Showing papers in "Archive of Applied Mechanics in 2010"

On generalized Cosserat-type theories of plates and shells: a short review and bibliography

Abstract: One of the research direction of Horst Lippmann during his whole scientific career was devoted to the possibilities to explain complex material behavior by generalized continua models. A representative of such models is the Cosserat continuum. The basic idea of this model is the independence of translations and rotations (and by analogy, the independence of forces and moments). With the help of this model some additional effects in solid and fluid mechanics can be explained in a more satisfying manner. They are established in experiments, but not presented by the classical equations. In this paper the Cosserat-type theories of plates and shells are debated as a special application of the Cosserat theory.

A higher-order theory for static and dynamic analyses of functionally graded beams

Abstract: The higher-order theory is extended to functionally graded beams (FGBs) with continuously varying material properties. For FGBs with shear deformation taken into account, a single governing equation for an auxiliary function F is derived from the basic equations of elasticity. It can be used to deal with forced and free vibrations as well as static behaviors of FGBs. A general solution is constructed, and all physical quantities including transverse deflection, longitudinal warping, bending moment, shear force, and internal stresses can be represented in terms of the derivatives of F. The static solution can be determined for different end conditions. Explicit expressions for cantilever, simply supported, and clamped-clamped FGBs for typical loading cases are given. A comparison of the present static solution with existing elasticity solutions indicates that the method is simple and efficient. Moreover, the gradient variation of Young’s modulus and Poisson’s ratio may be arbitrary functions of the thickness direction. Functionally graded Rayleigh and Euler–Bernoulli beams are two special cases when the shear modulus is sufficiently high. Moreover, the classical Levinson beam theory is recovered from the present theory when the material constants are unchanged. Numerical computations are performed for a functionally graded cantilever beam with a gradient index obeying power law and the results are displayed graphically to show the effects of the gradient index on the deflection and stress distribution, indicating that both stresses and deflection are sensitive to the gradient variation of material properties.

Acceleration waves and ellipticity in thermoelastic micropolar media

Abstract: Acceleration waves in nonlinear thermoelastic micropolar media are considered. We establish the kinematic and dynamic compatibility relations for a singular surface of order 2 in the media. An analogy to the Fresnel–Hadamard–Duhem theorem and an expression for the acoustic tensor are derived. The condition for acceleration wave’s propagation is formulated as an algebraic spectral problem. It is shown that the condition coincides with the strong ellipticity of equilibrium equations. As an example, a quadratic form for the specific free energy is considered and the solutions of the corresponding spectral problem are presented.

Dynamics and stability of turbocharger rotors

Abstract: The paper discusses the bifurcation and stability behavior of (automotive) turbochargers with full-floating ring bearings. Turbocharger rotors exhibit a highly nonlinear behavior due to the nonlinearities introduced by the floating ring bearings. A flexible multibody model of the rotor/bearing system is presented. Numerical run-up simulations are compared with corresponding test rig measurements. The nonlinear oscillation effects are thoroughly investigated by means of simulated and measured rotor vibrations. The influence of various system parameters on the bifurcation behavior of the rotor/bearing system is analyzed. The article examines rotors supported in full-floating ring bearings with plain circular bearing geometry in the inner and outer oil gap. By recapitulating the well-known oil whirl and oil whip phenomena for single and double oil film bearings, the paper gives an overview on the fundamental dynamic effects occurring in turbocharger systems.

Stress analysis of a functional graded material plate with a circular hole

Abstract: This paper is to study the two-dimensional stress distribution of a functional graded material plate (FGMP) with a circular hole under arbitrary constant loads. With using the method of piece-wise homogeneous layers, the stress distribution of the functional graded material plate having radial arbitrary elastic properties is derived based on the theory of the complex variable functions. As examples, numerical results are presented for the FGMPs having given radial Young’s modulus or Poisson’s ratio. It is shown that the stress is greatly reduced as the radial Young’s modulus increased, but it is less influenced by the variation of the Poisson’s ratio. Moreover, it is also found that the stress level varies when the radial Young’s modulus increased in different ways. Thus, it can be concluded that the stress around the circular hole in the FGMP can be effectively reduced by choosing the proper change ways of the radial elastic properties.

