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Higher-order constitutive relations for granular materials: a multi-scale approach

Periodic Reporting for period 1 - ICARUS (Higher-order constitutive relations for granular materials: a multi-scale approach)

Reporting period: 2019-07-01 to 2021-06-30

The mechanical behaviour of granular materials subjected to large deformations is important in many problems in science and engineering. Problems involving granular materials can cause significant losses in many branches of engineering, such as in energy and environmental geotechnics, chemical process industry, pharmaceutical industry and agriculture. Two examples are: (i) 476 European landslides over the past two decades have caused a total of 1370 deaths and 784 injuries with economic losses of 94 billion Euros and (ii) natural hazards have resulted in 1085 failures of global offshore facilities (with 303 events in Europe) over the past four decades.

Current numerical simulation methods using classical, zeroth-order constitutive relations give results that are dependent on the employed mesh size. This problem can be circumvented by using higher-order constitutive relations. However, current higher-order constitutive relations are heuristic, and thus in many cases the results are still mesh-size dependent. Using an innovative multi-scale approach, the project ICARUS aims to constructively challenge current higher-order continuum theories from a fundamental perspective, namely by consideration of the underlying microstructure, in order to obtain mesh independent solutions.

The overall objectives of ICARUS are to: (i) develop micromechanical expressions for three-dimensional higher-order strain and stress tensors for granular materials, (ii) construct higher-order constitutive models within the thermodynamic framework, based on micromechanical analyses of Discrete Element Method (DEM) simulations, and (iii) demonstrate their capabilities in solving “benchmark” geotechnical large-deformation problems. The investigation results in a computational simulation method that provides valuable insights in large-deformation engineering problems and thus will aid in assessing and reducing risks of natural hazards, with benefits for society.
The project ICARUS has achieved most of its objectives and milestones for the period, with relatively minor deviations. The main results of ICARUS include:
(i) Fabric evolution in granular materials has been investigated, using DEM simulations and x-ray tomography measurements. An evolution law has been developed which considers the influence of loading direction, void ratio, confining pressure, etc.
(ii) Experimental evidence has been provided for the first time for the Anisotropic Critical State Theory that forms one of the cornerstones for the theoretical description of the behaviour of granular materials.
(iii) The fabric response to stress probing in granular materials for two-dimensional, anisotropic granular assemblies has been obtained, which is accomplished by means of extensive sets of DEM simulations.
(iv) A coarse-graining approach has been developed to determine strain, higher-order strain, and stress in granular materials from the micro-scale information on particles and interparticle contacts, which is validated for both two-dimensional and three-dimensional cases.
(v) DEM simulations of granular materials with and without rolling resistances at interparticle contacts, have been performed in order to understand the relationship between mean particle rotations and continuum rotations.
(vi) An elastoplastic constitutive relation has been implemented in a finite element code in order to investigate the relationship between the width of shear band and the mesh size that is employed in numerical simulations of granular materials.

These results have significantly advanced the understanding of the behaviour of granular materials and have paved the way to tackle the challenges on large-deformation problems in granular materials. The results of ICARUS have been disseminated immediately through various channels, including 6 high-quality papers that have been submitted to high-impact factor, peer-reviewed journals allowing open access and 11 international conferences and workshops where top-ranked researchers in the field of granular materials and geomechanics were present.
The results of ICARUS can be applied in further investigations of the behaviour of granular materials: (i) The micromechanical expressions for the three-dimensional higher-order strain and stress tensors can be widely employed to analyse the results of DEM simulations by researchers with different purposes. (ii) The developed multi-scale higher-order methodology is applicable to other multi-scale and multi-physics problems, such as rainfall-induced slope instability in wet granular materials and erosion of geomaterials that causes collapse of dams in Europe.

ICARUS pursues the commercial exploitation of its results and developments, as it can significantly improve the safety and reliability of current design methods. The application of the developed approach in industry will greatly reduce maintenance costs to governments, and it will also contribute to new standardisation activities in geotechnical design in the EU. To deliver such a numerical simulation tool to the potential end-users, the developed method will first be validated in the “benchmark” problems. With assistance of the business developers of the Knowledge Transfer Office of the University of Twente, the Fellow is actively approaching potential users, such as software companies in geotechnical engineering design as well as researchers using large-deformation numerical codes. As the simulation tool is a novel module that can be implemented in existing simulation platforms of these companies, the Fellow is aiming at licensing (complying with H2020 rules) the developed simulation tool to these end-users.
Research Methodology