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Tempered martensitic steels with a high chromium content are used for power plant components at elevated temperatures under creep–fatigue conditions. In order to model the complex mechanical behavior of the alloy X20CrMoV12-1, a phase mixture model is used. This model is based on the distinction of hard and soft constituents, which are connected via an iso-strain approach. Nonlinear kinematic hardening and softening effects are taken into account by introducing a backstress and a softening variable. This paper focuses on the numerical implementation of the phase mixture model, i.e., the stress update algorithm and the consistent tangent operator. For implicit time integration of the governing equations, the backward Euler method in combination with Newton–Raphson iterations is applied. The model is implemented as user material subroutine into the commercial finite element code ABAQUS. For verification, several benchmarks considering uniaxial and multi-axial stress states are presented and analyzed. Furthermore, a thermo-mechanical fatigue test based on a typical sequence of start-ups and shutdowns of power plants is simulated.

This work is devoted to elastic properties of two-dimensional materials. A triangular crystal lattice was considered as an example of the two-dimensional structure. In-plane elastic properties of such a lattice with Lennard–Jones interaction among the particles were investigated as the functions of the curvature radius in three-dimensional space. It was shown that torque interaction between the particles taken into account in addition to the classical force interaction adds nonzero bending rigidity to the lattice. This bending rigidity was obtained as a function of the parameters of the interatomic bond stiffness. Dependence of bending rigidity on crystal lattice curvature was investigated.

The theory of plasticity operates with different yield criteria of incompressible behavior for isotropic materials. Mostly known are the criteria of Tresca, Schmidt-Ishlinsky and von Mises. The first two criteria have a hexagonal symmetry, and the criterion of von Mises has a rotational symmetry in the π-plane. All these criteria do not distinguish between tension and compression (no strength differential effect), but numerous problems are treated in the engineering practice using these criteria. Within this paper, the yield criteria with hexagonal symmetry for isotropic incompressible materials are compared. For this purpose, their geometries in the π-plane will be presented in polar coordinates. The radii at the angles of 15◦ and 30◦ will be related to the radius at 0◦. Based on these two relations, well-known criteria will be shown in one diagram. The extreme shapes of the yield surfaces are restricted by two criteria: the unified yield criterion (UYC) and the multiplicative ansatz criterion (MAC). The examinations of the UYC and MAC depict a linear combination of these extreme yield surfaces. The resulting criterion with two parameters describes all possible convex forms of hexagonal symmetry. On the other hand, this criterion has one disadvantage: It is not possible to solve explicitly the equation for the equivalent stress. Other known criteria (Sokolovsky, Ishlinsky-Ivlev, Dodd-Naruse, Drucker) are depicted in the proposed diagram and compared with the above mentioned criteria. Further criteria are derived from the consideration of solids with orthogonal symmetry planes in the shear stress space. New criteria are introduced for practical applications. The constraints of convexity are established for them. The proposed consideration of the yield criteria simplifies the selection of a proper criterion. The extreme solutions for the analysis of construction parts can be found using these criteria.

This paper presents a thermodynamic theory for elastic rods using the model of directed curves. In this model, the thin rod-like bodies are described as deformable curves with a triad of rigidly rotating vectors attached to each point. To account for the thermal effects in rods, we introduce two independent temperature fields: the absolute temperature field and the temperature deviation field. We present a complete derivation of the non-linear equations of thermoelastic rods, starting from the principles of thermodynamics. Finally, we prove the uniqueness of solution to the linearized equations of thermoelastodynamics for rods.

Starting with the Eshelby-type conservation law, path-independent line and surface integrals that allow the comparison of averaged strain-energy densities in the notch area for linear elastic and non-linear elastic material behaviors are derived. The analysis shows that a point (two-dimensional problems) and a curve (three-dimensional problems) exist on the notch boundary, where the values of the strain-energy densities are almost the same. The conditions are discussed, for which the equality of the strain energies is guaranteed. The theoretical results are illustrated by two finite-element examples.

Considering the viscoelastic behavior of polymer foams a new plate theory based on the direct approach is introduced and applied to plates composed of functionally graded materials (FGM). The governing two-dimensional equations are formulated for a deformable surface, the viscoelastic stiffness parameters are identified assuming linear-viscoelastic material behavior. The material properties are changing in the thickness direction. Solving some problems of the global structural analysis it will be demonstrated that in some cases the results significantly differ from the results based on the Kirchhoff-type theory.

The classical solution of the steady-state creep problem for a pressurized thick-walled cylinder is based on the power law constitutive equation. Several heat resistant steels show, however, the linear dependence of the creep rate on the applied stress within a certain stress range. In this paper we apply an extended constitutive equation which includes both the linear and the power law stress dependencies. The material constants are identified for the 9Cr1MoVNb steel at 600 °C. We recall the boundary value problem of steady-state creep for the thick cylinder under the plane strain condition. We present an approximate solution illustrating the stress redistributions as a result of the creep process. The analysis shows that for the certain range of the internal pressure both the linear and the power law creep must be taken into account. In this case the results according to the extended constitutive model essentially differ from the classical ones. The obtained solution is also applied to verify the developed user-defined creep material subroutine inside a commercial finite element code.

Classical and refined plate theories derived from linear continuum mechanics lead to correct results only if the transverse deflection of the plate is small compared to its thickness. In the case of large deflections, geometrical nonlinearities have to be incorporated. For the classical Kirchhoff plate theory, a suitable extension for moderate rotations has been presented by von Karman in 1911. Starting from the three-dimensional equations of nonlinear continuum mechanics, a family of von Karman-type plate theories is deduced. For the derivation, the kinematical variables are replaced by a series representation and the principle of virtual displacements is used. It can be shown that most plate theories can be obtained from this type of theory and that the kinematical assumptions must fulfill certain conditions to obtain a solvable system of equations.

Basing on the Nadai-Levy and the Vlasov-Kantorovich methods closed and approximate analytical solutions of Mindlin's plate equations in the case of rectangular plates are discussed. For elastic, homogeneous and isotropic plates three unknowns of the governing two-dimensional boundary value problem are formulated as series of products of functions depending on a single coordinate. Specifying the functions for one of the in-plane coordinate directions the governing partial differential equations for a special type of boundary conditions and the principle of virtual displacements for the general case yield a set of ordinary differential equations. The analytical solution of these equations provides expressions for functions depending on the other in-plane coordinate. For plates with simply supported edges for one of the coordinate directions and for arbitrary homogeneous boundary conditions for the other one the Nadai-Levy method provides a closed or exact solution in the sense that the infinite series for displacements and stress resultants can be truncated to obtain any desired accuracy. In the general case of nonsimply supported edges the iterative Vlasov-Kantorovich method yields an approximate analytical solution. Both methods are nonsensitive to a reduction of the thickness with respect to accuracy and represent the boundary layer solutions in terms of exponential functions. Applications to rectangular plates with various types of boundary conditions are presented.