Wave localization in randomly disordered layered three-component phononic crystals with thermal effects

Abstract: In this paper, the propagation and localization of elastic waves in randomly disordered layered three-component phononic crystals with thermal effects are studied. The transfer matrix is obtained by applying the continuity conditions between three consecutive sub-cells. Based on the transfer matrix method and Bloch theory, the expressions of the localization factor and dispersion relation are presented. The relation between the localization factors and dispersion curves is discussed. Numerical simulations are performed to investigate the influences of the incident angle on band structures of ordered phononic crystals. For the randomly disordered ones, disorders of structural thickness ratios and Lame constants are considered. The incident angles, disorder degrees, thickness ratios, Lame constants and temperature changes have prominent effects on wave localization phenomena in three-component systems. Furthermore, it can be observed that stopbands locate in very low-frequency regions. The localization factor is an effective way to investigate randomly disordered phononic crystals in which the band structure cannot be described.

Transient thermal stresses in two-dimensional functionally graded thick hollow cylinder with finite length

Abstract: In this paper transient thermal stresses in a thick hollow cylinder with finite length made of two-dimensional functionally graded material (2D-FGM) based on classical theory of thermoelasticity are considered. The volume fraction distribution of materials, geometry and thermal load are assumed to be axisymmetric but not uniform along the axial direction. The finite element method with graded material properties within each element is used to model the structure. Temperature, displacements and stress distributions through the cylinder at different times are investigated. Also the effects of variation of material distribution in two radial and axial directions on the thermal stress distribution and time responses are studied. The achieved results show that using 2D-FGM leads to a more flexible design so that time responses of structure, maximum amplitude of stresses and uniformity of stress distributions can be modified to a required manner by selecting suitable material distribution profiles in two directions.

Application of He's homotopy perturbation method to nonlinear shock damper dynamics

Abstract: In order to obtain the equations of motion of vibratory systems, we will need a mathematical description of the forces and moments involved, as function of displacement or velocity, solution of vibration models to predict system behavior requires solution of differential equations, the differential equations based on linear model of the forces and moments are much easier to solve than the ones based on nonlinear models, but sometimes a nonlinear model is unavoidable, this is the case when a system is designed with nonlinear spring and nonlinear damping. Homotopy perturbation method is an effective method to find a solution of a nonlinear differential equation. In this method, a nonlinear complex differential equation is transformed to a series of linear and nonlinear parts, almost simpler differential equations. These sets of equations are then solved iteratively. Finally, a linear series of the solutions completes the answer if the convergence is maintained; homotopy perturbation method (HPM) is enhanced by a preliminary assumption. The idea is to keep the inherent stability of nonlinear dynamic; the enhanced HPM is used to solve the nonlinear shock absorber and spring equations.

Atrial and ventricular fibrillation: computational simulation of spiral waves in cardiac tissue

Abstract: This manuscript proposes a novel, efficient finite element solution technique for the computational simulation of cardiac electrophysiology. We apply a two-parameter model that is characterized through a fast action potential and a slow recovery variable. The former is introduced globally as a nodal degree of free- dom, whereas the latter is treated locally as internal variable on the integration point level. This particular discretization is extremely efficient and highly modular since different cardiac cell models can be incorporated straightforwardly through only minor local modifications on the integration point level. In this manuscript, we illustrate the algorithm in terms of the Aliev-Panfilov model for cardiomyocytes. To ensure unconditional stability, a backward Euler scheme is applied to discretize the evolution equation for both the action potential and the recovery variable in time. To increase robustness and guarantee optimal quadratic convergence, we suggestanincrementaliterativeNewton-Raphsonschemeandillustratetheconsistentlinearizationoftheweak form of the excitation problem. The proposed algorithm is illustrated by means of two- and three-dimensional examples of re-entrant spiral and scroll waves characteristic of cardiac arrhythmias in atrial and ventricular fibrillation.

