An Exact Axisymmetric Solution in Anisotropic Plasticity

A hollow cylinder of incompressible material obeying Hill’s orthotropic quadratic yield criterion and its associated flow rule is contracted on a rigid cylinder inserted in its hole. Friction occurs at the contact surface between the hollow and solid cylinders. An axisymmetric boundary value problem for the flow of the material is formulated and solved, and the solution is in closed form. A numerical technique is only necessary for evaluating ordinary integrals. The solution may exhibit singular behavior in the vicinity of the friction surface. The exact asymptotic representation of the solution shows that some strain rate components and the plastic work rate approach infinity in the friction surface’s vicinity. The effect of plastic anisotropy on the solution’s behavior is discussed.

Numerical studies on the self-heating phenomenon of elastomers based on finite thermoviscoelasticity

Due to their typical material characteristics, elastomer components are used in almost all areas of engineering. In many cases, these components are subject to large cyclic deformations which result in hysteresis and dissipation-induced self-heating. Further they are exposed to varying ambient temperatures. Increased component temperatures can lead to the loss of a function or to total failure. Therefore, it is important to understand the causes and influences of critical temperatures and to identify them early in the development process under the condition of efficient applicability. In addition to the calculation time and accuracy, this also includes the experimental effort required to identify the material parameters and perform validation measurements. Within this work, the phenomenon of dissipative heating in elastomers is investigated in a numerical study using a modified model of the finite thermoviscoelasticity. For this purpose, a sufficiently simple material model was formulated and implemented under the assumption of the quasi-incompressible material behaviour. Based on this, the type and the characteristic features of the self-heating effect are specifically considered, and its dependence on thermal and mechanical initial and boundary conditions is studied. Thus, a new suitable parameter is introduced, which is particularly useful to identify critical loads. Analogously, the identification of dissipation-sensitive temperature ranges is presented. The utility of the general steadystate equilibrium condition as initial condition is also shown. Furthermore, the influence of the material properties on the steadystate equilibrium is demonstrated for the first time through parameter studies. Based on these findings, recommendations for modelling, calculation and experimental parameterisation are proposed.

A novel semi-implicit scheme for elastodynamics and wave propagation in nearly and truly incompressible solids

This paper presents a novel semi-implicit scheme for elastodynamics and wave propagation problems in nearly and truly incompressible material models. The proposed methodology is based on the efficient computation of the Schur complement for the mixed displacement-pressure formulation using a lumped mass matrix for the displacement field. By treating the deviatoric stress explicitly and the pressure field implicitly, the critical time step is made to be limited by shear wave speed rather than the bulk wave speed. The convergence of the proposed scheme is demonstrated by computing error norms for the recently proposed LBB-stable BT2/BT1 element. Using the numerical examples modelled with nearly and truly incompressible Neo-Hookean and Ogden material models, it is demonstrated that the proposed semi-implicit scheme yields significant computational benefits over the fully explicit and the fully implicit schemes for finite strain elastodynamics simulations involving incompressible materials. Finally, the applicability of the proposed scheme for wave propagation problems in nearly and truly incompressible material models is illustrated.

Experimental Study on the Design and Behavior of Concrete Pavement Joint Sealants

Joints in concrete pavement are intended to provide freedom of movement in a concrete slab relative to the volumetric effects. Changes such as this can occur owing to drying shrinkage, temperature changes, and moisture differences that develop within the slab. A key reason to seal the rigid pavement joints is to prevent, or at least reduce, the amount of water from rainfall events infiltrating the pavement structure, which can ultimately contribute to subbase erosion, loss of support, and the build-up of a fine, incompressible material on the face of the joint. The strength of the joint sealant bond and stress of the interface between the sealant and the face of the joint reservoir play important roles in joint sealant failure. Thus, in this research, experimental coupling tests were conducted to investigate the geometric characteristics of the sealant/joint reservoir design. The stress–strain relationship on the interface was investigated according to its geometry, both with regard to the shape factor (SF) and the degree of curvature (DoC). The SF and DoC were evaluated through a tensile test of the joint sealant based on these geometric characteristics. Also discussed are the shape factors (SFs) of the joint sealant currently being recommended, the SF most appropriate for a narrow-width joint, and the surface finish of the joint sealant. Based on this study, the effects of sealant geometries (i.e., SF and DoC) should be considered during design and installation. Also, further research into more realistic SFs for narrow-width joints and self-leveling sealants is recommended.

