Multi-length Scale Research Articles

Coupling of Extension and Twist in Single-Walled Carbon Nanotubes

This paper presents a study of the deformation behavior of single-walled carbon nanotubes (SWNTs) subjected to extension and twist. The interatomic force description is provided by the Tersoff-Brenner potential for carbon. The rolling of a flat graphene sheet into a SWNT is first simulated by minimizing the energy per atom, the end result being the configuration of an undeformed SWNT. The Cauchy-Born rule is then used to connect the atomistic and continuum descriptions of the deformation of SWNTs, and leads to a multilength scale mechanics framework for simulating deformation of SWNTs under applied loads. Coupled extension and twist of SWNTs is considered next. As an alternative to the Cauchy-Born rule for coupled extension-twist problems, a direct map is formulated. Analytic expressions are derived for the deformed bond lengths using the Cauchy-Born rule and the direct map for this class of deformations. Numerical results are presented for kinematic coupling, for imposed extension and imposed twist problems, using the Cauchy-Born rule as well as the direct map, for representative chiral, armchair and zig-zag SWNTs. Results from both these approaches are carefully compared.

A finite element multiscale capability for nonlinear quasistatic stress analysis

Failure modeling is inherently a multi length scale phenomenon that requires a failure model and a computational method that solves for stress/strain gradients at interesting locations. Focusing on the computational method, we recognize that the mesh resolution must be relatively fine in regions where failure is expected and relatively coarse elsewhere. Furthermore, in some modeling approaches the topology in the structural model is different than that required in the fine scale model where failure is to be predicted. This necessarily precludes approaches such as h-adaptivity. We are therefore led to consider multiscale approaches to solve these problems.This work describes an approach to solve multiple (a reference scale and fine scale) coupled boundary value problems for the purpose of nonlinear quasistatic stress analysis. Two examples are included: one example illustrates the multiscale solution strategy to perform quasistatic stress analysis and the other demonstrates the computational beginnings of the ability to model material failure.

On the synergy between texture classification and deformation process sequence selection for the control of texture-dependent properties

Because of the computational complexity involved in multi-length scale formulations involving polycrystal plasticity, innovative algorithms need to be incorporated in techniques for designing processes to realize materials with optimized properties. This paper demonstrates the synergy between classification of fcc polycrystal texture and multi-scale process design for achieving desired properties in such materials. The inverse problem of designing processing stages that lead to a desired texture or texture-dependent property is addressed by mining a database of orientation distribution functions (ODFs). Given a desired ODF, the hierarchical classifier matches its ODF features in the form of pole density functions of important orientation fibers to a class of textures in the database. Texture classes are affiliated with processing information; hence, enabling identification of multiple process paths that lead to a desired texture. The process parameters identified by the classifier are fine-tuned using a gradient optimization algorithm driven by continuum sensitivity analysis of texture evolution. An adaptive reduced-order model for texture evolution based on proper orthogonal decomposition in which the reduced ODF modes corresponding to the intermediate stages of the design process are adaptively selected from the database is employed.

A generalized, multilength scale framework for thermo-diffusional-mechanically coupled, nonlinear, laminated plate theories with delaminations

A new type of plate theory based on a general, unified, theoretical framework for the response of (von Karman) nonlinear, delaminated plate theories in the presence of thermo-diffusional-mechanical coupling is presented. The theory is based on the unique use of two length scale expansions obtained from a superposition of global and local effects for the displacement, temperature, and solute concentration fields. The orders and forms of these local and global displacement, temperature, and solute fields are arbitrary. The theory incorporates delamination and/or nonlinear elastic or inelastic interfacial behavior for the mechanical, thermal, and concentration effects in a unified fashion through the use of generalized interfacial constitutive (cohesive) relations. The mathematical framework introduces new types of coupling effects between the different length scale effects of all three fields. The resulting unified theoretical framework can be used to consider the general thermo-diffusionally-mechanically coupled response of laminated (or homogeneous) plates in the presence of delaminations, buckling, and/or nonlinear material behavior. The author is unaware of any previous attempts to develop plate theory formulations capable of considering the multitude of effects incorporated into the proposed framework. It is shown that existing displacement-based plate theories for both the mechanical as well as thermo-mechanical behavior of laminated plates can be obtained via suitable specializations of the proposed framework. New types of plate theories can be obtained through various specializations of the proposed general theory.

