Modeling and numerical analysis of the thread rolling process

The paper presents the physical and mathematical models of deformations (displacements and strains) and the stress in the cold process of the thread rolling. The process is considered as a geometrical and physical nonlinear, initial as well as a boundary value problem. The phenomena of a typical incremental step were described using a step-by-step incremental procedure, in the updated Lagrangian formulation. The state of strains was described by Green-Lagrange's tensor, while the state of stress was described by the second symmetrical Pioli-Kirchhoff's tensor. The object was treated as an elastic (in the reversible zone) and visco-plastic body (in the non-reversible zone) with mixed hardening. The variational equation of the motion in three dimensions for this case was proposed. Then, the finite elements methods (FEM) and dynamic explicit method (DEM) were used to obtain the solution. In a numerical analysis, boundary condition for a displacement increment, was determined in the model investigation. The results of a numerical analysis were compared and verified in an experimental investigation. Examples of calculations of the influence of a friction coefficient on the state of the deformation and stress, and an example application for this method of thread rolling were presented. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical analysis of chip formation during machining for different value of failure strain

Grinding is a very complicated processing. To increase quality of product and minimize the cost of abrasive machining, we should know physical phenomena which exist during the process. The first step to solution of this problem is analysis of machining process with a single abrasive grain. In the papers [1, 2] the thermo-mechanical models of this process are presented, but in this work attention is concentrated on chip formation and his separation from object. The influence of failure strain ε_f on states of strain and stress in surface layer during machining is explained. The phenomena on a typical incremental step were described using step-by-step incremental procedure, with updated Lagrangian formulation. Then, the Finite Element Method (FEM) and Dynamic Explicit Method (DEM) were used to obtain the solution. Application was developed in the ANSYS system, which makes possible a complex time analysis of the physical phenomena: states of displacements, strains and stress. Numerical computations of the strain have been conducted with the use of two methodologies. The first one requires an introduction of boundary conditions for displacements in the contact area determined in modeling investigation, while the second – a proper definition of the contact zone through the introduction of finite elements of TARGET and CONTACT types, without the necessity to introduce boundary conditions. This model includes variational equations of the object's motion and deformation. Examples of calculations for the displacement, strain and stress field in the surface layer zones were presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical analysis of micromachining of C45 steel by single abrasive grain

Grinding is a very complicated processing. To increase quality of product and minimize the cost of abrasive machining, we should know physical phenomena which exist during the process. The first step to solution of this problem is analysis of machining process with a single abrasive grain. In the paper [1] the thermo–mechanical models of this process are presented, but in this work attention is concentrated on chip formation and his separation from object for different velocity of abrasive grain. The phenomena on a typical step time were described using step–by–step incremental procedure, with updated Lagrangian formulation. Then, the finite elements methods (FEM) and dynamic explicit method (DEM) were used to obtain the solution. Application was developed in the ANSYS system, which makes possible a complex time analysis of the physical phenomena – states of: displacements, strains and stress. Numerical computations of the strain have been conducted with the use of two methodologies. The first one requires an introduction of boundary conditions for displacements in the contact area determined in modeling investigation, while the second – a proper definition of the contact zone, without the necessity to introduce boundary conditions in the contact area. Examples of calculations for the intensity of stress in the surface layer zones were presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Numerical Analysis of the External Round Thread Rolling

The papers [1] describe modeling of the contact problem in the external thread rolling process. This paper shown an application of obtained model for the thread with round outline. The mathematical model of process, were presented. The variational and finite element method, were used. The algorithm of numerical analysis in ANSYS system, were elaborated. Numerical computions of displacements, strains and stresses have been conducted without the necessity to introduce boundary condition in the contact zone – a proper definition of the contact zone by single surface auto 2D. Exemplary results of numerical analysis for various condition of the process realization in the discretized model has been presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical analysis of shot peening on surfaces in Ansys application

ABSTRACT: Paper presents the posibility to application of Finite Element Method (FEM) to analysis of strain and stress states in surface layer of object. The application in Ansys/Ls – Dyna programme using incremental procedure in updated Lagrangian formulation was developed. Examples of calculations of influence of different distance of leaving traces for the strain and stress field in the surface layer zone were presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The forms of the relation between the stress and strain tensors in a non-linearly elastic material

New relations for the stress and strain tensors, which comprise energy pairs, are obtained for a non-linearly elastic material using a similar method to that employed by Novozhilov, based on a trigonometric representation of the tensors. Shear strain and stress tensors, not used previously, are introduced in a natural way. It is established that the unit tensor, the deviator and the shear tensor form an orthogonal tensor basis. The stress tensor can be expanded in a strain-tensor basis and vice versa. By using this expansion, the non-linear law of elasticity can be written in a compact and physically clear form. It is shown that in the frame of the principal axes the stresses are expressed in terms of the strains and vice versa using linear relations, while the non-linearity is contained in the coefficients, which are functions of mixed invariants of the tensors, introduced by Novozhilov, the generalized moduli of bulk compression and shear and the phase of similitude of the deviators. Relations for different energy pairs of tensors are considered, including for tensors of the true stresses and strains, where the generalized moduli of elasticity have a physical meaning for large strains.     

