Bridging Length Scales Research Articles

Reduced order modeling and experimental validation of steady turbulent convection in connected domains

The characterization and design of complex thermo/fluid electronics systems such as electronic racks requires attention to multiple length scales and transport phenomena, including conduction at the chip package level and convection at rack level. Detailed numerical calculations or experimental measurements are often time consuming and computationally expensive or simply infeasible. An efficient strategy to bridge length scales in multi-scale characterization is presented. Reduced order models for various system components obtained using proper orthogonal decomposition (POD) are assembled to model the complete system through flow network modeling (FNM). Boundary profile capturing capability at the interfaces of components is incorporated into the flux matching based POD approach, without introducing extra computation. The simulation errors of the component reduced order models are within 7.4% for temperature, velocity and pressure fields, compared to full-field computational simulations. Assembled component models result in a 12% error norm at the system level. Experimental validation with a representative electronic cabinet shows a difference of less than 10% in chip junction temperatures prediction.

Theoretical coarse-graining approach to bridge length scales in diblock copolymer liquids

A microscopic theory for coarse graining diblock copolymers into dumbbells of interacting soft colloidal particles has been developed based on the solution of liquid-state integral equations. The Ornstein-Zernike equation is solved to provide a mesoscopic description of the diblock copolymer system at the level of block centers of mass, and at the level of polymer centers of mass. Analytical forms of the total correlation functions for block-block, block-monomer, and center-of-mass pairs are obtained for a liquid of structurally symmetric diblock copolymers as a function of temperature, density, chain length, and chain composition. The theory correctly predicts thermodynamically driven segregation of diblocks into microdomains as a function of temperature (chi parameter). The coarse-grained description contains contributions from density and concentration fluctuations, with the latter becoming dominant as temperature decreases. Numerical calculations for the block coarse-grained total correlation functions, as a function of the proximity of the system to its phase transition, are presented. Comparison with united atom molecular dynamics simulations are carried out in the athermal regime, where simulations and theory quantitatively agree with no need of adjustable parameters.

Bridging length scales in colloidal liquids and interfaces from near-critical divergence to single particles

Boiling and condensation are among the best recognized phase transitions of condensed matter. Approaching the critical point, a liquid becomes indistinguishable from its vapour, the interfacial thickness diverges and the system is dominated by long-wavelength density fluctuations1. Long wavelength usually means hundreds of particle diameters, but here we consider the limits of this assumption, using a mesoscopic analogue of simple liquids, a colloid–polymer mixture2,3. We simultaneously visualize both the colloidal particles and near-critical density fluctuations, and reveal particle-level images of the critical clusters and liquid–gas interface. Surprisingly, we find that critical scaling does not break down until the correlation length approaches the size of the constituent particles, where there is a smooth transition to non-critical classical behaviour. Our results could provide a framework for unifying the disparate particle and correlation length scales, and bring new insight into the nature of the liquid–gas interface and the limit of the critical regime.

Numerical Analysis of Nonlocal Anisotropic Continuum Damage

This article deals with the numerical analysis of anisotropic continuum damage in ductile metals based on thermodynamic laws and nonlocal theories. The proposed model is based on a generalized macroscopic theory within the framework of nonlinear continuum damage mechanics taking into account the kinematic description of the damage. A generalized yield condition is employed to describe the plastic flow characteristics of the matrix material, whereas the damage criterion provides a realistic representation of material degradation. The nonlocal theory of inelastic continua is established, which incorporates the macroscopic interstate variables and their higher-order gradients which properly describe the change in the internal structure and investigate the size effect of statistical inhomogeneity of the heterogeneous material. The idea of bridging length scales is made by using the higher-order gradients only in the evolution equations of the equivalent inelastic strain measures. This leads to a system of elliptic partial differential equations which is solved using the finite difference method. The applicability of the proposed continuum damage theory is demonstrated by finite element analyses of the inelastic deformation process of tension specimens.

Bridging length scales in polymer melt relaxation for macromolecules with specific localstructures

We extend our generalized Langevin equation for cooperative dynamics (CDGLE), amany-chain approach, to investigate liquids composed of macromolecules with differentlocal chemical structure. In particular, the specific role of semiflexibility and localarchitecture on the overall polymer dynamics is explored. The theory predictscentre-of-mass diffusion in good agreement with simulations for liquids of macromoleculeswith slightly branched monomeric architectures.