Design across length scales: a reduced-order model of polycrystal plasticity for the control of microstructure-sensitive material properties

Development of techniques for the control of material properties of polycrystal materials that are inherently dependent on preferred orientations (texture) is addressed. To account for the infinite degrees of freedom of microstructural features, a model reduction on the micro-scale is introduced. Reduced-order models are developed to model the evolution of microstructure described by an orientation distribution function using a finite element discretization of the orientation space. This reduced-order modeling approach is based on the technique of proper orthogonal decomposition (POD) and the method of snapshots. Furthermore, novel design problems are introduced for the control of microstructure based on realistic polycrystalline plasticity. Specifically, a gradient based optimization framework is introduced using a multi-length scale continuum sensitivity method (CSM). The model reduction is extended to the sensitivity analysis and is a key element for the success of computational design of deformation processes. Numerical examples that highlight the benefits of the continuum sensitivity method and model reduction are presented. In addition, the potential of the presented techniques towards process design for obtaining desired material properties is demonstrated with the control at a material point of the elastic modulus in fcc copper. A desired distribution of the elastic modulus is achieved through an optimal selection of the velocity gradient.

Structural, magnetic, and transport studies of La0.8MnO3 films

A study of the properties of La0.8MnO3 films of varying thickness was performed. Transport and magnetization measurements show that the ferromagnetic (metallic) volume fraction of the film varies from ∼ 1/4 for ultrathin 60 Å films to ∼ 1/2 for 1600 Å films. Multilength scale structural measurements reveal that near 300 Å, a transition from highly strained ultrathin films to relaxed bulk-like films occurs. The transition region is characterized by low surface roughness, high crystallite orientation, and broad d-spacing distributions.

Buckling of composite plates by global–local plate theory

The bifurcation buckling problem of laminated composite plates is formulated within the framework of a multilength scale plate theory. This theory is a combination of single-layer and layer-wise theories. It is generated by representing the displacement as the sum of global and local effects that introduce a coupling between the two length scales. Comparisons between the presently predicted buckling loads of homogeneous and orthotropic laminated plates and the exact solutions show a very good correlation. Furthermore, the theory accurately predicts the buckling load of symmetric cross-ply plates as compared with the results of a layer-wise approach. This accuracy is achieved with reduced computation expense. The global–local plate theory is general enough to incorporate delamination effects. As a result of the inclusion of these effects, the buckling loads of plates with imperfect interlaminar bonding are predicted.

Multi-length scale modeling of CVD of diamond Part II A combined atomic-scale/grain-scale analysis

Chemical vapor deposition of polycrystalline diamond films is studied by combining an atomic-scale kinetic Monte Carlo model with two 〈one three-dimensional and one two-dimensional〉 grain-scale models. The atomic-scale model is used to determine the growth rates of 〈111〉- and 〈100〉-oriented surface facets, the surface morphology of the facets and the extent of incorporation of the crystal defects. Using the atomic-scale modeling predicted growth rates for the 〈111〉- and 〈100〉-oriented facets, grain-scale modelling is carried out to determine the evolution of grain structure, surface morphology and crystallographic texture in the polycrystalline diamond films. It is found that depending on the relative growth rates of the 〈111〉- and 〈100〉-oriented facets, which can be controlled by selecting the CVD processing conditions, one can obtain either 〈110〉-textured films with a relatively smooth faceted surface or 〈100〉-textured films with a highly pronounced deep facets. In both cases, however, the film surface is composed entirely of the 〈111〉 facets. This findings are found to be fully consistent with the available experimental results.