Free vibrations of rotating composite conical shells with stringer and ring stiffeners

Abstract: In this paper, an analytical solution for the free vibration of rotating composite conical shells with axial stiffeners (stringers) and circumferential stiffener (rings), is presented using an energy-based approach. Ritz method is applied while stiffeners are treated as discrete elements. The conical shells are stiffened with uniform interval and it is assumed that the stiffeners have the same material and geometric properties. The study includes the effects of the coriolis and centrifugal accelerations, and the initial hoop tension. The results obtained include the relationship between frequency parameter and circumferential wave number as well as rotating speed at various angles. Influences of geometric properties on the frequency parameter are also discussed. In order to validate the present analysis, it is compared with other published works for a non-stiffened conical shell; other comparison is made in the special case where the angle of the stiffened conical shell goes to zero, i.e., stiffened cylindrical shell. Good agreement is observed and a new range of results is presented for rotating stiffened conical shells which can be used as a benchmark to approximate solutions.

Two-temperature generalized thermoelastic infinite medium with cylindrical cavity subjected to moving heat source

Abstract: In this work, a problem of thermoelastic interactions in an elastic infinite medium with cylindrical cavity thermally shocked at its bounding surface and subjected to moving heat source with constant velocity has been solved. The governing equations are taken in the context of two-temperature generalized thermoelasticity theory (Youssef model). The analytical solution with direct approach in the Laplace transforms domain has been obtained. The derived analytical expressions have been computed for specific situations. Numerical results for the dynamical and conductive temperatures, stress, strain, and displacement are represented graphically with comparisons by one-temperature generalized thermoelasticity (Lord–Shulman model).

Mechanical competence of bone-implant systems can accurately be determined by image-based micro-finite element analyses

Abstract: The precise failure mechanisms of bone implants are still incompletely understood. Micro-computed tomography in combination with finite element analysis appears to be a potent methodology to determine the mechanical stability of bone-implant constructs. To assess this microstructural finite element (μFE) analysis approach, pull-out tests were designed and conducted on ten sheep vertebral bodies into which orthopedic screws were inserted. μFE models of the same bone-implant constructs were then built and solved, using a large-scale linear FE-solver. μFE calculated pull-out strength correlated highly with the experimentally measured pull-out strength (r2 = 0.87) thereby statistically supporting the μFE approach. These results suggest that bone-implant constructs can be analyzed using μFE in a detailed and unprecedented way. This could potentially facilitate the development of future implant designs leading to novel and improved fracture fixation methods.

Remodeling and growth of living tissue: a multiphase theory

Abstract: A continuum triphase model (i.e., a solid filled with fluid containing nutrients) based on the theory of porous media (TPM) is proposed for the phenomenological description of growth and remodeling phenomena in isotropic and transversely isotropic biological tissues. In this study, particular attention is paid on the description of the mass exchange during the stress–strain- and/or nutrient-driven phase transition of the nutrient phase to the solid phase. In order to define thermodynamically consistent constitutive relations, the entropy inequality of the mixture is evaluated in analogy to Coleman and Noll (Arch Ration Mech Anal 13:167–178, 1963). Thereby, the choose of independent process variables is motivated by the fact that the resulting phenomenological description derives both a physical interpretability and a comprehensive description of the coupled processes. Based on the developed thermodynamical restrictions constitutive relations for stress, mass supply and permeability are proposed. The resulting system of equation is implemented into a mixed finite element scheme. Thus, we obtain a coupled calculation concept to determine the solid motion, inner pressure as well as the solid, fluid and nutrient volume fractions.

