Analysis of textile composite structures with finite Volume-p-Elements

Anisotropic textile composites show nonlinear deformation and complex fai- lure behaviour. In particular three-dimensional reinforced textile composites are characterised by an orthotropic material behaviour. To achieve the full po- tential of textile composites the material and especially the failure behaviour has to be analysed particularly for regions dominated by three-dimensional stress distributions, e. g. load introduction areas. For these purposes finite volume-p-elements based on hierarchical shape functions are being developed. Furthermore the constitutive model is en- hanced to simulate material degradation and failure processes. Based on an anisotropic continuum damage model the material degradation is described with tensorial damage variables that characterise the crack density observed in experimental studies of Non-Crimp-Fabrics with E-Glass fibres. The deter- mination of the onset of degradation and the strength prediction is enabled by coupling the damage model with a failure criterion for three-dimensional reinforced plastics. Due to control the spatial adaptivity of polynomial order of the shape functi- ons different a posteriori error estimators are evaluated and compared espe- cially with respect to the applicability on structural models representing or- thotropic material behaviour. Experimental analyses were used to determine the parameters of the consti- tutive model. Besides the in-plane properties the through-thickness material properties are assumed to be primarily important for textile composites. The- refore a modified Arcan testing device was developed which provides test results for biaxial tension and shear load combinations taking the material thickness direction into account. Finally simulations and experimental analyses of a thick double holed plate - the loadintroduction of an elevator bucket - demonstrate the applicability of the material model and finite element implementation

Complex Societies and the Growth of the Law

While a large number of informal factors influence how people interact, modern societies rely upon law as a primary mechanism to formally control human behaviour. How legal rules impact societal development depends on the interplay between two types of actors: the people who create the rules and the people to which the rules potentially apply. We hypothesise that an increasingly diverse and interconnected society might create increasingly diverse and interconnected rules, and assert that legal networks provide a useful lens through which to observe the interaction between law and society. To evaluate these propositions, we present a novel and generalizable model of statutory materials as multidimensional, time-evolving document networks. Applying this model to the federal legislation of the United States and Germany, we find impressive expansion in the size and complexity of laws over the past two and a half decades. We investigate the sources of this development using methods from network science and natural language processing. To allow for cross-country comparisons over time, we algorithmically reorganise the legislative materials of the United States and Germany into cluster families that reflect legal topics. This reorganisation reveals that the main driver behind the growth of the law in both jurisdictions is the expansion of the welfare state, backed by an expansion of the tax state.Comment: 22 pages, 6 figures (main paper); 28 pages, 11 figures (supplementary information

Measuring Law Over Time: A Network Analytical Framework with an Application to Statutes and Regulations in the United States and Germany

How do complex social systems evolve in the modern world? This question lies at the heart of social physics, and network analysis has proven critical in providing answers to it. In recent years, network analysis has also been used to gain a quantitative understanding of law as a complex adaptive system, but most research has focused on legal documents of a single type, and there exists no unified framework for quantitative legal document analysis using network analytical tools. Against this background, we present a comprehensive framework for analyzing legal documents as multi-dimensional, dynamic document networks. We demonstrate the utility of this framework by applying it to an original dataset of statutes and regulations from two different countries, the United States and Germany, spanning more than twenty years (1998-2019). Our framework provides tools for assessing the size and connectivity of the legal system as viewed through the lens of specific document collections as well as for tracking the evolution of individual legal documents over time. Implementing the framework for our dataset, we find that at the federal level, the United States legal system is increasingly dominated by regulations, whereas the German legal system remains governed by statutes. This holds regardless of whether we measure the systems at the macro, the meso, or the micro level.Comment: 32 pages, 13 figures (main paper); 32 pages, 14 figures (supplementary information

Multilevel modelling of mechanical properties of textile composites: ITOOL Project

The paper presents an overview of the multi-level modelling of textile composites in the ITOOL project, focusing on the models of textile reinforcements, which serve as a basis for micromechanical models of textile composites on the unit cell level. The modelling is performed using finite element analysis (FEA) or approximate methods (method of inclusions), which provide local stiffness and damage information to FEA of composite part on the macro-level