej. Uzyskane wyniki mogą być wykorzystane do projektowania urządzeń ortodontycznych za pomocą śruby Hyrax, a także do planowania osteotomii podczas chirurgicznego wspomagania szybkiego rozszerzania się szczęki