Abstract

Abstract

Abstract

In materials with a strain‐softening characteristic behavior, classical continuum mechanics favors uncontrolled strain localization in numerical analyses. Several methods have been proposed to regularize the problem. Two such localization limiters developed to overcome spurious instabilities in computational failure analysis are examined and compared. A disturbance analysis, on both models, is performed to obtain the closed‐form solution of propagating wave velocities as well as the velocities at which the energy travels. It also shows that in spite of forcing the same stress‐strain response, the wave equation does not yield similar results. Both propagations of waves are dispersive, but the internal length of each model is different when equivalent behavior is desired. In fact, the previously suggested derivations of gradient models from nonlocal integral models were not completely rigorous. The perturbation analysis is pursued in the discrete space where computations are done, and the closed form solutions are also obtained. The finite‐element discretization introduces an added dispersion associated to the regularization technique. Therefore, the influence of the discretization on the localization limiters can be evaluated. The element size must be smaller than the internal length of the models in order to obtain sufficient accuracy.

Abstract

Non-local models guaranty that finite element computations on strain softening materials remain sound up to failure from a theoretical and computational viewpoint. The non-locality prevents strain localization with zero global dissipation of energy, and consequently finite element calculations converge upon mesh refinements to non-zero width localization zones. One of the major drawbacks of these models is that the element size needed in order to capture the localization zone must be smaller than the intemallength. Hence, the total number of degrees of freedom becomes rapidly prohibitive for most engineering applications and there is an obvious need for mesh adaptivity. This paper deals with the application of the arbitrary Lagrangian-Eulerian (ALE) formulation, well known in hydrodynamics and fluid-structure interaction problems, to transient strain localization in a non-local damageable material. It is shown that the ALE formulation which is employed in large boundary motion problems can also be well suited for non-linear transient analysis of softening materials where localization bands appear. The remeshing strategy is based on the equidistribution of an indicator that quantifies the interelement jump of a selected state variable. Two well known one-dimensional examples illustrate the capabilities of this technique: the first one deals with localization due to a propagating wave in a bar, and the second one studies the wave propagation in a hollow sphere.

Abstract

The prediction of local field statistics from effective properties is an open problem in the field of micromechanics. Partial information on the local field statistics is accessible from homogenization assumptions. In particular, exact phase-wise second moments of stresses can be calculated analytically from the effective strain energy density. In recent years, full-field calculations have become efficient enough to sample large ensembles of microstructures in the plastic regime (e.g. Gehrig et. al [4]). In the present work, the maximum entropy method known from statistical thermodynamics is used to estimate first and second moments of local stresses from known eigenstrain distributions. The simple and refined formulations of the maximum entropy method proposed by Kreher and Pompe [9] are considered. While the simple method yields satisfactory results for a large amount of material classes (cf. Krause and Böhlke [7]), we prove that it does not respect the linearity of the eigenstrain problem. We further show that neither method corresponds to the exact second moments of stresses known from the effective strain energy density. By incorporating additional information, we find an improved maximum entropy method. As an example, we analyze stress fluctuations in polycristalline titanium.For the exact analytical solution and the maximum entropy methods, we use the singular approximation and the Hashin-Shtrikman bounds. For comparison, we numerically approximate full-field statistics using an FFT approach. In all methods, the stress fluctuations caused by the anisotropy of the single crystal strongly influence the elastic-plastic transition.

Abstract

This work deals with the simulation of strain localization phenomena through the Strong Discontinuity Approach (SDA) for three dimensional (3D) problems. The main assumptions of this work are the isothermal quasi-static regime, small deformations and rotations, and a material describes as homogeneous and isotropic.

Abstract

Abstract

Abstract

The working paper studies the approaches of the digital economy leaders (the US, the EU and China) to data governance and approaches they promote in international institutions. Data can generate not only profits for tech giants, but also social value. However, the market forces by themselves will not create data-based public goods. Government actions are needed at the county level and inter-state and multilateral institutions cooperation at the international level. The study is highly relevant, since to date despite numerous initiatives to establish coordination mechanisms and data regulation, cooperation on data governance is highly fragmented and gridlocked due to contradictions and tough competition between key players. One of the key disagreements is related to the regulation of cross-border data flows. The working paper aims to explore contradictions between the regulatory practices of the key actors in digital economy, the US, EU and China in the first place, and approaches they promote in international institutions (the WTO, G20, G7, OECD). In particular, the author looks into the G20 agenda on data governance and the Initiative on free data flow with trust, its challenges, and risks of cooperation stagnation. The working paper presents possible scenarios of future cooperation on data governance, their risks and perspectives, including the establishment of the Digital Economy and Data Governance Board by the G20, G7 initiative on shaping global digital order, deepening of cooperation on data governance within the G7 and the OECD, and the UNCTAD proposal on building a multilevel distributed polycentric data-governance model with the UN central role. The author concludes with a proposal on BRICS cooperation aimed at shaping inclusive multilateral data governance.