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Numerical simulation of ultrasonic wave propagation using higher order methods in space and time
(2015)
The paper discusses the efficient simulation of ultrasonic wave propagation.
It is demonstrated that a combination of higher methods in space and time leads to a significant performance boost. Higher order spectral elements are used for the spatial
discretization. A comparison with standard finite elements shows the advantages when using explicit time integration schemes. For the temporal discretization, an efficient explicit fourth order Nyström method is presented. Its computational efficiency for wave propagation problems is compared to a second order Velocity Verlet integration.
Concrete is one of the most attractive building materials consumed by humans more than any other material, except water. The particular importance of concrete for a sustainable, energy-efficient economy is highlighted by the fact that about 5% of worldwide CO2 emissions are created from the cement industry.
Concrete is a very complex material. Its properties are time dependent, which includes the solidification after casting or creep and shrinkage. In addition, concrete is a quasi-brittle material which requires to model the softening behavior including the challenge of appropriate regularization strategies. Many characteristic features are strongly related to its complex heterogeneous structure, including particles and mortar on the mesoscale or the CSH-phases on the micro scale.
At first, a short introduction to the generation of mesoscale geometries as a three phase composite including particles, mortar matrix and the interfacial transition zone is given. Afterwards, the numerical model including meshing (XFEM and aligned meshes) as well as regularized material models for the mortar phase are presented.
The focus of the presentation is the discussion of multiscale approaches to combine mesoscale models with realistic macroscale models. This includes a concurrent approach using an adaptive transition between mesoscale and macroscale models which are coupled using the mortar method. A second hierarchical approach is based on the concept of FE², which is extended to incorporate softening by solving a fine scale boundary value problem for each macroscopic integration point.
In this work an approach for smoothing the oscillations of normal impact is presented. In addition, a higher order time discretization scheme in association with a higher order spatial discretization, like the spectral element method, is investigated regarding its convergence rates.
In this work an approach for smoothing the oscillations of normal contact is presented. On the other side a higher order time discretization scheme in association with a higher order spatial discretization, like the spectral element method, is used. The contact constraints are reformulated in order to get an explicit equation for the motion.
Concrete is one of the most important building materials world wide. The safety of constructions build from concrete is of utmost importance in daily life. As a consequence, accurate predictions of the structural behavior over the entire lifetime of concrete structures are required to ensure a prescribed safety level. A lack of exact models and/or stochastically varying constitutive parameters are compensated by large safety factors.
The nonlinear structural performance is strongly related to the constitutive behavior of concrete. Arbitrary complex models can be used to describe the macroscopic constitutive behavior of concrete. The parameters in these models often lack any physical meaning. Consequently, the fitting can only be performed by an inverse analysis. In contrast, models on finer scales are able to simulate the physical phenomena more accurately and are thus better suited to understand the failure mechanisms. In addition, the macroscopically observed strong nonlinearities can at least partially be explained by the direct modeling of the material heterogeneities on finer scales.
The presentation discusses several phenomena that are strongly related to the internal microstructure of concrete. This includes the discrepancy between the unique results of a numerical model and the stochastic scatter observed in real experiments. A short discussion on the generation of random mesoscale geometries to model aggregates and mortar matrix explicitly and random fields are given. The strong nonlinearities especially for stresses close to the peak strength are usually the result of failure in the mortar matrix or the interfacial transition zone, whereas the aggregates are inert and often can accurately be modeled by a linear elastic model. The different constitutive properties lead to eigenstresses that strongly in uence the macroscopic behavior. In addition, this effect is even more pronounced when dealing with multiphysics phenomena such as drying, creep and shrinkage, fatigue or thermal problems. It will be demonstrated for several examples that simple models on the fine scale can be superimposed and coupled to obtain a macroscopically nonlinear behavior, where the superposition principle does not hold any longer. Finally, a short discussion on upscaling techniques to couple mesoscale models with large scale structural problems is given.
Concrete is a complex material. Its properties evolve over time, especially at early age, and are dependent on environmental conditions, i.e. temperature and moisture conditions, as well as the composition of the material.
This leads to a variety of macroscopic phenomena such as hydration/solidification/hardening, creep and shrinkage, thermal strains, damage and inelastic deformations. Most of these phenomena are characterized by specific set of model assumptions and often an additive decomposition of strains into elastic, plastic, shrinkage and creep components is performed. Each of these phenomena are investigated separately and a number of respective independent models have been designed. The interactions are then accounted for by adding appropriate correction factors or additional models for the particular interaction. This paper discusses the importance of reconsider even in the experimental phase the model assumptions required to generalize the experimental data into models used in design codes. It is especially underlined that the complex macroscopic behaviour of concrete is strongly influenced by its multiscale and multiphyscis nature and two examples (shrinkage and fatigue) of interacting phenomena are discussed.