By Y.-L. Shen
"Constrained Deformation of fabrics: units, Heterogeneous buildings and Thermo-Mechanical Modeling" provides an in-depth examine the mechanical analyses and modeling of complicated small-scale constructions 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 prompted via the exterior or inner actual confinement. A continuum mechanics-based process is used, including discussions on micro-mechanisms, to regard the topic in a scientific demeanour lower than the unified topic. Readers will locate precious info at the right program of thermo-mechanics in numerical modeling in addition to within the interpretation and prediction of actual fabric habit, in addition to many case stories. also, specific recognition is paid to useful engineering relevance. therefore real-life reliability concerns are mentioned intimately to serve the wishes of researchers and engineers alike.
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Extra info for Constrained Deformation of Materials: Devices, Heterogeneous Structures and Thermo-Mechanical Modeling
Since the edge effect is excluded, the simulation utilizes the generalized plane strain formulation, which is two-dimensional (2D) but accounts for a uniform deformation in the y-direction. 2b shows the evolution of stresses sxx, syy and the von Mises effective stress se in Al as a function of applied strain exx (szz is zero throughout the deformation). The Al film and Si substrate experience the same applied strain exx. 28), tensile stress syy starts to build up right from the elastic stage. Upon yielding, a constant von Mises effective stress ensues, the magnitude of which is equal to the Al yield strength (200 MPa).
3 (a) Schematic showing the Al film/Si substrate model used in the axisymmetric finite element analysis, before and after the imposed temperature change (drawing not to scale). Only a thin segment of the structure is needed for the analysis if the appropriate boundary conditions are applied. 3a). This treatment fulfills the “plane-remains-plane” scenario in pure bending, and the film-edge effect is thus excluded. 2. A temperature change of DT = −300° C is simulated. During the process the stress in the Al film can be directly obtained from the model output, and the curvature can be simply calculated from the geometric relation between lines AB and CD.
3 Film on a Compliant Substrate There are circumstances that thin films are bonded to a much more compliant substrate. One application area is stretchable electronics, where small features of micro-components are deposited on a polymeric substrate [84–87]. On the more fundamental side, thin metal films are frequently deposited on a compliant substrate (such as polyimide) and the assembly is subject to mechanical testing to obtain the “free-standing” film behavior [5, 88–95]. An implicit assumption for this type of testing is that the substrate material is very compliant, so it tends not to “interfere” with the intrinsic deformation characteristics of the thin film.