A duality‐based method for generating geometric representations of polycrystals

Rimoli, Julián J.; Ortiz, Michael

doi:10.1002/nme.3090

Cited by 7 publications

(3 citation statements)

References 30 publications

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“…Given the grain size field, we generate a polycrystalline structure by following a procedure similar to the one proposed in [31], with the only difference that we adopt a dual based on the discrete Hodge operator [32] instead of a barycentric one. In this way, we entirely avoid the grain boundary energy relaxation step.…”

Section: Verification Of Separation Of Scales Assumptionmentioning

confidence: 99%

Exploiting length-dependent effects for the design of single-material systems with enhanced thermal transport properties

Bouquet

Burgaud

Rimoli

2016

International Journal of Heat and Mass Transfer

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Topology optimization approaches for thermal transport problems generally rely on the presence of high contrast in thermal conductivity between constituent materials. Even though this might result in topological configurations that are optimal according to some desired thermal metric, the resulting systems might be impractical from a mechanical standpoint: high contrast in thermal conductivity generally translates into disparate ranges of thermal expansion, which in turn may lead to mechanical failure. In this paper, we focus on the combination of multi-scale modeling and topology optimization techniques for the design of polycrystalline single-material systems with enhanced thermal transport properties. Spatial variation of the length-dependent thermal conductivity is achieved by grading the characteristic grain size of the microstructure. We adopt a multi-scale approach to compute the attainable range of thermal conductivity due to grain-size effect, given maximum and minimum grain sizes and an operating temperature range. Then, we utilize an adaptive topology optimization technique to obtain an optimal grain size distribution, while accounting for manufacturing constraints. Through a series of specific examples, we demonstrate the extent to which thermal transport properties can be optimized without resorting to the adoption of multi-material systems.

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Section: Verification Of Separation Of Scales Assumptionmentioning

confidence: 99%

Exploiting length-dependent effects for the design of single-material systems with enhanced thermal transport properties

Bouquet

Burgaud

Rimoli

2016

International Journal of Heat and Mass Transfer

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“…• A barycentric subdivision is applied to the initial K-means mesh An algorithm for performing a barycentric subdivision to simplicial meshes of any dimension is detailed in [18], and explained in the subsequent paragraphs for completeness. Towards this end, we first describe (briefly) the concept of simplicial complex and subdivisions of a simplicial complex (triangulation).…”

Section: Reducing Mesh Induced Toughness Through Conjugatedirections mentioning

confidence: 99%

Meshing strategies for the alleviation of mesh-induced effects in cohesive element models

Rimoli

Rojas

2015

Int J Fract

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One of the main approaches for modeling fracture and crack propagation in solid materials is adaptive insertion of cohesive elements, in which line-like (2D) or surface-like (3D) elements are inserted into the finite element mesh to model the nucleation and propagation of failure surfaces. In this approach, however, cracks are forced to propagate along element boundaries, following paths that in general require more energy per unit crack extension (greater driving forces) than those followed in the original continuum, which in turn leads to erroneous solutions. In this work we illustrate how the introduction of a discretization produces two undesired effects, which we term mesh-induced anisotropy and meshinduced toughness. Subsequently, we analyze those effects through polar plots of the path deviation ratio (a measure of the ability of a mesh to represent straight lines) for commonly adopted meshes. Finally, we propose to reduce those effects through K-means meshes and through a new type of mesh, which we term conjugate-directions mesh. The behavior of all meshes under consideration as the mesh size is reduced is analyzed through a numerical study of convergence.

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“…The ensemble of crystals is generated using the relaxed dual complex (RDC) method proposed by Rimoli and Ortiz. 45 The RDC method takes as input an initial triangulation of the domain. The triangulation is then refined appropriately to provide suitably sized grains.…”

Section: Energetic Molecular Crystalsmentioning

confidence: 99%

Analysis of thermomechanical response of polycrystalline HMX under impact loading through mesoscale simulations

Hardin¹,

Rimoli²,

Zhou³

2014

AIP Advances

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We investigate the response of polycrystalline HMX 3,5,3,5, under impact loading through a 3-dimensional mesoscale model that explicitly accounts for anisotropic elasticity, crystalline plasticity, and heat conduction. This model is used to quantify the variability in temperature and stress fields due to random distributions of the orientations of crystalline grains in HMX under the loading scenarios considered. The simulations carried out concern the response of fully dense HMX polycrystalline ensembles under impact loading at imposed boundary velocities from 50 to 400 m/s. The polycrystalline ensemble studied consists of a geometrically arranged distribution of bi-modally sized and shaped grains. To quantify the effect of crystalline slip, two models with different numbers of available slip systems are used, reflecting differing characterizations of the slip systems of the HMX molecular crystal in the literature. The effects of microstructure and anisotropy on the distribution of heating and stress evolution are investigated. The results obtained indicate that crystalline response anisotropy at the microstructure level plays an important role in influencing both the overall response and the localization of stress and temperature. The overall longitudinal stress is up to 16% higher and the average temperature rise is only half in the material with fewer potential slip systems compared to those in the material with more available slip systems. Local stresses can be as high as twice the average stresses. The results show that crystalline anisotropy induces significant heterogeneities in both mechanical and thermal fields that previously have been neglected in the analyses of the behavior of HMX-based energetic materials. C 2014 Author(s)

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A duality‐based method for generating geometric representations of polycrystals

Cited by 7 publications

References 30 publications

Exploiting length-dependent effects for the design of single-material systems with enhanced thermal transport properties

Exploiting length-dependent effects for the design of single-material systems with enhanced thermal transport properties

Meshing strategies for the alleviation of mesh-induced effects in cohesive element models

Analysis of thermomechanical response of polycrystalline HMX under impact loading through mesoscale simulations

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