Theoretical Investigation of the Electronic, Elastic, Vibration, Thermodynamic and Transport Properties of PtAsP Mixed Pyrite Phase

Theoretical investigation on the elastic constants, phonon frequencies, thermodynamic and the transport properties of PtAsP mixed cubic pyrite phase was performed using the first-principles calculations based on the density functional theory. The calculated equilibrium crystal parameter is in excellent agreement with experimental data. The derived bulk and shear moduli are much higher than other theoretical data, suggesting that PtAsP may be a highly incompressible material. The detailed analyses of the electronic structures showed that PtAsP is an indirect energy gap compound and is elastically and dynamically stable. By using the harmonic Debye model, some thermodynamic properties including vibration free energy and constant volume heat capacity were calculated. The evaluation of the transport properties showed that PtAsP is a p-type material with capacity for improved performance when its charge carrier concentration is between 1016 cm3 and 1018 cm3.

Formulation of the problem of finite deformations of a semi-toroidal shell under the internal pressure

Рассматривается нелинейно-упругая осесимметричная модель полутороидальной оболочки, закрепленной по основаниям, под действием внутреннего давления. Предложен подход к формулировке мер, определяющих напряженно-деформированное состояния оболочки. Для несжимаемого материала получена замкнутая система нелинейных обыкновенных дифференциальных уравнений относительно неизвестных функций. С помощью метода конечных элементов дана оценка напряженно-деформированного состояния оболочки в случае малых деформаций. A nonlinear elastic axisymmetric model of a semi-toroidal shell fixed at the bases under the internal pressure is considered. An approach to the formulation of measures that determine the stress-strain state of the shell is proposed. For an incompressible material, a closed system of nonlinear ordinary differential equations for unknown functions is obtained. The finite element method is used to estimate the stress-strain state of the shell in the case of small deformations.

The effect of large deformation on Poisson’s ratio of brain white matter: An experimental study

A more Accurate description of the mechanical behavior of brain tissue could improve the results of computational models. While most studies have assumed brain tissue as an incompressible material with constant Poisson’s ratio of almost 0.5 and constructed their modeling approach according to this assumption, the relationship between this ratio and levels of applied strains has not yet been studied. Since the mechanical response of the tissue is highly sensitive to the value of Poisson’s ratio, this study was designed to investigate the characteristics of the Poisson’s ratio of brain tissue at different levels of applied strains. Samples were extracted from bovine brain tissue and tested under unconfined compression at strain values of 5%, 10%, and 30%. Using an image processing method, the axial and transverse strains were measured over a 60-s period to calculate the Poisson’s ratio for each sample. The results of this study showed that the Poisson’s ratio of brain tissue at strain levels of 5% and 10% was close to 0.5, and assuming brain tissue as an incompressible material is a valid assumption at these levels of strain. For samples under 30% compression, this ratio was higher than 0.5, which could suggest that under strains higher than the brain injury threshold (approximately 18%), tissue integrity was impaired. Based on these observations, it could be concluded that for strain levels higher than the injury threshold, brain tissue could not be assumed as an incompressible material, and new material models need to be proposed to predict the material behavior of the tissue. In addition, the results showed that brain tissue under unconfined compression uniformly stretched in the transverse direction, and the bulging in the samples is negligible.

POLAR-SYMMETRIC DEFORMATION OF AN ELASTIC CYLINDER UNDER TEMPERATURE-HUMIDITY EXPOSURE

The actual scientific and technical problem of polar-symmetric deformation of an elastic cylinder under conditions of temperature and humidity influences is considered. An exact analytical solution to this problem is obtained with the determination of unambiguous expressions for stresses, deformations and radial displacement. The obtained solution allows solving this problem for an incompressible material with μ = 1/2 as a special case.