Strength and Notch Sensitivity of Porous‐Matrix Oxide Composites

The effects of matrix strength on the notched and unnotched tensile properties of a family of porous‐matrix oxide composites are examined both experimentally and theoretically. Experiments are performed on three composites, distinguished from one another by the amount of binding alumina within the matrix. Increases in alumina concentration produce elevations in unnotched tensile and shear strengths, but the benefits are offset by an increase in notch sensitivity. The degree of notch sensitivity is rationalized on the basis of a model that accounts for interactions between notch tip tensile and shear bands. The model predictions are cast in terms of the ratio of the notch length to a characteristic bridging length scale. These results, in turn, form the basis for a simple analytical formula for notched strength, accounting for effects of elastic anisotropy and finite sample size. The utility of this formula in predicting notched strength is assessed. Issues associated with bridging law shapes and bridging length scales are addressed. The effect of alumina concentration on notch sensitivity is discussed in terms of its influence on the bridging length scale, dictated by the interplay between the unnotched tensile strength, the longitudinal Young's modulus, the degree of in‐plane elastic anisotropy, and the fracture energy. The net result is a decreasing bridging length scale and hence increasing notch sensitivity as the matrix is strengthened with alumina.

Bridging between micro- and macroscales of materials by mesoscopic models

The importance of bridging length scales for materials is illustrated by three examples, nematic liquid crystals, strength of materials, and epitaxial growth. Emphasis is on the microscopic scale, with first-principles calculations of molecule–surface interaction, stacking-fault energies, interlayer interactions, diffusion barriers, and adsorbate–adsorbate interactions. Some pilot examples of using such information on the meso- and macroscales with models using director fields, misfit densities of dislocation, and monomer and island densities are presented. The area is predicted to have a great future.

Developments and trends in continuum plasticity

Multiscale modeling applied to meso and macro scale continuum calculations is a broad field with a long history. It encompasses hardening relations based on dislocation density, porosity related ductile failure models, crystal plasticity, composite media and numerous other general topics dating back more than half a century. There are also a myriad of more recent activities that can be grouped under this subject heading. Emphasis will be placed on efforts described at the Bodega Bay workshop aimed at bridging length scales rather than focusing on model developments at any particular length scale. Also, areas will be highlighted where additional connections should be possible with available tools; methods exist but need to be exercised; and critical experiments are needed for validation.

Multi-scale modeling of dislocation processes

Connecting microscopic mechanisms of deformation to macroscopic behavior requires an appropriate formalism that bridges the length scales of these processes. We propose a simple constitutive relation relating dislocation velocity to the net force that provides a formalism for the incorporation of specific dislocation mechanisms into the description of global plastic deformation. We then employ this approach to describe macroscopic deformation behavior controlled by forest intersection. An activation volume tensor and the activation enthalpy for deformation now become functions of the three-dimensional state of stress. Concepts presented in this work provide a framework for further development of multi-scale computational models that bridge length scales in the description of plastic deformation.

Design of experiments for constitutive model selection: application to polycrystal elastoviscoplasticity

To bridge length scales in plastic flow of polycrystalline fcc metals, the salient features of 3D polycrystalline elastoviscoplasticity at the crystal level (mesoscale) were studied to determine the relative influences on macroscale behaviour. This 3D study builds upon the 2D planar double-slip analysis performed by Horstemeyer and McDowell in which the relative influence of the constitutive-law features on macroscale properties in polycrystal plasticity were quantified for oxygen-free, high-conductivity copper. The mesoscale constitutive-law features considered include single-crystal elastic properties, slip-system-level hardening law, latent hardening, slip-system-level kinematic hardening, and intergranular constraint relation. Volume-averaged macroscale responses included the effective flow stress, plastic spin, elastic moduli, hardening behaviour, and axial extension (for the free-end torsion case). Each response was evaluated at 10% and 50% effective strain levels under rectilinear shear straining. In the existing literature, only one type of behaviour (e.g. texture or stress-strain response) is typically considered when assessing these various elements of the constitutive framework. In this paper, we develop a more comprehensive understanding of the relative importance of constitutive-law features as deformation proceeds. This study suggests that the design of experiments methodology is a valuable tool to assist in selecting relevant features for polycrystalline simulations and for development of macroscale unified-creep-plasticity models. In general, the results indicated that the intergranular constraint and kinematic hardening were more influential overall than the type of constitutive model used, whether isotropic or anisotropic elasticity was used, and whether or not latent hardening was used. Finally, 3D results were similar to the previous 2D planar double-slip study of Horstemeyer and McDowell, except that latent hardening had a stronger influence on the 3D macroscale responses than the 2D macroscale responses.