Buckling and postbuckling of a compressed thin film bonded on a soft elastic layer: a three-dimensional analysis

Abstract: The wrinkling of a stiff thin film bonded on a soft elastic layer and subjected to an applied or residual compressive stress is investigated in the present paper. A three-dimensional theoretical model is presented to predict the buckling and postbuckling behavior of the film. We obtained the analytical solutions for the critical buckling condition and the postbuckling morphology of the film. The effects of the thicknesses and elastic properties of the film and the soft layer on the characteristic wrinkling wavelength are examined. It is found that the critical wrinkling condition of the thin film is sensitive to the compressibility and thickness of the soft layer, and its wrinkling amplitude depends on the magnitude of the applied or residual in-plane stress. The bonding condition between the soft layer and the rigid substrate has a considerable influence on the buckling of the thin film, and the relative sliding at the interface tends to destabilize the system.

Experimental and numerical studies of guided wave damage detection in bars with structural discontinuities

Abstract: This paper deals with longitudinal and flexural wave propagations in steel bars with structural discontinuities. Numerical simulations were performed using the spectral element method and compared with experimental studies conducted on an intact bar as well as on bars with an additional mass, a notch and a grooved weld. To model longitudinal wave propagation including lateral deformations, special rod spectral elements in time domain (based on Love and Mindlin–Herrmann theories) were formulated. The effect of the three discontinuities on wave propagation is discussed, and the applicability of longitudinal and flexural waves to non-destructive damage detection is investigated.

Transient thermopiezoelectric response of a one-dimensional functionally graded piezoelectric medium to a moving heat source

Abstract: The thermopiezoelectricity problem of a one-dimensional (1-D), finite length, functionally graded medium excited by a moving heat source is investigated in this paper. The Lord and Shulman theory of generalized coupled thermoelasticity is employed to account for both the finite speed of thermal waves and coupling of temperature field with displacement and electric fields. Except thermal relaxation time and specific heat, which are taken to be constant for simplicity, all other properties are assumed to vary exponentially along the length through an arbitrary non-homogeneity index. Laplace transform has been used to eliminate the time effect, and three coupled fields, namely, displacement, temperature, and electric fields are obtained analytically in the Laplace domain. The solutions are then inverted to time domain using a numerical Laplace inversion method. Numerical examples are displayed to illustrate the effects of non-homogeneity index, length and thermal relaxation time on the results. When the medium is homogeneous, the results of the current paper are reduced to exactly the same results available in the literature.

Quadrature element analysis of planar frameworks

Abstract: The recently proposed weak form quadrature element method (QEM) is extended to the analysis of planar frameworks which are characterized by C1 continuity. Weak form quadrature elements for planar frameworks are developed. Examples are presented and comparison with the results of the finite element method is made to demonstrate the effectiveness and high computational efficiency of the QEM.

Numerical study on a vertical plate with variable viscosity and thermal conductivity

Abstract: Free convection over an isothermal vertical plate immersed in a fluid with variable viscosity and thermal conductivity is studied in this paper. We consider the two-dimensional, laminar and unsteady boundary layer equations. Using the appropriate variables, the basic governing equations are transformed to non-dimensional governing equations. These equations are then solved numerically using a very efficient implicit finite difference scheme known as Crank–Nicolson scheme. The fluid considered in this study is of viscous incompressible fluid of temperature dependent viscosity and thermal conductivity. The effect of varying viscosity and thermal conductivity on velocity, temperature, shear stress and heat transfer rate are discussed. The velocity and temperature profiles are compared with previously published works and are found to be in good agreement.

