In the paper, preliminary studies on formulation of a new constitutive equation of bone tissue are presented. A bone is modelled as a viscoelastic material. Thus, not only are elastic properties of the bone taken into account, but also both short-term and long-term viscoelastic properties are considered. A potential function is assumed for the bone, constant identification on the basis of experimental stress-strain curve fitting is completed and a preliminary constitutive equation is formulated. The experiments consisted of compressive tests performed on a cuboids-like bone sample of the following dimensions: 10x5x7.52 mm. The specimen was compressed along the highest dimension at the strain rates 0.016 s to the -1 and 0.00016 s to the -1. In addition to this, stress relaxation test was performed to identify long-term viscoelastic constants of bone. In the experiments, only displacement in the load direction was measured. The bone sample was extracted from a bovine femur. The form of the proposed potential function is such that it models a bone as a transversely isotropic material. For the sake of simplicity, it is assumed that the bone is incompressible. After the material constant identification the strain energy function proved to be adequate to describe bone behaviour under compressive load. Due to the fact that the function is convex, the results of the studies can be utilised in modelling of bone tissue in finite element analyses of an implant-bone system. Such analyses are very helpful in the process of a new prosthesis design as one can preoperatively verify the construction of the new implant and optimise its shape.

Analytical and numerical nonlinear solutions for rotating variable-thickness functionally graded solid and annular disks with viscoelastic orthotropic material properties are presented by using the method of successive approximations. Variable material properties such as Young’s moduli, density and thickness of the disk, are first introduced to obtain the governing equation. As a second step, the method of successive approximations is proposed to get the nonlinear solution of the problem. In the third step, the method of effective moduli is deduced to reduce the problem to the corresponding one of a homogeneous but anisotropic material. The results of viscoelastic stresses and radial displacement are obtained for annular and solid disks of different profiles and graphically illustrated. The calculated results are compared and the effects due to many parameters are discussed.

The main purpose of the study is to investigate the mechanical properties around an underground gas storage cavern in bedded salt rock. Firstly, considering the characteristics of the salt rock formation in China, the mechanical model was simplified into a hollow cylinder, which containing non-salt interlayer. In terms of elastic theory, Love displacement function was developed, and the elastic general solution of stress and deformation components were obtained after determining the undetermined coefficients. Under the same condition, numerical simulation was carried out. The validity of the elastic general solution is verified by comparing to numerical simulation results. Furthermore, Based on the feasible general elastic solution, viscoelastic solution was obtained through Laplace transformation and inverse Laplace transform, which could provide reference for the study on the stability and tightness of underground gas storage carven during operation to some extent.

Three-layered, annular plate with viscoelastic core is subjected to loads acting in the plane of the plate facings. One formulates the dynamic, stability problem concerning the action of time-dependent compressive stress on a plate with imperfection. This problem has been solved. One created the basic system of differential equations in which the approximation finite difference method was used for calculations. The essential analysis of the problem was concentrated on evaluation of the influence of the plate imperfection rate and the rate of plate loading growth on the results of calculation of critical parameters at the moment of loss of plate stability. It determines the analysed problem of sensitivity of the plate to imperfection and loading. In the evaluation of the dynamics of this problem, the dynamic factor defined as the quotient of the critical, dynamic load to the static one was used. The idea of dynamic factor and the type of the accepted criterion of the loss of plate stability were taken from the Volmir's work. The observations were confirmed by comparable results of calculations of plate models built in finite element method using the ABAQUS system. The analysis of the stress state in an exemplary plate model calculated in FEM demonstrated the importance of the strength condition in total evaluation of the plate work. One achieved satisfactory correctness of results in both methods.