Topology optimisation of manufacturable microstructural details without length scale separation using a spectral coarse basis preconditioner

Wave propagation in materials with embedded two different microstructures is considered. Each microstructure is characterized by its own length scale. The dual internal variables approach is adopted yielding in a Mindlin-type model including both microstructures. Equations of motion for microstructures are coupled with the balance of linear momentum for the macromotion, but not coupled with each other. Corresponding dispersion curves are provided and scale separation is pointed out.

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Homogenization of fault frictional properties

Geophysical Journal International ◽

10.1093/gji/ggz327 ◽

2019 ◽

Vol 219 (2) ◽

pp. 1203-1211 ◽

Cited By ~ 2

Author(s):

Sohom Ray ◽

Robert C Viesca

Keyword(s):

Spatial Distribution ◽

Length Scale ◽

Fault Models ◽

Problem Parameter ◽

Scale Separation ◽

Frictional Properties ◽

State Dependent ◽

Characteristic Wavelength ◽

Nonlinear Solutions ◽

Do So

SUMMARY The frictional properties of large faults are expected to vary in space. However, fault models often assume that properties are homogeneous, or nearly so. We investigate the conditions under which the details of variations may be neglected and properties homogenized. We do so by examining the behaviour of nonlinear solutions for unstably accelerating fault slip under frictional heterogeneity. We consider a rate- and state-dependent fault friction in which the characteristic wavelength for the property variations is a problem parameter. We find that homogenization is permissible only when that wavelength shows scale separation from an elasto-frictional length scale. However, fault models also often include property transitions that occur over distances comparable to the elasto-frictional length. We show that under such comparable variations, the dynamics of earthquake-nucleating instabilities is controlled by the properties’ spatial distribution.

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Biomimetic materials: An introduction

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100129735 ◽

1992 ◽

Vol 50 (2) ◽

pp. 1020-1021 ◽

Cited By ~ 1

Author(s):

M. Sarikaya ◽

J. T. Staley ◽

I. A. Aksay

Keyword(s):

Self Assembly ◽

Structural Control ◽

Hierarchical Structures ◽

Ceramic Composites ◽

Advanced Materials ◽

Length Scale ◽

Spider Webs ◽

Biomimetic Materials ◽

Synthetic Materials ◽

All Ceramic

Biomimetics is an area of research in which the analysis of structures and functions of natural materials provide a source of inspiration for design and processing concepts for novel synthetic materials. Through biomimetics, it may be possible to establish structural control on a continuous length scale, resulting in superior structures able to withstand the requirements placed upon advanced materials. It is well recognized that biological systems efficiently produce complex and hierarchical structures on the molecular, micrometer, and macro scales with unique properties, and with greater structural control than is possible with synthetic materials. The dynamism of these systems allows the collection and transport of constituents; the nucleation, configuration, and growth of new structures by self-assembly; and the repair and replacement of old and damaged components. These materials include all-organic components such as spider webs and insect cuticles (Fig. 1); inorganic-organic composites, such as seashells (Fig. 2) and bones; all-ceramic composites, such as sea urchin teeth, spines, and other skeletal units (Fig. 3); and inorganic ultrafine magnetic and semiconducting particles produced by bacteria and algae, respectively (Fig. 4).

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Facet Topography and Dislocation Structure as a Possible Source for Electrical Heterogeneity in [001] TILT Bicrystals of YBa2Cu3O7-δ

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100164155 ◽

1996 ◽

Vol 54 ◽

pp. 338-339

Author(s):

I-Fei Tsu ◽

D.L. Kaiser ◽

S.E. Babcock

Keyword(s):

Grain Boundary ◽

Critical Current Density ◽

Critical Current ◽

Current Density ◽

Electromagnetic Properties ◽

Length Scale ◽

Density Values ◽

Current Densities ◽

Applied Fields ◽

A Current

A current theme in the study of the critical current density behavior of YBa2Cu3O7-δ (YBCO) grain boundaries is that their electromagnetic properties are heterogeneous on various length scales ranging from 10s of microns to ˜ 1 Å. Recently, combined electromagnetic and TEM studies on four flux-grown bicrystals have demonstrated a direct correlation between the length scale of the boundaries’ saw-tooth facet configurations and the apparent length scale of the electrical heterogeneity. In that work, enhanced critical current densities are observed at applied fields where the facet period is commensurate with the spacing of the Abrikosov flux vortices which must be pinned if higher critical current density values are recorded. To understand the microstructural origin of the flux pinning, the grain boundary topography and grain boundary dislocation (GBD) network structure of [001] tilt YBCO bicrystals were studied by TEM and HRTEM.

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