Computational homogenization for multiscale crack modeling: implementational and computational aspects

A computational homogenization procedure for cohesive and adhesive crack modeling of materials with a heterogeneous microstructure has been recently presented in Computer Methods in Applied Mechanics and Engineering (2010, DOI:10.1016/j.cma.2010.10.013). The macroscopic material properties of the cohesive cracks are obtained from the inelastic deformation manifested in a localization band (modeled with a continuum damage theory) at the microscopic scale. The macroscopic behavior of the adhesive crack is derived from the response of a microscale sample representing the microstructure inside the adhesive crack. In this manuscript, we extend the theory presented in Computer Methods in Applied Mechanics and Engineering (2010, DOI:10.1016/j.cma.2010.10.013) with implementation details, solutions for cyclic loading, crack propagation, numerical analysis of the convergence characteristics of the multiscale method, and treatment of macroscopic snapback in a multiscale simulation. Numerical examples including crack growth simulations with extended finite elements are given to demonstrate the performance of the method

Computational homogenization for multiscale crack modeling: implementational and computational aspects

This is the peer reviewed version of the following article: [Nguyen, V. P., Lloberas-Valls, O., Stroeven, M. and Sluys, L. J. (2012), Computational homogenization for multiscale crack modeling. Implementational and computational aspects. Int. J. Numer. Meth. Engng, 89: 192–226. doi:10.1002/nme.3237], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.3237/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-ArchivingA computational homogenization procedure for cohesive and adhesive crack modeling of materials with a heterogeneous microstructure has been recently presented in Computer Methods in Applied Mechanics and Engineering (2010, DOI:10.1016/j.cma.2010.10.013). The macroscopic material properties of the cohesive cracks are obtained from the inelastic deformation manifested in a localization band (modeled with a continuum damage theory) at the microscopic scale. The macroscopic behavior of the adhesive crack is derived from the response of a microscale sample representing the microstructure inside the adhesive crack. In this manuscript, we extend the theory presented in Computer Methods in Applied Mechanics and Engineering (2010, DOI:10.1016/j.cma.2010.10.013) with implementation details, solutions for cyclic loading, crack propagation, numerical analysis of the convergence characteristics of the multiscale method, and treatment of macroscopic snapback in a multiscale simulation. Numerical examples including crack growth simulations with extended finite elements are given to demonstrate the performance of the methodPeer ReviewedPostprint (author's final draft

On the existence of representative volumes for softening quasi-brittle materials: a failure zone averaging scheme

The concept of the representative volume element (RVE) for softening materials is revised in this contribution. It is demonstrated by means of numerical simulations that there exists a sample which is statistically representative for quasi-brittle materials with random microstructure like concrete. This finding is an important ingredient for homogenization-based multiscale modelling of softening materials.Peer ReviewedPostprint (author's final draft

POROSIMETRY BY DOUBLE-RANDOM MULTIPLE TREE STRUCTURING IN VIRTUAL CONCRETE

Two different porosimetry methods are presented in two successive papers. Inspiration for the development came from the rapidly-exploring random tree (RRT) approach used in robotics. The novel methods are applied to virtual cementitious materials produced by a modern concurrent algorithm-based discrete element modeling system, HADES. This would render possible realistically simulating all aspects of particulate matter that influence structure-sensitive features of the pore network structure in maturing concrete, namely size, shape and dispersion of aggregate and cement particles. Pore space is a complex tortuous entity. Practical methods conventionally applied for assessment of pore size distribution may fail or present biased information. Among them, mercury intrusion porosimetry and 2D quantitative image analysis are popular. The mathematical morphology operator “opening” can be applied to sections and even provide 3D information on pore size distribution, provided isotropy is guaranteed. Unfortunately, aggregate grain surfaces lead to pore anisotropy. The presented methods allow exploration of pore space in the virtual material, after which pore size distribution is derived from star volume measurements.  In addition to size of pores their continuity is of crucial importance for durability estimation. Double-random multiple tree structuring (DRaMuTS), presented herein, and random node structuring (RaNoS) provide such information. The latter method will be introduced in a next issue of IA&S

Homogenization-based multiscale crack modelling: from micro-diffusive damage to macro-cracks

