On vectorially parameterized natural strain measures of the non-linear Cosserat continuum

AbstractThe natural Lagrangian stretch and wryness tensors of the non-linear Cosserat continuum are expressed in terms of the general finite rotation vector. These expressions are then specialized for seven particular definitions of the rotation vectors known in the literature. It is expected that some of the vectorially parameterized strain measures derived here may be more convenient than others in specific applications

Existence theorems in the geometrically non-linear 6-parametric theory of elastic plates

In this paper we show the existence of global minimizers for the geometrically exact, non-linear equations of elastic plates, in the framework of the general 6-parametric shell theory. A characteristic feature of this model for shells is the appearance of two independent kinematic fields: the translation vector field and the rotation tensor field (representing in total 6 independent scalar kinematic variables). For isotropic plates, we prove the existence theorem by applying the direct methods of the calculus of variations. Then, we generalize our existence result to the case of anisotropic plates. We also present a detailed comparison with a previously established Cosserat plate model.Comment: 19 pages, 1 figur

Linear Micropolar Elasticity Analysis of Stresses in Bones under Static Loads

We discuss the finite element modeling of porous materials such as bones using the linear micropolar elasticity. In order to solve static boundary-value problems, we developed new finite elements, which capture the micropolar behavior of the material. Developed elements were implemented in the commercial software ABAQUS. The modeling of a femur bone with and without implant under various stages of healing is discussed in details.Рассматривается моделирование таких пористых материалов, как кость, методом конечных элементов с помощью линейной микрополярной теории упругости. Для решения статических краевых задач разработаны новые конечные элементы, которые воспринимают микрополярное поведение этого материала. Разработанные элементы были реализованы в коммерческом программном комплексе ABAQUS. Рассматривается моделирование бедренной кости с имплантатом и без него на различных стадиях заживлени

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

Thermomechanics of shells undergoing phase transition

International audienceThe resultant, two-dimensional thermomechanics of shells undergoing diffusionless, displacive phase transitions of martensitic type of the shell material is developed. In particular, we extend the resultant surface entropy inequality by introducing two temperature fields on the shell base surface: the referential mean temperature and its deviation, with corresponding dual fields: the referential entropy and its deviation. Additionally, several extra surface fields related to the deviation fields are introduced to assure that the resultant surface entropy inequality be direct implication of the entropy inequality of continuum thermomechanics. The corresponding constitutive equations for thermoelastic and thermoviscoelastic shells of differential type are worked out. Within this formulation of shell thermomechanics, we also derive the thermodynamic continuity condition along the curvilinear phase interface and propose the kinetic equation allowing one to determine position and quasistatic motion of the interface relative to the base surface. The theoretical model is illustrated by two axisymmetric numerical examples of stretching and bending of the circular plate undergoing phase transition within the range of small deformations

On natural strain measures of the non-linear micropolar continuum

AbstractWe discuss three different ways of defining the strain measures in the non-linear micropolar continuum: (a) by a direct geometric approach, (b) considering the strain measures as the fields required by the structure of local equilibrium conditions, and (c) requiring the strain energy density of the polar-elastic body to satisfy the principle of invariance under superposed rigid-body deformations. The geometric approach (a) generates several two-point deformation measures as well as some Lagrangian and Eulerian strain measures. The ways (b) and (c) allow one to choose those Lagrangian strain measures which satisfy the additional mechanical requirements. These uniquely selected relative strain measures are called the natural ones. All the strain measures discussed here are formulated in the general coordinate-free form. They are valid for unrestricted translations, stretches and changes of orientations of the micropolar body, and are required to identically vanish in the absence of deformation. The relation of the Lagrangian stretch and wryness tensors derived here to the ones proposed in the literature is thoroughly discussed

Propagation of linear compression waves through plane interfacial layers and mass adsorption in second gradient fluids

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