Automatic Implementation of Elasto-plastic Incremental Formulations at Finite Strains using Hyper-Dual Numbers

Numerical simulation of standard dissipative materials undergoing finite strains remains an important and challenging topic in computational mechanics. The incremental variational formulation (IVF), firstly proposed by Ortiz et al. [1], provides a general variational framework which is suitable for the implementation of a broad range of constitutive laws for standard dissipative materials. The IVF recasts the inelasticity theory as an equivalent optimization problem where the incremental stress potential is minimized with respect to the internal variables. However, their implementation often requires more effort than classical formulations due to high-order tensor derivatives. In this contribution, a novel implementation of IVFs is presented to arrive at a fully automatic and robust scheme with computer accuracy using hyper-dual numbers (HDNs). The HDNs, which are originally developed by Fike [2], derive exact and automatic derivative calculations without any cumbersome choice of perturbation values. Its uncomplicated implementation for associative finite strain elasto-plasticity and its performance is illustrated by a representative numerical example. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analytical inverse solution for coupled thermoelastic problem for the evaluation of contact stress during steel strip rolling

Knowledge of the contact stress between roll and strip is a critical factor in modern, high-speed rolling mills. Previously two inverse analytical methods have been developed to determine the elastic contact stress on the one hand and the heat flux or the temperature in the whole roll (and especially at the surface) on the other hand, by measuring the stress tensor inside the roll body with fibre optics and by measuring the temperature with a thermocouple fully embedded at only one point inside the roll. However measurements done by fibre optics take into account the elastic stress and the thermal stress. However the contact stress was determined under isothermal assumption, which is strongly incorrect for hot rolling conditions. In this paper, the coupled thermoelastic problem is solved analytically using the theorem of superposition and the expression of the temperature field exhibited previously. A significant improvement of the accuracy of the inverse method for reconstructing the contact stress is observed by taking into account thermal stress. Hot rolling simulation is given to demonstrate this result. The computation time is studied to rapidly optimise the industrial parameters during the rolling process, and considering that both inverse methods have been run, the computation of thermal stress does not cost significant additional CPU times.     

A solid shell finite element formulation to simulate the behaviour of thin dielectric elastomer structures

To analyse the behaviour of thin structures of dielectric elastomer (DE) material a solid shell finite element is presented. The main characteristics of DEs are a non-linear hyper elastic behaviour, the quasi-incompressibility, and the ability to transform electric energy into mechanical work. Applying a voltage to thin DE structures may produce large elongation strains of 120-380%. These large strains, the efficient electro-mechanical coupling, and the light weight make DEs very attractive for the usage in actuators. Thus, there is a need for detailed research. With respect to the electro-mechanical coupling a constitutive model is presented. An electric stress tensor and a total stress tensor are introduced by considering the electrical body force and couple in the balance of linear momentum and angular momentum, respectively. The governing equations are derived and embedded in the solid shell formulation. The element formulation is based on a Hu-Washizu mixed variational principle using six independent fields: displacements, electric potential, strains, electric field, mechanical stresses, and dielectric displacements. It allows large deformations and accounts for physical nonlinearities to capture two of the main characteristics of DEs. The shell element could be applied for the modelling of arbitrary curved thin structures. The ability of the present element formulation is demonstrated in several examples. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimization the shape of finite element in shot peening process

This paper contains modelling and numerical simulations of shot peening process. The application in Ansys/LS – Dyna programme were elaborated. The phenomena of shot peening process on a typical incremental step were described using a step-by-step incremental procedure, with an updated Lagrangian formulation.Finite elements methods (FEM) and the dynamic explicit method (DEM) were used to obtain the solution. The main purpose of this article is to determinate optimal model of shot peening process (convergence resulting for minimal number of finite elements and their optimal shapes). Examples of calculations were presented. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Anisotropic elasto-plastic damage formulation for finite strains using a damage structural tensor and the effective stress concept

