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.

A very good knowledge of material properties is required in the analysis of severe plastic deformation problems in which the classical material processing methods are accelerated by the application of the additional cyclic load. A general fuzzy logic-based approach is proposed for the analysis of experimental and numerical data in this paper. As an application of the fuzzy analysis, the calibration of Chaboche–Lemaitre model hardening parameters of PA6 aluminum is considered here. The experimental data obtained in a symmetrical strain-controlled cyclic tension–compression test were used to estimate the material’s hardening parameters. The numerically generated curves were compared to the experimental ones. For better fitting of numerical and experimental results, the optimization approach using the least-square method was applied. Unfortunately, commonly accepted calibration methods can provide various sets of hardening parameters. In order to choose the most reliable set, the fuzzy analysis was used. Primarily selected values of hardening parameters were assumed to be fuzzy input parameters. The error of the hysteresis loop approximation for each set was used to compute its membership function. The discrete value of this error was obtained in the defuzzification step. The correct selections of hardening parameters were verified in ratcheting and mean stress relaxation tests. The application of the fuzzy analysis has improved the convergence between experimental and numerical stress–strain curves. The fuzzy logic allows analyzing the variation of elastic–plastic material response when some imprecisions or uncertainties of input parameters are taken into consideration.

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In the framework of the couple stress theory, we discuss the effective elastic properties of a metal open-cell foam. In this theory, we have the couple stress tensor, but the microrotations are fully described by displacements. To this end, we performed calculations for a representative volume element which give the matrices of elastic moduli relating stress and stress tensors with strain and microcurvature tensors.

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.