Onset of convection in a couple-stress fluid-saturated porous medium: effects of non-uniform temperature gradients

Abstract: Onset of convection in a layer of couple-stress fluid-saturated porous medium is investigated for different types of basic temperature gradients. The boundaries are considered to be adiabatically insulated to temperature perturbations. The eigenvalue equations of the perturbed state obtained from the normal mode analysis are solved analytically using a regular perturbation technique with wave number as a perturbation parameter and also numerically using the Galerkin technique. The critical stability parameters obtained from these two techniques are in excellent agreement and an increase in the value of couple-stress parameter is found to delay the onset of convection. The results also indicate that the piecewise linear temperature profile hastens the onset of convection when compared to linear, parabolic, and inverted parabolic temperature profiles. In addition, the influence of thermal depth on the critical conditions is assessed in the case of piecewise linear temperature profiles, and it is observed that the critical thermal depth decreases marginally with an increase in the couple-stress parameter.

A note on flow geometries and the similarity solutions of the boundary layer equations for a nonlinearly stretching sheet

Abstract: In this note we extend the results of Akyildiz et al. [Similarity solutions of the boundary layer equations for a nonlinearly stretching sheet. Mathematical Methods in the Applied Sciences (www.interscience.wiley.com). doi: 10.1002/mma.1181] for any n > 0, where n is a nonlinear stretching parameter. Thus, the proof presented for the existence of the similarity solutions for the boundary layer equation for a nonlinearly stretching sheet presented in Akyildiz et al. hold not only for positive odd integer values of n, but also for any real value of n > 0: That is, n can be any positive real. We accomplish this by defining the stretching velocity of the sheet as u = csgn(x)|x| n , −∞ < x < ∞, at y = 0 (instead of u = cx n , 0 < x < ∞, y = 0) and accordingly modifying the similarity variables. This definition for u at the stretching surface eliminates the restrictions on n in all future research results related to flow and heat transfer over nonlinear stretching surfaces.

An interface crack with contact zones in a piezoelectric/piezomagnetic bimaterial

Abstract: An interface crack with a frictionless contact zone at the right crack tip between two semi-infinite piezoelectric/piezomagnetic spaces under the action of a remote mechanical loading, magnetic and electric fluxes as well as concentrated forces at the crack faces is considered. Assuming that all fields are independent on the coordinate x 2 co-directed with the crack front, the stresses, the electrical and the magnetic fluxes as well as the derivatives of the jumps of the displacements, the electrical and magnetic potentials are presented via a set of analytic functions in the (x 1, x 3)-plane with a cut along the crack region. Two cases of magneto-electric conditions at the crack faces are considered. The first case assumes that the crack is electrically and magnetically permeable, and in the second case the crack is assumed electrically permeable while the open part of the crack is magnetically impermeable. For both these cases due to the above-mentioned representation the combined Dirichlet–Riemann boundary value problems have been formulated and solved exactly. Stress, electric and magnetic induction intensity factors are found in a simple analytical form. Transcendental equations and a closed form analytical formula for the determination of the real contact zone length have been derived for both cases of magnetic conditions in the crack region. For a numerical illustration of the obtained results a bimaterial BaTiO3–CoFe2O4 with different volume fractions of BaTiO3 has been used, and the influence of the mechanical loading and the intensity of the magnetic flux upon the contact zone length and the associated intensity factors as well as the energy release rate has been shown.

Ultrasound propagation in cancellous bone

Abstract: Wave propagation in fluid-saturated cancellous bone is studied on the basis of two approaches: The thermodynamic-consistent Theory of Porous Media (TPM) and Biot’s theory. Phase velocities in the low-frequency range, calculated with the Biot-Gassmann relations, Wyllie’s equation and the TPM, are demonstrating that a simple, so-called hybrid biphasic TPM model is able to capture the main acoustical effects in cancellous bones. Furthermore, an extension towards high-frequency wave propagation is discussed on the basis of the constitutive relations for the momentum exchange of the fluid and the solid phases. Further numerical results show that, in the high-frequency (ultrasound) range a viscous correction as well as an added mass effect (tortuosity) needs to be taken into account to explain experimentally obtained results.

