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The purpose of this paper is to develop a concurrent multiscale computational method for granular materials in the quasi-static loading regime.

Overlapped-coupling between a micropolar linear elastic one-dimensional (1D) mixed finite element (FE) model and a 1D chain of Hertzian nonlinear elastic, glued, discrete element (DE) spheres is presented. The 1D micropolar FEs and 1D chain of DEs are coupled using a bridging-scale decomposition for static analysis.

It was found that an open-window DE domain may be coupled to a micropolar continuum FE domain via an overlapping region within the bridging-scale decomposition formulation for statics. Allowing the micropolar continuum FE energy in the overlapping region to contribute to the DE energy has a smoothing effect on the DE response, especially for the rotational degrees of freedom (dofs).

The paper focusses on 1D examples, with elastic, glued, DE spheres, and a linear elastic micropolar continuum implemented in 1D.

A concurrent computational multiscale method for granular materials with open-window DE resolution of the large shearing region such as at the interface with a penetrometer skin, will allow more efficient computations by reducing the more costly DE domain calculations, but not at the expense of generating artificial boundary effects between the DE and FE domains.

Open-window DE overlapped-coupling to FE continuum domain, accounting for rotational dofs in both DE and FE methods. Contribution of energy from micropolar FE in overlap region to underlying DE particle energy.

This paper aims to introduce a multiscale computational method for structural failure analysis with inheriting simulation of moving trans-scale boundary (MTB). This method is motivated from the error in domain bridging caused by cross-scale damage evolution, which is common in structural failure induced by damage accumulation.

Within the method, vulnerable regions with high stress level are described by continuum damage mechanics, while elastic structural theory is sufficient for the rest, dividing the structural model into two scale domains. The two domains are bridged to generate mixed dimensional finite element equation of the whole system. Inheriting simulation is developed to make the computation of MTB sustainable.

Numerical tests of a notched three-point bending beam and a steel frame show that this MTB method can improve efficiency and ensure accuracy while capturing the effect of material damage on deterioration of components and structure.

The proposed MTB method with inheriting simulation is an extension of multiscale simulation to structural failure analysis. Most importantly, it can deal with cross-scale damage evolution and improve computation efficiency significantly.

The purpose of this paper is to extend the bridge scale method (BSM) developed for granular materials with only the solid phase to that taking into account the effects of wetting process in porous continuum. The granular material is modeled as partially saturated porous Cosserat continuum and discrete particle assembly in the coarse and fine scales, respectively.

Based on the mass and momentum conservation laws for the three phases, i.e. the solid skeleton, the pore water and the pore air, the governing equations for the unsaturated porous Biot-Cosserat continuum model in the coarse scale are derived. In light of the passive air pressure assumption, a reduced finite element model for the model is proposed. According to the decoupling of the fine and coarse scale calculations in the BSM, the unsaturated porous Cosserat continuum model using the finite element method and the discrete element model using the discrete element method for granular media are combined.

The numerical results for a 2D example problem of slope stability subjected to increasing rainfall along with mechanical loading demonstrate the applicability and performance of the present BSM. The microscopic mechanisms of macroscopic shear band developed in the slope are demonstrated.

Do not account for yet the effects of unsaturated pore water in the fine scale.

The novel BSM that couples the Biot-Cosserat porous continuum modeling and the discrete particle assembly modeling in both coarse and fine scales, respectively, is proposed to provide a micro-macro discrete-continuum two-scale modeling approach for numerical simulations of the hydro-mechanical coupling problems in unsaturated granular materials.

The purpose of this paper is to develop a discrete element (DE) and multiscale modeling methodology to represent granular media at their particle scale as they interface solid deformable bodies, such as soil‐tool, tire, penetrometer, pile, etc., interfaces.

A three‐dimensional ellipsoidal discrete element method (DEM) is developed to more physically represent particle shape in granular media while retaining the efficiency of smooth contact interface conditions for computation. DE coupling to finite element (FE) facets is presented to demonstrate initially the development of overlapping bridging scale methods for concurrent multiscale modeling of granular media.

