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Auflistung nach Autor:in "Steinmann, P."

1 - 5 von 5
  • Textdokument
    Comparative tensor visualisation within the framework of consistent time-stepping schemes
    (Visualization of large and unstructured data sets, 2008) Mohr, R.; Bobach, T.; Hijazi, Y.; Reis, G.; Steinmann, P.; Hagen, H.
    Nowadays, the design of so-called consistent time-stepping schemes that basically feature a physically correct time integration, is still a state-of-the-art topic in the area of numerical mechanics. Within the proposed framework for finite elastoplasto-dynamics, the spatial as well as the time discretisation rely both on a Finite Element approach and the resulting algorithmic conservation properties have been shown to be closely related to quadrature formulas that are required for the calculation of time-integrals. Thereby, consistent integration schemes, which allow a superior numerical performance, have been developed based on the introduction of an enhanced algorithmic stress tensor, compare [MMS06]-[MMS07c]. In this contribution, the influence of this consistent stress enhancement, representing a modified time quadrature rule, is analysed for the first time based on the spatial distribution of the tensor-valued difference between the standard quadrature rule, relying on a specific evaluation of the well-known continuum stresses, and the favoured nonstandard quadrature rule, involving the mentioned enhanced algorithmic stresses. This comparative analysis is carried out using several visualisation tools tailored to set apart spatial and temporal patterns that allow to deduce the influence of both step size and material constants on the stress enhancement. The resulting visualisations indeed confirm the physical intuition by pointing out locations where interesting changes happen in the data.
  • Textdokument
    Deriving global material properties of a microscopically heterogeneous medium - computational homogenisation and opportunities in visualisation
    (Visualization of large and unstructured data sets, 2008) Hirschberger, C. B.; Ricker, S.; Steinmann, P.; Sukumar, N.
    In order to derive the overall mechanical response of a microscopically material body, both the theoretical and the numerical framework of multi scale consideration coined as computational homogenisation is presented. Instead of resolving the actual heterogeneous microstructure in all detail for its simulation, representative micro elements are considered which provide the material properties for the coarse or rather scale. This procedure allows for a smaller and less inexpensive computation. However both the chance and challenge of visualising the decisive features arise on two scales.
  • Textdokument
    Finite elasto-plasto-dynamics a challenges & solutions
    (Visualization of large and unstructured data sets, 2008) Mohr, R.; Menzel, A.; Steinmann, P.
    In this contribution, we deal with time-stepping schemes for geometrically nonlinear multiplicative elasto-plasto-dynamics. Thereby, the approximation in space as well as in time rely both on a Finite Element approach, providing a general framework which conceptually includes also higher-order schemes. In this context, the algorithmic conservation properties of the related integrators strongly depend on the numerical computation of time integrals, particularly, if plastic deformations are involved. However, the application of adequate quadrature rules enables a fulfilment of physically motivated balance laws and, consequently, the consistent integration of finite elasto-plasto-dynamics. Using exemplarily linear Finite Elements in time, the resulting integration schemes are analysed regarding the obtained conservation properties and assessed in comparison to classical time-stepping schemes which commonly adopt a time-discretisation procedure based on Finite Differences. 88 On the one hand, computational modelling of materials and structures often demands the incorporation of inelastic and dynamic effects. On the other hand, the performance of classical time integration schemes for structural dynamics, as for instance developed in [HHT77, New59], is strongly restricted when dealing with highly nonlinear systems. In a nonlinear setting, advanced numerical techniques are required to satisfy the classical balance laws as for instance balance of linear and angular momentum or the classical laws of thermodynamics. Nowadays, energy and momentum conserving time integrators for dynamical systems, like multibody systems or elasto-dynamics, are well-established in the computational dynamics community, compare e.g. [BB99, BBT01a, BBT01b, Gonz00, KC99, ST92]. In contrast to the commonly used time discretisation based on Finite Differences, one-step implicit integration algorithms relying on Finite Elements in space and time were developed, for instance, in Betsch and Steinmann [BS00a, BS00b, BS01]. Therein, conservation of energy and angular momentum have been shown to be closely related to quadrature formulas required for numerical integration in time. Furthermore, specific algorithmic energy conserving schemes for hyperelastic materials can be based on the introduction of an enhanced stress tensor for time shape functions of arbitrary order, compare Gross et al. [GBS05]. However, most of the proposed approaches are restricted to conservative dynamical systems. Nevertheless, the consideration of plastic deformations in a dynamical framework, involving dissipation effects, is of cardinal importance for various applications in engineering. In the last years, notable contributions dealing with finite elasto-plasto-dynamics have been published by Meng and Laursen [ML02a, ML02b], Noels et al. [NSP06] and Armero [Arm05, Arm06, AZ06]. In this contribution, we follow the concepts which have been proposed for hyperelasticity in [BS01, GBS05] and pickup the general framework of Galerkin methods in space and time, developing integrators for finite multiplicative elasto-plasto-dynamics with pre-defined conservation properties, compare Mohr et al. [MMS06a, MMS07c, MMS07a, MMS07b]. By means of a representative numerical example, the excellent performance of the resulting schemes, which base on linear Finite Elements in time combined with different quadrature rules, will be demonstrated and compared with the performance of well-accepted standard integrators. 2 Semi-Discrete Dynamics To set the stage, we start with some basic notation of geometrically nonlinear continuum mechanics. First, the nonlinear deformation map $φ$(X, t) : B0 $\times $[0, T ] $\rightarrow $Bt shall be
  • Textdokument
    Geometric numerical integration of simple dynamical systems
    (Visualization of large and unstructured data sets, 2008) Schmitt, P. R.; Steinmann, P.
    Understanding the behavior of a dynamical system is usually accomplished by visualization of its phase space portraits. Finite element simulations of dynamical systems yield a very high dimensionality of phase space, i.e. twice the number of nodal degrees of freedom. Therefore insight into phase space structure can only be gained by reduction of the model's dimensionality. The phase space of Hamiltonian systems is of particular interest because of its inherent geometric features namely being the co-tangent bundle of the configuration space of the problem and therefore having a natural symplectic structure. In this contribution a class of geometry preserving integrators based on Lie-groups and -algebras is presented which preserve these geometric features exactly. Examples of calculations for a simple dynamical system are detailed.
  • Textdokument
    Towards completeness, a multiscale approach of confined particulate systems
    (Visualization of large and unstructured data sets, 2008) Meier, H. A.; Steinmann, P.; Kuhl, E.
    Numerical simulation and computational visualization of the failure characteristics of confined granular assemblies, e.g., sand, gravel or other types of loose aggregates, is the focal point of this publication. In general, standard continuum descriptions are exhausted if applied to loose granular materials, while discrete formulations fail to describe huge overall particulate structures. We propose a complete two scale homogenization procedure, including both a continuous and a discontinuous scale. Thus, we combine the capability of discrete methods to describe the behavior of the single grains and the possibility of a continuum approach to discretize the overall structure. Connections between the two scales are based on the concept of introducing a representative volume element on the discrete microscale. Driven by quantities from the macroscale, the representative volume element acts like a material law, returning the needed quantities to the continuous macro level. The particular challenge of this work lies in defining the connection between these two scales in terms of physical quantities and equations on the one hand and in terms of introducing appropriate visual tools which ultimately yield an improved understanding of these complex coupling mechanism on the other hand.