Using the strain equivalence principle and the effective stress concept an anisotropic finite strain damage model is proposed as a direct extension of the classical isotropic LEMAITRE damage model to the anisotropic finite strain case. The damage tensor is included as a structural tensor in the complementary energy potential. This approach allows to consider a wide range of anisotropic damage phenomena on the level of continuum mechanics. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Linear Precision for Toric Surface Patches

We classify the homogeneous polynomials in three variables whose toric polar linear system defines a Cremona transformation. This classification includes, as a proper subset, the classification of toric surface patches from geometric modeling which have linear precision. Besides the well-known tensor product patches and Bézier triangles, we identify a family of toric patches with trapezoidal shape, each of which has linear precision. Furthermore, Bézier triangles and tensor product patches are special cases of trapezoidal patches.     

“A new approach to formulate the general strength theories for anisotropic discontinuous materials” Part B General form of polynomial to describe the strength of anisotropic discontinuous materials

A new approach to describe the failure hypersurface on the basis of assumptions presented in Part A reveals the new form of failure stress polynomial. In the presented theory new terms such as: unit tensor object, object formed on the basis of unit tensor object, the first, second and third form of the anisotropy failure function, and the first and the second type of object axis, were defined. On the basis of these terms the coefficients of their polynomials were formulated as values of the appropriate objects. The presented theory divides the six dimensional hyperspace of stresses into eight parts in which eight intersected hypersurfaces constitute the failure hypersurface. Six hypersurfaces may be assigned to two of three mutually coupled sets of elements. In general cases the theory may be used to describe the failure hypersurface for anisotropic structures where tensorial relationships do not occur. The obtained polynomial is transformed to tensor polynomial on the assumption that the failure stress tensorial relationships describe the failure hypersurface of anisotropic materials.     

A contribution to the plastic behavior of cellular bone

In a first approximation the inelastic behavior of cellular bone is modelled by an isotropic elastic-plastic material. Plastic strains can deduced using a yield-criterion and a plastic potential which depends on invariants of the stress tensor. Irreversible (plastic) volumetric strains occur. The plastic material functions can be determined in an uniaxial experiment with a Laser Extensometer. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multiscale damage simulation

Numerous materials show a softening behaviour at dynamic loading. The decrease of stress is caused by the evolution in the microscale in terms of areas where the local stiffness is reduced, e.g. due to micro-void growth. For a numerical treatment of this material behaviour, phenomenological damage approaches are used in daily engineering practice. For a better understanding of the micromechanical process of such phenomenological models, multiscale methods are becoming increasingly important. The physical quantities that are responsible for the microstructural evolution associated with the damage process are transferred into the numerical model. In this context, the method of configurational forces will be used to describe the geometrical changes of damaged areas. With the help of homogenization, macro- and microscale will be coupled. In consequence, each Gaussian point of the macroscale is modelled by an own microstructure (RVE), where the microscale evolves during the loading process according to observable damage phenomena. Hereby, we present the general case of hyperelastic materials at finite strains. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Regularity of stresses in Prandtl-Reuss perfect plasticity

We study the differential properties of solutions of the Prandtl-Reuss model. We prove that in dimensions n = 2, 3 the stress tensor has locally square-integrable first derivatives: . The result is based on discretization of time and uniform estimates of solutions of the incremental problems, which generalize the estimates in the case of Hencky perfect plasticity. Counterexamples to the regularity of displacements and plastic strains in the quasistatic case are presented.      

A variant of the theory of local strains

A variant of the theory of local strains giving the stress tensor as a function of a given strain tensor is formulated. The stresses in an orthogonal coordinate system are established by means of a functional that averages the local stresses expressed by the local stress function. This function is determined by the given strain program. It is shown that in certain practical problems these relations are more convenient than those previously proposed.Mekhanika Polimerov, Vol. 3, No. 5, pp. 800–802, 1967     

Analysis of the effect of transverse shear strains on the stability of multilayer cylindrical shells under external pressure

The effect of transverse shear strains on the critical pressure is investigated using the results of the solution obtained for the problem of the stability "in the small" of elastic multilayer cylindrical shells of regular structure with alternating light and stiff layers. Attention is drawn to the need to estimate the state of stress of the shells in the critical-load zone with the object of studying the desirability of taking the shear effect into account in the stability calculations. The results obtained can be used in calculating the stability of shells made from resin-based composites (glass-reinforced plastics, graphite-reinforced plastics, etc.). The numerical calculations were carried out using a computer.Translated from Mekhanika Polimerov, No. 6, pp. 1066–1070, November–December, 1973.