Multi-length scale modeling of CVD of diamond Part I A combined reactor-scale/atomic-scale analysis

Chemical vapor deposition of the (111)- and (100)-oriented single-crystalline diamond films is studied by combining a reactor-scale model with an atomic-scale model. The reactor-scale model is based on the solution of a continuum fluid-flow/heat-transfer boundary value problem for a reactive gas in contact with a deposition surface. The atomic-scale modeling is carried out using a kinetic Monte Carlo method. A consistency between the two modeling schemes is achieved by: (a) using the reactor-scale modeling predictions as input to the atomic-scale modeling scheme and; (b) using the atomic-scale modeling results to identify the surface reactions which govern and, hence, should be used in reactor-scale modeling of the deposition of (111)- and (100)-oriented diamond films. It is found that by properly combining the two types of models, consistent predictions for the film deposition rates can be obtained over a relatively large range of the CVD processing conditions. In addition, different phenomena are found to govern the deposition process for (111)- and (100)-oriented films. In the case of (111)-oriented films, the film growth rate appears to be controlled by the nucleation of new layers. Contrary in the case of (100)-oriented films, both the nucleation and growth processes seem to have comparable effects.

Application of image processing for simulation of mechanical response of multi-length scale microstructures of engineering alloys

Microstructures of engineering alloys often contain features at widely different length scales. In this contribution, a digital image processing technique is presented to incorporate the effect of features at higher length scales on the damage evolution and local fracture processes occurring at lower length scales. The method is called M-SLIP: Microstructural Scale Linking by Image Processing. The technique also enables incorporation of the real microstructure at different length scales in the finite element (FE)-based simulations. The practical application of the method is demonstrated via FE analysis on the microstructure of an aluminum cast alloy (A356), where the length scales of micropores and silicon particles differ by two orders of magnitude. The simulation captures the effect of nonuniformly distributed micropores at length scales of 200 to 500 µm on the local stresses and strains around silicon particles that are at the length scales of 3 to 5 µm. The procedure does not involve any simplifying assumptions regarding the microstructural geometry, and therefore, it is useful to model the mechanical response of the real multi-length scale microstructures of metals and alloys.

A generalized multilength scale nonlinear composite plate theory with delamination

A new type of plate theory for the nonlinear analysis of laminated plates in the presence of delaminations and other history-dependent effects is presented. The formulation is based on a generalized two length scale displacement field obtained from a superposition of global and local displacement effects. The functional forms of global and local displacement fields are arbitrary. The theoretical framework introduces a unique coupling between the length scales and represents a novel two length scale or local-global approach to plate analysis. Appropriate specialization of the displacement field can be used to reduce the theory to any currently available, variationally derived, displacement based (discrete layer, smeared, or zig-zag) plate theory. The theory incorporates delamination and/or nonlinear elastic or inelastic interfacial behavior in a unified fashion through the use of interfacial constitutive (cohesive) relations. Arbitrary interfacial constitutive relations can be incorporated into the theory without the need for reformulation of the governing equations. The theory is sufficiently general that any material constitutive model can be implemented within the theoretical framework. The theory accounts for geometric nonlinearities to allow for the analysis of buckling behavior. The theory represents a comprehensive framework for developing any order and type of displacement based plate theory in the presence of delamination, buckling, and/or nonlinear material behavior as well as the interactions between these effects. The linear form of the theory is validated by comparison with exact solutions for the behavior of perfectly bonded and delaminated laminates in cylindrical bending. The theory shows excellent correlation with the exact solutions for both the inplane and out-of-plane effects and the displacement jumps due to delamination. The theory can accurately predict the through-the-thickness distributions of the transverse stresses without the need to integrate the pointwise equilibrium equations. The use of a low order of the general theory, i.e. use of both global and local displacement fields, reduces the computational expense compared to a purely discrete layer approach to the analysis of laminated plates without loss of accuracy. The increased efficiency, compared to a solely discrete layer theory, is due to the coupling introduced in the theory between the global and local displacement fields.

Multiscale Modeling of Recrystallization

AbstractWe propose a multi length scale approach to modeling recrystallization which links a dislocation model, a cell growth model and a macroscopic model. Although this methodology and linking framework will be applied to recrystallization, it is also applicable to other types of phase transformations in bulk and layered materials. Critical processes such as the dislocation structure evolution, nucleation, the evolution of crystal orientations into a preferred texture, and grain size evolution all operate at different length scales. In this paper we focus on incorporating experimental measurements of dislocation substructures, misorientation measurements of dislocation boundaries, and dislocation simulations into a mesoscopic model of cell growth. In particular, we show how feeding information from the dislocation model into the cell growth model can create realistic initial microstructures.