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Following earlier work on the combined finite/discrete element simulation of shot peening process in 2D case, 3D representation of the problem is established with respect to DE modelling and contact interaction laws. An important relevant computational issue regarding the critical time step is carefully studied, and a new time stepping scheme that can ensure both short and long term stability of the contact models is developed. Numerical tests are performed to evaluate the proposed normal and frictional contact interaction laws with various model parameters. The influences of single and multiple shot impact, as well as element sizes are also numerically investigated. The established contact interaction laws can also be applied to other multi‐body dynamic simulations.

This work is concerned with computational modelling of viscoplastic fluids. The flows considered are assumed to be incompressible, while the viscoplastic laws are obtained by incorporating a yield stress below which the fluid is assumed to remain non‐deformable. The Bingham fluid is chosen as a model problem and is considered in detail in the text. The finite element formulation adopted in this work is based on a version of the stabilised finite element method, known as the Galerkin/least‐squares method, originally developed by Hughes and co‐workers. This methodology allows use of low and equal order interpolation of the pressure and velocity fields, thus providing an efficient finite element framework. The Newton‐Raphson method has been chosen for solution of the incremental non‐linear problem arising through the temporal discretisation of the evolution problem. Numerical examples are provided to illustrate the main features of the described methodology.

This work is concerned with the computational modelling of non‐linear solid material behaviour in the finite strain regime. Based on the recent computational formulations for modelling of inelastic material behaviour, a generalized material model is presented for inelastic materials incorporating classical elastic, viscoelastic, plastic and viscoplastic material description, all operating in the finite strain regime. The underlying rheological model corresponds to the combined action of several rheological components, such as Hooke, Maxwell and Prandtl elements, arranged in parallel. This work summarizes the theoretical basis of the material model and presents the computational treatment in the framework of a finite element solution procedure. Numerical examples are provided to illustrate the scope of the described computational strategy.

To obtain more reliable crash simulations the history of the structure related to the forming process is considered. For this goal the variables defining the current state have to be transferred from one mesh to the other in order to maintain a consistent discretization of the whole structure consisting of several pre‐formed parts. This is accomplished here by remeshing the structure after the forming process and by transferring the current mechanical properties. In performing such a transfer a numerical error cannot be avoided; the results of this approach are therefore compared with computations in which this transfer is not applied to assess the performance of the presented procedure.

In this work we present interrelations between different finite rotation parametrizations for geometrically exact classical shell models (i.e. models without drilling rotation). In these kind of models the finite rotations are unrestricted in size but constrained in the 3‐d space. In the finite element approximation we use interpolation that restricts the treatment of rotations to the finite element nodes. Mutual relationships between different parametrizations are very clearly established and presented by informative commutative diagrams. The pluses and minuses of different parametrizations are discussed and the finite rotation terms arising in the linearization are given in their explicit forms.

This paper outlines a dynamic domain decomposition‐based parallel strategy for combined finite/discrete element analysis of multi‐fracturing solids and discrete systems. Attention is focused on the parallelised interaction detection between discrete objects. Two graph representation models for discrete objects in contact are proposed which lay the foundation of the current development. In addition, a load imbalance detection and re‐balancing scheme is also suggested to enhance the parallel performance. Finally, numerical examples are provided to illustrate the parallel performance achieved with the current implementation.

The purpose of this paper is to use symmetry conditions for the reduction of computing times in problems involving finite element‐based multi‐scale constitutive models of nonlinear heterogeneous media.

Two types of representative volume element (RVE) symmetry often found in practice are considered: staggered‐translational and point symmetry. These are analyzed under three types RVE of kinematical constraints: periodic boundary fluctuations (typical of periodic media), linear boundary displacements (which gives an upper bound for the macroscopic stiffness) and the minimum kinematical constraint (corresponding to uniform boundary tractions and providing a lower bound for the macroscopic stiffness).

Numerical examples show that substantial savings in computing times are achieved by taking advantage of such symmetries. These are particularly pronounced in fully coupled two‐scale analyses, where the macroscopic equilibrium problem is solved simultaneously with a large number of microscopic equilibrium problems at Gauss‐point level. Speed‐up factors in excess of seven have been found in such cases, when both symmetry conditions considered are present at the same time.

This paper extends the original considerations of Ohno et al. to account for other RVE kinematical constraints, namely, the linear boundary displacement and the minimum kinematical constraint (or uniform boundary traction model). Provides a more precise assessment of the impact of the use of such symmetries on computing times by means of numerical examples. In addition, for completeness, the direct enforcement of such constraints within a Newton‐based finite element solution procedure for the RVE equilibrium problem is detailed in the paper.

As known from nearly incompressible elasticity, selective reduced integration (SRI) is a simple and effective method of overcoming the volumetric locking problem in 2D and 3D solid elements. This method of finite elastoviscoplasticity is discussed as are its well‐known limitations. In this context, an isochoric‐volumetric decoupled material behavior is assumed and thus the additive deviatoric‐volumetric decoupling of the consistent algorithmic moduli tensor is essential. By means of several numerical examples, the performance of elements using selective reduced integration is demonstrated and compared to the performance of other elements such as the enhanced assumed strain elements. It is shown that a minor modification, with little numerical effort, leads to rather robust element behaviour. The application of this process to so‐called solid‐shell elements for thin‐walled structures is also discussed.

Classical mixed formulations of the boundary‐value problem of linear elasticity are reviewed, and a new three‐field formulation is introduced. The formulation is an extension of the classical Hu‐Washizu approach, and takes the form of a non‐standard mixed problem. Convergence of finite element approximations of both the old and new methods are discussed, with an emphasis on their behaviour in the incompressible limit. Conditions for the stability and uniform convergence of the new method are presented, and it is shown that the Pian‐Sumihara basis, when used in the new formulation, leads to a convergent method.

Being extensively used in metallurgy, rotating magnetic fields are also becoming increasingly interesting for application in crystal growth, where they are intended to act by stabilizing the melt flow. For this purpose, it is important to understand the basic interactions of the magnetically induced flow and other flow components like time‐dependent buoyant convection. So a three‐dimensional finite volume method was developed in order to numerically study the effect of a rotating magnetic field on convection in a cylindrical melt volume. The equations of mass, momentum, and heat transport are solved together with the potential equations describing the electromagnetic field. The numerical computation of the Lorenz force distribution is validated by comparison with an analytical solution. The effects of magnetic field parameters on the temperature distributions and the flow patterns in the considered configurations are analysed.