Modal parameter identification based on ARMAV and state-space approaches

Abstract: An accurate prediction for the response of civil and mechanical engineering structures subject to ambient excitation requires the information of dynamic properties of these structures including natural frequencies, damping ratios and mode shapes. Since the excitation force is not available as a measured signal, we need to develop techniques which are capable of accurately extracting the modal parameters from output-only data. This article presents the results of modal parameter identification using two time-domain methods as follows: the autoregressive moving average vector (ARMAV) method and the state–space method. These methods directly work with the recorded time signals and allow the analysis of structures where only the output is measured, while the input is unmeasured and unknown. The equivalence between ARMAV and state–space approaches for the problem of modal parameter identification of vibrating systems is shown in the article. Using only the singular value decomposition of a block Hankel matrix of sample covariances, it is shown that these two approaches give identical modal parameters in the case where the block Hankel matrix has full row rank. The time-domain modal identification algorithms have a serious problem of model order determination: when extracting structural modes these algorithms always generate spurious modes. A modal indicator to differentiate spurious and structural modes is presented. Numerical and experimental examples are given to show the effectiveness of the ARMAV or state–space approaches in modal parameter identification using response data only.

Numerical investigation of turbulent free jet flows issuing from rectangular nozzles: the influence of small aspect ratio

Abstract: In this research, the fluid and thermal characteristics of a rectangular turbulent jet flow is studied numerically. The results of three-dimensional jet issued from a rectangular nozzle are presented. A numerical method employing control volume approach with collocated grid arrangement was employed. Velocity and pressure fields are coupled with SIMPLEC algorithm. The turbulent stresses are approximated using k–\({\varepsilon}\) model with two different inlet conditions. The velocity and temperature fields are presented and the rates of their decay at the jet centerline are noted. The velocity vectors of the main flow and the secondary flow are illustrated. Also, effect of aspect ratio on mixing in rectangular cross-section jets is considered. The aspect ratios that were considered for this work were 1:1 to 1:4. The results showed that the jet entrains more with smaller AR. Special attention has been drawn to the influence of the Reynolds number (based on hydraulic diameter) as well as the inflow conditions on the evolution of the rectangular jet. An influence on the jet evolution is found for smaller Re, but the jet is close to a converged state for higher Reynolds numbers. The inflow conditions have considerable influence on the jet characteristics.

A three-dimensional constitutive model for shape memory alloys

Abstract: Shape memory alloys (SMAs) are materials that, among other characteristics, have the ability to present high deformation levels when subjected to mechanical loading, returning to their original form after a temperature change. Literature presents numerous constitutive models that describe the phenomenological features of the thermomechanical behavior of SMAs. The present paper introduces a novel three-dimensional constitutive model that describes the martensitic phase transformations within the scope of standard generalized materials. The model is capable of describing the main features of the thermomechanical behavior of SMAs by considering four macroscopic phases associated with austenitic phase and three variants of martensite. A numerical procedure is proposed to deal with the nonlinearities of the model. Numerical simulations are carried out dealing with uniaxial and multiaxial single-point tests showing the capability of the introduced model to describe the general behavior of SMAs. Specifically, uniaxial tests show pseudoelasticity, shape memory effect, phase transformation due to temperature change and internal subloops due to incomplete phase transformations. Concerning multiaxial tests, the pure shear stress and hydrostatic tests are discussed showing qualitatively coherent results. Moreover, other tensile–shear tests are conducted modeling the general three-dimensional behavior of SMAs. It is shown that the multiaxial results are qualitative coherent with the related data presented in the literature.