The existence of a representative volume element (RVE) for a class of quasi-brittle materials having a random heterogeneous microstructure in tensile, shear and mixed mode loading is demonstrated by deriving traction–separation relations, which are objective with respect to RVE size. A computational homogenization based multiscale crack modelling framework, implemented in an FE2 setting, for quasi-brittle solids with complex random microstructure is presented. The objectivity of the macroscopic response to the micro-sample size is shown by numerical simulations. Therefore, a homogenization scheme, which is objective with respect to macroscopic discretization and microscopic sample size, is devised. Numerical examples including a comparison with direct numerical simulation are given to demonstrate the performance of the proposed metho

Homogenization-based multiscale crack modelling: from micro-diffusive damage to macro-cracks

The existence of a representative volume element (RVE) for a class of quasi-brittle materials having a random heterogeneous microstructure in tensile, shear and mixed mode loading is demonstrated by deriving traction–separation relations, which are objective with respect to RVE size. A computational homogenization based multiscale crack modelling framework, implemented in an FE2 setting, for quasi-brittle solids with complex random microstructure is presented. The objectivity of the macroscopic response to the micro-sample size is shown by numerical simulations. Therefore, a homogenization scheme, which is objective with respect to macroscopic discretization and microscopic sample size, is devised. Numerical examples including a comparison with direct numerical simulation are given to demonstrate the performance of the proposed method.Peer ReviewedPostprint (author's final draft

On the existence of representative volumes for softening quasi-brittle materials: a failure zone averaging scheme

The concept of the representative volume element (RVE) for softening materials is revised in this contribution. It is demonstrated by means of numerical simulations that there exists a sample which is statistically representative for quasi-brittle materials with random microstructure like concrete. This finding is an important ingredient for homogenization-based multiscale modelling of softening materials

The build-up, configuration, and dynamical sensitivity of the Eurasian ice-sheet complex to Late Weichselian climatic and oceanic forcing

The Eurasian ice-sheet complex (EISC) was the third largest ice mass during the Last Glacial Maximum (LGM), after the Antarctic and North American ice sheets. Despite its global significance, a comprehensive account of its evolution from independent nucleation centres to its maximum extent is conspicuously lacking. Here, a first-order, thermomechanical model, robustly constrained by empirical evidence, is used to investigate the dynamics of the EISC throughout its build-up to its maximum configuration. The ice flow model is coupled to a reference climate and applied at 10 km spatial resolution across a domain that includes the three main spreading centres of the Celtic, Fennoscandian and Barents Sea ice sheets. The model is forced with the NGRIP palaeo-isotope curve from 37 ka BP onwards and model skill is assessed against collated flowsets, marginal moraines, exposure ages and relative sea-level history. The evolution of the EISC to its LGM configuration was complex and asynchronous; the western, maritime margins of the Fennoscandian and Celtic ice sheets responded rapidly and advanced across their continental shelves by 29 ka BP, yet the maximum aerial extent (5.48 × 106 km2) and volume (7.18 × 106 km3) of the ice complex was attained some 6 ka later at c. 22.7 ka BP. This maximum stand was short-lived as the North Sea and Atlantic margins were already in retreat whilst eastern margins were still advancing up until c. 20 ka BP. High rates of basal erosion are modelled beneath ice streams and outlet glaciers draining the Celtic and Fennoscandian ice sheets with extensive preservation elsewhere due to frozen subglacial conditions, including much of the Barents and Kara seas. Here, and elsewhere across the Norwegian shelf and North Sea, high pressure subglacial conditions would have promoted localised gas hydrate formation

FLECS, a Flexible Coupling Shell Parallel Application to Fluid-Structure Interaction

In this paper we discuss the second version of FLECS, a generic, open-source coupling shell that can be used to join two or more arbitrary solvers. In general multidisciplinary computations are very computing-intensive. A remedy against long computing times is large-scale parallelism. The challenge of the present parallelization work is to obtain acceptable computing times and to get rid of severe memory requirements that exist on sequential machines, for the generic flow problems at hand. The aim is to provide a flexible platform for developing new data transfer algorithms and coupling schemes