The paper presents the application of the discrete element method to modelling of granular material filling and discharge in 3D flat-bottomed hopper. A mathematical model, as well as the developed software code, operates with spherical visco-elastic non-cohesive frictional particles. The evolution of granular flow, internal forces and densification (rarefaction) are characterized by macroscopic parameters such as the discharge rates, the porosity fields and the wall pressures, as well as by microscopic evaluations in terms of coordination number, velocity patterns and inter-particle contact forces. It was shown that qualitative characterization of flow may be done even by relatively rough models with small number of particles, which required to be increased, however, for more precise description of the localized phenomena. Unsatisfactory evaluation of the stress peak during discharge is presented as an illustrative example. The main focus of the paper is the analysis of particle friction effect and the consistency of micro and macro-phenomena in the time-dependent flow process.

Normal shock wave, terminating a local supersonic area on an airfoil, not only limits aerodynamic performance but also becomes a significant source of a high-speed impulsive noise on the rotor blade of a helicopter. It is proposed to apply passive control to disintegrate the shock wave by smearing pressure gradients created by the shock. Details of the flow structure obtained by this method are studied numerically. A new boundary condition of a perforated wall is verified against experimental data for a passive control of the shock wave in a channel flow and on an airfoil. This method of shock wave disintegration is proven to work for internal flows in transonic nozzles and appears to be effective for transonic airfoils as well. The substitution of a shock wave by a gradual compression changes completely the source of the high-speed impulsive noise and bears potential of its reduction.

This paper presents vector, scalar and variational forms of motion/equilibrium equations of atomic lattices. An automated method is suggested for constructing the matrices and vectors of equations based on summing the corresponding local matrices and vectors of atomic pairs. The exact expression for the tangential stiffness matrix of an atomic pair is obtained where both the change in the segment length of a straight line connecting atoms in this pair and rotation of the segment are taken into account.

(Translated from the original paper in Polish by Anna Strek under scientific supervision of Ryszard B. Pecherski) Prof. M.T. Huber (1872-1950)

Imperfect transmission conditions are evaluated in the case of weakly compressible elastic interphase between different bonded elastic materials. It is shown that the corresponding conditions can be different in comparison with those for the elastic compressible interface.

A constitutive theory, finite element formulation and topology optimization for anti-vibration rubber are presented. Many vibration isolators made of rubbers are operating under small oscillatory load superimposed on large static deformation. A~viscoelastic constitutive equation for rubber is proposed considering the influence of large static pre-deformation on the dynamic properties. The proposed model is derived through linearization of Simo's viscoelastic constitutive model and introduction of static deformation correction factor. And then the model is implemented in a finite element code to analyze the behavior of rubber elements under general loading conditions. Dynamic tests are performed in order to verify the model under multi-axial deformation. The computed results by the FEA code are compared with the experimental results and the suggested constitutive equation with static deformation correction factor shows good agreement with the test values. For the stability and low transmissibility of isolation systems, both static and dynamic performance must be concurrently considered in the design process. The continuum-based design sensitivity analyses (DSA) of both the static hyperelastic model and dynamic viscoelastic model are developed. And then the topology optimization methodology is used in order to generate the system layouts considering both the static and dynamic performance.

Material instabilities in fiber-reinforced nonlinearly elastic solids are examined under plane deformation. In particular, the materials under consideration are isotropic nonlinearly elastic models augmented by a function that accounts for the existence of a unidirectional reinforcing. This function describes the anisotropic (transversely isotropic) character of the material and is referred to as a reinforcing model. The onset of failure is signalled by the loss of ellipticity of the governing differential equations. Previous work has dealt with the analysis of specific reinforcing models and has established that the loss of ellipticity for such augmented isotropic materials requires contraction in the reinforcing direction. The loss of ellipticity was related to fiber kinking. Here we generalize these results and establish sufficient conditions for the ellipticity of the governing equations of equilibrium for more general reinforcing models to be guaranteed. We also establish necessary conditions for failure of ellipticity. The incipient loss of ellipticity is interpreted in terms of fiber kinking, fiber de-bonding, fiber splitting and matrix failure in fiber-reinforced composite materials. Attention is restricted to incompressible materials in this paper.

The paper is devoted to the identification and verification of the constitutive description of plastic flow accounting for the hierarchy of shear banding, which is proposed in the companion paper [1]. The numerical identification was carried out with use of the experimental results obtained in channel-die test for polycrystalline copper [2]. To verify the identified model, numerical simulation of the forging process was made and the calculated values of load subjected to the punch versus its displacement were compared with pertinent experimental data given in [11].

A domain of influence theorem is proved for a linear thermoelastic solid with a Cattaneo's type heat conduction law and a scalar internal variable. The obtained result is applied to prove the hyperbolicity of a semiempirical heat conduction theory, describing the propagation of thermal waves in crystals at low temperatures.

We analyze the stability of a homogeneous solution of coupled nonlinear equations governing simple shearing deformations of a strain-rate gradient-dependent thermoviscoplastic body in which thermal disturbances propagate at a finite speed. The homogeneous solution is perturbed by an infinitesimal amount and equations linear in the perturbation variables axe derived. Conditions for these perturbations to grow are deduced. The shear band spacing, L s , is defined as L s = inf t 0 ≥0 (2 π / ξ m ( t 0 )) where ξ m is the wave number of the perturbation introduced at time t 0 that has the maximum growth rate at time t 0 . It is found that the thermal relaxation time (i.e. the ratio of the coefficient of the second time-derivative of the temperature in the heat equation to that of the first time-derivative) significantly affects the shear band spacing and the value of t 0 for which ξ m ( t 0 ) is maximum.