Experimental study on interaction of aerodynamics with flexible wings of flapping vehicles in hovering and cruise flight

Abstract: Flapping wings are promising lift and thrust generators, especially for very low Reynolds numbers. To investigate aeroelastic effects of flexible wings (specifically, wing’s twisting stiffness) on hovering and cruising aerodynamic performance, a flapping-wing system and an experimental setup were designed and built. This system measures the unsteady aerodynamic and inertial forces, power usage, and angular speed of the flapping wing motion for different flapping frequencies and for various wings with different chordwise flexibility. Aerodynamic performance of the vehicle for both no wind (hovering) and cruise condition was investigated. Results show how elastic deformations caused by interaction of inertial and aerodynamic forces with the flexible structure may affect specific power consumption. This information was used here to find a more suitable structural design. The best selected design in our tests performs up to 30% better than others (i.e., less energy consumption for the same lift or thrust generation). This measured aerodynamic information could also be used as a benchmarking data for unsteady flow solvers.

Interaction between a moving two-mass oscillator and an infinite homogeneous structure: Green’s functions method

Abstract: This paper deals with the interaction between a vehicle and a slab track using the model of moving wheel for both frequency and time-domain. The vehicle is reduced to a moving two-mass oscillator and the slab track is considered as an infinite structure consisting of elastically supported double Euler–Bernoulli beams. In order to perform the time-domain analysis, a semi-analytical method based on the outstanding properties of the time-domain Green’s functions of the slab track has been developed. The method allows the computing of the non-linear wheel/rail contact (the contact loss and the non-linear contact stiffness). The vehicle/track interaction due to the polygonal wheel and the corrugated rail has been investigated and the running velocity and non-linear wheel/rail contact influences have been pointed out.

Micromechanical modelling of skeletal muscles: from the single fibre to the whole muscle

Abstract: The structure of a skeletal muscle is dominated by its hierarchical architecture in which thousands of muscle fibres are arranged within a connective tissue network. The single muscle fibre consists of many force-producing cells, known as sarcomeres, which contribute to the contraction of the whole muscle. There are a lot of questions concerning the optimisation of muscle strength and agility. To answer these questions, numerical testing tools, e.g. in the form of finite element models can be an adequate alternative to standard experimental investigations. The present approach is crucially based on the use of the finite element method. The material behaviour of the muscle is additively split into a so-called active and a passive part. To describe the passive part special unit cells consisting of one tetrahedral element and six truss elements have been derived. Embedded into these unit cells are non-linear truss elements which represent bundles of muscle fibres. Besides the representation of the material model, this contribution focuses on the application to anatomically based 3D problems, as the animal soleus muscle of the rat.

A thermodynamics framework and numerical aspects for transformation-induced plasticity at large strains

Abstract: In this work, we present a macroscopic material model for simulation transformation-induced plasticity, which is an important phenomenon in metal forming processes. The model is formulated within a thermodynamic framework at large strains. In order to account for both, phase transformation and plasticity, yield functions are related to these effects. Then, applying the concept of maximum dissipation evolution equations are obtained for the inelastic strains, the transformation strains, a hardening variable and the volume fraction of martensite. Furthermore the numerical implementation of the constitutive equations into a finite element program is described. In a numerical example we investigate the austenite-to-martensite phase transformation in a shaft subjected to thermo-mechanical loading in a hybrid-forming process.

Contact stresses: a short survey of models and methods of computations

Abstract: Contact stresses are identified as normal and tangential forces between contacting solids. The normal stresses are modeled using unilateral and complementary conditions, elastic response and normal compliance. Friction laws describe the tangential traction. Friction of materials depends on pressure, sliding velocity, surface temperature, time of contact, surface roughness and presence of wear debris. Phenomenological, micro-mechanical and atomic-scale models as well as non-classical models of anisotropic and heterogeneous friction are important steps in the development of friction modeling. Sophisticated friction models are desirable in vibrating systems, materials processing, rolling contacts, rubber and polymers, geomechanics, bioengineering and living systems. Main numerical methods in contact mechanics are: finite element method, boundary element method and discrete element method. To include specific contact constraints, the following computing techniques are applied: Lagrange multipliers, penalty function, perturbated and augmented Lagrangian methods, mathematical programming methods. The advances of adhesion and impact modeling are outlined in this paper.