A closed‐form solution of ellipsoidal particle contact resolution and stiffness is presented and demonstrated for two particle, and many particle contact simulations, during gravity deposition, and quasi‐static oedometer, triaxial compression, and pile penetration. The DE‐FE facet coupling demonstrates the potential to alleviate artificial boundary effects in the shear deformation region between DEM granular media and deformable solid bodies.

The research is being extended to couple more robustly the ellipsoidal DEM code and a higher order continuum FE code via overlapping bridging scale methods, in order to remove dependence of penetration/shear resistance on the boundary placement for DE simulation.

When concurrent multiscale computational modeling of interface conditions between deformable solid bodies and granular materials reaches maturity, modelers will be able to simulate the mechanical behavior accounting for physical particle sizes and flow in the interface region, and thus design their tool, tire, penetrometer, or pile accordingly.

A closed‐form solution for ellipsoidal particle contact is demonstrated in this paper, and the ability to couple DE to FE facets.

The purpose of this paper is to develop a method to model entire structures on a large scale, at the same time taking into account localized non-linear phenomena of the discrete microstructure of cohesive-frictional materials.

Finite element (FEM) based continuum methods are generally considered appropriate as long as solutions are smooth. However, when discontinuities like cracks and fragmentation appear and evolve, application of models that take into account (evolving) microstructures may be advantageous. One popular model to simulate behavior of cohesive-frictional materials is the discrete element method (DEM). However, even if the microscale is close to the macroscale, DEMs are computationally expensive and can only be applied to relatively small specimen sizes and time intervals. Hence, a method is desirable that combines efficiency of FEM with accuracy of DEM by adaptively switching from the continuous to the discrete model where necessary.

An existing method which allows smooth transition between discrete and continuous models is the quasicontinuum method, developed in the field of atomistic simulations. It is taken as a starting point and its concepts are extended to applications in structural mechanics in this paper. The kinematics in the method presented herein is obtained from FEM whereas DEM yields the constitutive behavior. With respect to the constitutive law, three levels of resolution – continuous, intermediate and discrete – are introduced.

The overall concept combines model adaptation with adaptive mesh refinement with the aim to obtain a most efficient and accurate solution.

In recent years, the partially averaged Navier–Stokes (PANS) methodology has earned acceptability as a viable scale-resolving bridging method of turbulence. To further enhance its capabilities, especially for simulating separated flows past bluff bodies, this paper aims to combine PANS with a non-linear eddy viscosity model (NLEVM).

The authors first extract a PANS closure model using the Shih’s quadratic eddy viscosity closure model [originally proposed for Reynolds-averaged Navier–Stokes (RANS) paradigm (Shih et al., 1993)]. Subsequently, they perform an extensive evaluation of the combination (PANS + NLEVM).

The NLEVM + PANS combination shows promising result in terms of reduction of the anisotropy tensor when the filter parameter (f_k) is reduced. Further, the influence of PANS filter parameter f on the magnitude and orientation of the non-linear part of the stress tensor is closely scrutinized. Evaluation of the NLEVM + PANS combination is subsequently performed for flow past a square cylinder at Reynolds number of 22,000. The results show that for the same level of reduction in f_k, the PANS + NLEVM methodology releases significantly more scales of motion and unsteadiness as compared to the traditional linear eddy viscosity model (LEVM) of Boussinesq (PANS + LEVM). The authors further demonstrate that with this enhanced ability the NLEVM + PANS combination shows much-improved predictions of almost all the mean quantities compared to those observed in simulations using LEVM + PANS.

Based on these results, the authors propose the NLEVM + PANS combination as a more potent methodology for reliable prediction of highly separated flow fields.

Combination of a quadratic eddy viscosity closure model with PANS framework for simulating flow past bluff bodies.

This paper aims to present a geometrical void model in conjunction with a multiscale method to evaluate the effect of interraster distance, bead (raster) width and layer height, on the voids concentration (volume) and subsequently calculate the final mechanical properties of the fused deposition modeling parts at constant infill.

A geometric model of the voids inside the representative volume element (RVE) is combined with a two-scale asymptotic homogenization method. The RVEs are subjected to periodic boundary conditions solved by finite element (FE) to calculate the effective mechanical properties of the corresponding RVEs. The results are validated with literature and experiments.

