Plenary Lectures 2017

The phenomenological approach of continuum mechanics is based on axioms and on experiments. While the balance equations are accepted as physical laws experiments form the basis of constitutive modelling, e.g. the quality of a stress-strain relation at finite deformations strongly depends on the underlying data. On the one hand, experiments leading to homogeneous stress and strain states are typically preferred due to their simple evaluation. On the other hand, multiaxial stress and deformation states are required to match the three dimensional state in a real component. Even if it is still an unsolved task to measure inhomogeneous stress distributions in a specimen, optical strain measurement became a very powerful tool to reconstruct the inhomogeneous displacement field at least on the surface of a specimen. Therefore, the evaluation of inhomogeneous experiments, e.g. true biaxial tests, offers new possibilities in the validation of constitutive equations. In most cases, due to the inhomogeneity and the non-linearity of the resulting boundary value problem, the identification of the material parameters becomes an inverse problem. The present contribution addresses the application of modern experimental techniques for the design of experiments, their realisations and, finally, the parameter identification. Special focus is given to inhomogeneous experiments and to the miniaturisation of experiments.

Structural mechanics since its beginnings has developed very strongly with respect to more accurate modelling and analysis. A key role in this development play numerical methods, especially those based on the concept of finite elements. This high degree of presision, however, is undermined by imprecise and/or incomplete knowledge about the describing parameters of the models and the environmental actions on the structures, such as e.g. wind or earthquakes. Even with a substantially increased effort for experimental evidence, it is frequently not possible to arrive at deterministic descriptions for these parameters. Therefore uncertainty-based (e.g. probabilistic) analysis becomes mandatory. This lecture will highlight some selected points how stochastic structural mechanics can contribute to solve open problems related to the development of structural design procedures.

A common practice in structural problems involving heterogeneous materials with well separated scales, is to use homogenized, or effective, constitutive relations. In linear elasticity the structure of the homogenized constitutive relations is strictly preserved in the change of scales. The linear effective properties can be computed once for all by solving a finite number of unit-cell problems.
Unfortunately there is no exact scale-decoupling in multiscale nonlinear problems which would allow one to solve only a few unit-cell problems and then use them subsequently at  a larger scale. Computational approaches developed to investigate the response of representative volume elements along specific loading paths, do not provide constitutive relations. Most of the huge body of information generated in the course of these costly computations is often lost.
Model reduction techniques, such as the Non Uniform Transformation Field Analysis, may be used to exploit the information generated along such computations and, at the same time, to account for the commonly observed patterning of the local plastic strain field. A new version of the model will be proposed in this talk, with the aim of preserving the underlying variational structure of the constitutive relations, while using approximations which are common in nonlinear homogenization.

Many components in modern product cannot be modeled easily or properly: they need to be characterized experimentally. In vibration analysis of complex structural and mechatronical systems, it is highly desirable to build models of assemblies where some components are modeled numerically (e.g. by Finite Elements) whereas others are characterized experimentally. Building substructured models from experimental measurements enables engineers to rapidly detect troublesome parts, identify excitation sources and optimize the dynamics of their design. Such strategies form the basis of so-called Transfer Path Analysis techniques (TPA).
Although the mathematical theory of TPA is rather straightforward, its mechanical interpretation is not intuitive and applying simple ideas to real measurements is a real challenge. If you think that measurements are always the reality … think again: measured dynamic properties of structures (typically Frequency Response Functions) are not only inaccurate, but do often not even satisfy fundamental mechanical properties such as passivity or reciprocity. Such errors render a straightforward application of the theory illusory. 
In the presentation, we will discuss a framework to describe the simple algebra needed in substructuring techniques for structural vibration analysis and we will discuss how the vibration source of active components can be indirectly measured. Also we will outline some important tricks and twists that are needed to use measured components in an assembly. The methods will be illustrated on an industrial example.