Model-Free Data-Driven Methods in Mechanics: Material Data Identification and Solvers

This paper presents an integrated model-free data-driven approach to solid mechanics, allowing to perform numerical simulations on structures on the basis of measures of displacement fields on representative samples, without postulating a specific constitutive model. A material data identification procedure, allowing to infer strain-stress pairs from displacement fields and boundary conditions, is used to build a material database from a set of mutiaxial tests on a non-conventional sample. This database is in turn used by a data-driven solver, based on an algorithm minimizing the distance between manifolds of compatible and balanced mechanical states and the given database, to predict the response of structures of the same material, with arbitrary geometry and boundary conditions. Examples illustrate this modelling cycle and demonstrate how the data-driven identification method allows importance sampling of the material state space, yielding faster convergence of simulation results with increasing database size, when compared to synthetic material databases with regular sampling patterns.Comment: Revised versio

Deim-based pgd for multi-parametric nonlinear model reduction

A new technique for efficiently solving parametric nonlinear reduced order models in the Proper Generalized Decomposition (PGD) framework is presented here. This technique is based on the Discrete Empirical Interpolation Method (DEIM)[1], and thus the nonlinear term is interpolated using the reduced basis instead of being fully evaluated. The DEIM has already been demonstrated to provide satisfactory results in terms of computational complexity decrease when combined with the Proper Orthogonal Decomposition (POD). However, in the POD case the reduced basis is a posteriori known as it comes from several pre-computed snapshots. On the contrary, the PGD is an a priori model reduction method. This makes the DEIM-PGD coupling rather delicate, because different choices are possible as it is analyzed in this work

An overview of the proper generalized decomposition with applications in computational rheology

We review the foundations and applications of the proper generalized decomposition (PGD), a powerful model reduction technique that computes a priori by means of successive enrichment a separated representation of the unknown field. The computational complexity of the PGD scales linearly with the dimension of the space wherein the model is defined, which is in marked contrast with the exponential scaling of standard grid-based methods. First introduced in the context of computational rheology by Ammar et al. [3] and [4], the PGD has since been further developed and applied in a variety of applications ranging from the solution of the Schrödinger equation of quantum mechanics to the analysis of laminate composites. In this paper, we illustrate the use of the PGD in four problem categories related to computational rheology: (i) the direct solution of the Fokker-Planck equation for complex fluids in configuration spaces of high dimension, (ii) the development of very efficient non-incremental algorithms for transient problems, (iii) the fully three-dimensional solution of problems defined in degenerate plate or shell-like domains often encountered in polymer processing or composites manufacturing, and finally (iv) the solution of multidimensional parametric models obtained by introducing various sources of problem variability as additional coordinates

Differentiating ‘the user’ in DSR: Developing demand side response in advanced economies

This paper reports on the current state of Demand Side Response (DSR) in the UK – an early adoptor amongst advanced economies – and the role of the end user in determining its future. Through 21 expert interviews we establish the current state of DSR, and expectations for its development. Whilst non-domestic DSR appears healthy, if fragile, domestic DSR is considered to be currently unviable, it's future success dependant on market innovations. In following how that situation is expected to change, we highlight key assumptions about prospective end users. These assumptions are shaping the efforts of the industry actors tasked with delivering DSR. We identify two visions of the user, one passive whilst technologies automate on their behalf, the other integrated to the point of themselves being an automaton. We detail a series of concerns about the limitations of these user visions, and the ability of industry to reach beyond them towards a more differentiated view. We conclude with a call to broaden the institutional landscape tasked with delivering DSR, in order to foster a greater diversity of end user roles, and ultimately greater demand responsiveness from a broader user base

Molecular imaging for stem cell therapy in the brain

In this work, we suggest a method, based on the data driven computational mechanics framework introduced by Kirchdoerfer and Ortiz, to extract representative strain-stress couples from a collection of non-homogenous full field measurements corresponding to different loading conditions

On implicit racial prejudice against infants

Because of the innocence and dependence of children, it would be reassuring to believe that implicit racial prejudice against out-group children is lower than implicit prejudice against out-group adults. Yet, prior research has not directly tested whether or not adults exhibit less spontaneous prejudice toward child targets than adult targets. Three studies addressed this issue, contrasting adults with very young child targets. Studies 1A and B revealed that participants belonging to an ethnic majority group (White Europeans) showed greater spontaneous favorability toward their ethnic in-group than toward an ethnic out-group (South Asians), and this prejudice emerged equally for infant and adult targets. Study 2 found that this pattern occurred even when race was not a salient dimension of categorization in the implicit measure. Thus, there was a robust preference for in-group children over out-group children, and there was no evidence that this prejudice is weaker than that exhibited toward adults

Digital energy visualizations in the workplace: the e-Genie tool

Building management systems are designed for energy managers; there are few energy-feedback systems designed to engage staff. A tool, known as e-Genie, was created with the purpose of engaging workplace occupants with energy data and supporting them to take action to reduce energy use. Building on research insights within the field, e-Genie’s novel approach encourages users to make plans to meet energy-saving goals, supports discussion and considers social energy behaviours (e.g. discussing energy issues, taking part in campaigns) as well as individual actions. A field-based study of e-Genie indicated that visualizations of energy data were engaging and that the discussion ‘Pinboard’ was particularly popular. Pre- and post-survey (N = 77) evaluation of users indicated that people were significantly more concerned about energy issues and reported engaging more in social energy behaviour after about two weeks of e-Genie being installed. Concurrently, objective measures of electricity use decreased over the same period, and continued decreasing over subsequent weeks. Indications are that occupant-facing energy-feedback visualizations can be successful in reducing energy use in the workplace; furthermore, supporting social energy behaviour in the workplace is likely to be a useful direction for promoting action

On secondary loops in LAOS via self-intersection of Lissajous–Bowditch curves

When the shear stress measured in large amplitude oscillatory shear (LAOS) deformation is represented as a 2-D Lissajous–Bowditch curve, the corresponding trajectory can appear to self-intersect and form secondary loops. This self-intersection is a general consequence of a strongly nonlinear material response to the imposed oscillatory forcing and can be observed for various material systems and constitutive models. We derive the mathematical criteria for the formation of secondary loops, quantify the location of the apparent intersection, and furthermore suggest a qualitative physical understanding for the associated nonlinear material behavior. We show that when secondary loops appear in the viscous projection of the stress response (the 2-D plot of stress vs. strain rate), they are best interpreted by understanding the corresponding elastic response (the 2-D projection of stress vs. strain). The analysis shows clearly that sufficiently strong elastic nonlinearity is required to observe secondary loops on the conjugate viscous projection. Such a strong elastic nonlinearity physically corresponds to a nonlinear viscoelastic shear stress overshoot in which existing stress is unloaded more quickly than new deformation is accumulated. This general understanding of secondary loops in LAOS flows can be applied to various molecular configurations and microstructures such as polymer solutions, polymer melts, soft glassy materials, and other structured fluids