By Y.-L. Shen
"Constrained Deformation of fabrics: units, Heterogeneous constructions and Thermo-Mechanical Modeling" provides an in-depth examine the mechanical analyses and modeling of complex small-scale constructions and heterogeneous fabric structures. Mechanical deformations in skinny movies and miniaturized fabrics, in general present in microelectronic units and applications, MEMS, nanostructures and composite and multi-phase fabrics, are seriously encouraged via the exterior or inner actual confinement. A continuum mechanics-based method is used, including discussions on micro-mechanisms, to regard the topic in a scientific demeanour below the unified topic. Readers will locate worthy details at the right software of thermo-mechanics in numerical modeling in addition to within the interpretation and prediction of actual fabric habit, in addition to many case reports. also, specific awareness is paid to useful engineering relevance. hence real-life reliability matters are mentioned intimately to serve the wishes of researchers and engineers alike.
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Additional resources for Constrained Deformation of Materials: Devices, Heterogeneous Structures and Thermo-Mechanical Modeling
5 shows three simple one-dimensional examples of such models under an applied stress s. 5a, consists of a spring and a dashpot in series. Its governing constitutive relation is de s 1 ds . 5b. The governing equation becomes s =h de + Ee . 25) h b s h E E c h E1 E2 Fig. 5c shows a type of so called standard linear solid model, which is composed of a spring element in parallel with a Maxwell model. 5 as EE de 1 ds E1 = + s − 1 2 e . 26) It is noted that multi-component springs and dashpots are frequently needed to characterize realistic viscoelastic behavior.
It can be seen that the patterns of s 11 and s 22 form a mutual mirror reflection about the 45° axis, as expected due to the symmetric setup of the problem. There is also a significant shear stress field of s 12 . 7 MPa. Note this is not the maximum tensile stress in the material because the stress values of the individual components are a consequence of the chosen coordinate system. 1 MPa is seen. Note this is still not the largest stress we are seeking because the von Mises stress is defined to be an all-positive scalar quantity dominated by the deviatoric contribution of the stress tensor.
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. 3b shows the evolution of srr stress (which is the biaxial stress in this case) and curvature k as a function of the temperature change DT resulting from the modeling.
Constrained Deformation of Materials: Devices, Heterogeneous Structures and Thermo-Mechanical Modeling by Y.-L. Shen