By Y.-L. Shen
"Constrained Deformation of fabrics: units, Heterogeneous constructions and Thermo-Mechanical Modeling" offers an in-depth examine the mechanical analyses and modeling of complicated small-scale buildings and heterogeneous fabric platforms. Mechanical deformations in skinny movies and miniaturized fabrics, typically present in microelectronic units and programs, MEMS, nanostructures and composite and multi-phase fabrics, are seriously motivated via the exterior or inner actual confinement. A continuum mechanics-based procedure is used, including discussions on micro-mechanisms, to regard the topic in a scientific demeanour below the unified subject. Readers will locate invaluable info at the right program of thermo-mechanics in numerical modeling in addition to within the interpretation and prediction of actual fabric habit, besides many case reports. also, specific awareness is paid to functional engineering relevance. therefore real-life reliability concerns are mentioned intimately to serve the wishes of researchers and engineers alike.
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Additional info for Constrained Deformation of Materials: Devices, Heterogeneous Structures and Thermo-Mechanical Modeling
The individual stress components can continue to increase after yielding, even in a non-strain hardening metal. In other words, in experimental measurements the apparent strain hardening given by the measured axial stress in metal may be misleading or prone to quantitative errors. These attributes should be duly accounted for when performing analyses or interpreting experimental data. The same type of lateral constraint also exists, in a local manner, in deflection tests of microbeams consisting of a metal film on a substrate [3, 4] (see also sections below).
It is possible that, if DT is sufficiently large, reversed yielding in tension may occur during cooling. , welding and heat treatment), as well as in advanced heterogeneous materials and devices under physical constraint. 2 E xample: Thermoelastic Deformation of Bi-material Layers In the second example we consider a layered structure consisting of two different materials subjected to a uniform temperature change. The thermal expansion mismatch between the two layers induces internal stresses and an overall shape change (curvature) of the initially flat plate.
We focus on regions away from the remote free ends, and the plane stress assumption ( s yy = 0 ) is first employed in the analysis. 29) where e 0 is the strain at the interface and k is the curvature. This relation conforms to the pure bending assumption that any cross section perpendicular to the axis of the beam remains planar and perpendicular to the curved axis during bending. The stresses in the two layers are s 1 = s xx ,1 = E1 (e − a1 DT ) and s 2 = s xx ,2 = E2 (e − a 2 DT ) . 31) 0 respectively.