Bead width from 0.2 to 0.3 mm, reported a decrease of 25% and 24% void volume for a constant layer height (0.1 and 0.2 mm – 75% infill). It is reported that the void’s volume increased up to 14%, 32% and 36% for 75%, 50% and 25% infill by varying layer height (0.1–0.2  and 0.3 mm), respectively. For elastic modulus, 14%, 9% and 10% increase is reported when the void’s volume is decreased from 0.3 to 0.1 mm at a constant 75% infill density. The bead width and layer height have an inverse effect on voids volume.

This work brings values: a multiscale-geometric model capable of predicting the voids controllability by varying interraster distance, layer height and bead width. The idealized RVE generation slicer software and Solidworks save time and cost (<10 min, $0). The proposed model can effectively compute the mechanical properties together with the voids analysis.

The purpose of this paper is to solve non‐linear parametric thermal models defined in degenerated geometries, such as plate and shell geometries.

The work presented in this paper is based in a combination of the proper generalized decomposition (PGD) that proceeds to a separated representation of the involved fields and advanced non‐linear solvers. A particular emphasis is put on the asymptotic numerical method.

The authors demonstrate that this approach is valid for computing the solution of challenging thermal models and parametric models.

This is the first time that PGD is combined with advanced non‐linear solvers in the context of non‐linear transient parametric thermal models.

This paper aims to describe the obtainment of Ti-6Al-4V parts with a hierarchical arrangement of pores by additive manufacturing, aiming at designing orthopedic implants.

The experimental methodology compares microstructural and mechanical properties of Menger pre-fractal sponges of Ti-6Al-4V alloy, manufactured by laser powder bed fusion (LPBF) and electron beam powder bed fusion (EBPBF), with three different porosity volumes. The pore arrangement followed the formation sequence of the Menger sponge, with hierarchical order from 1 to 3.

The LPBF parts presented a martensitic microstructure, while the EBPBF parts presented an α + ß microstructure, independently of its wall thickness. The LPBF parts presented higher mechanical resistance and effective stiffness than the EBPBF parts with similar porosity volume. The stiffness values of the Menger pre-fractal sponges of Ti-6Al-4V alloy, between 4 and 29 GPa, are comparable to those of the cortical bone. Furthermore, the deformation behavior presented by the Menger pre-fractal sponges of Ti-6Al-4V alloy did not follow the Gibson and Ashby model's prediction.

To the best of the authors' knowledge, this is the first study to obtain Menger pre-fractal sponges of Ti-6Al-4V alloy by LPBF and EBPBF. The deformation behavior of the obtained porous parts was contrasted with the Gibson and Ashby model's prediction.

The purpose of this paper is to investigate the potential, both analytically and practically, of understanding research methods as bridging devices. Methods can bridge theory and empirics, but it is argued that they can perform several bridging functions: between theory and praxis, between analysis and strategy and between past and future. The focus is on those forms of bridging relevant for understanding and effectuating change in governance, at community level and at the scale of organizations.

The paper develops a perspective on methods as bridging devices. It uses the newly minted methods of governance path and context mapping as a case study. These methods conceptually derive from evolutionary governance theory (EGT) and were developed and tested in Canadian empirical research. The case helps to develop insight in features, forms and limitations of methods as bridging devices in governance research and practice. The authors then use the case to further develop the initial concept of bridging more generally, emphasizing the shifting balance between methods as bridging and creating boundaries.

Both the case study and the theoretical analysis underline the necessary imperfection of any method as bridging device. The authors affirm the potential of method to perform different bridging functions at the same time, while revealing clear tradeoffs in each role. Tradeoffs occur with adapted versions of the method producing new strengths and weaknesses in new contexts. In each of the forms of bridging involved neither side can be reduced to the other, so a gap always remains. It is demonstrated that the practice of bridging through method in governance is greatly helped when methods are flexibly deployed in ongoing processes of bricolage, nesting and modification. Governance enables the continuous production of new framing devices and other methods.

The idea of methods as bridging devices is new, and can assist the development of a broader understanding of the various forms and functions of research methods. Moreover, it helps to discern roles of research methods in the functioning of governance. The context of governance helps to recognize the multi-functionality of research methods, and their transformation in a context of pressured decision-making. Moreover, this approach contributes to the understanding of governance as adumbrated by EGT.