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 complex small-scale constructions and heterogeneous fabric platforms. Mechanical deformations in skinny motion pictures and miniaturized fabrics, more often than not 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 less than the unified subject. Readers will locate necessary info 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 reviews. also, specific cognizance is paid to sensible engineering relevance. hence real-life reliability matters are mentioned intimately to serve the desires of researchers and engineers alike.
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Additional resources for Constrained Deformation of Materials: Devices, Heterogeneous Structures and Thermo-Mechanical Modeling
15) 2 Plastic yielding commences when the magnitude of s e reaches sy, the yield strength of the material under uniaxial loading. 15) is reduced to 3 s ij′ s ij′ , where J 2 is the second invariant of the 2 deviatoric stress tensor s ij′ . The von Mises yield condition, in conjunction with the associated flow rule [6, 7], is commonly employed in computational modeling of metal deformation involving plasticity. Upon yielding, the total strain of an elastic-plastic material, e ij , is the sum of the elastic part e ije and the plastic part e ijp .
6a. For simplicity only the longitudinal stress and strain are considered so the problem becomes one-dimensional in nature. We further assume that the material is elastic-perfectly plastic with all properties (Young’s modulus E, CTE a, and yield strength sy) independent of temperature. 6b. Starting from a stress-free condition, the rod is subject to heating (with positive DT). The total strain etot is thus the sum of thermal, elastic and plastic strains ( e t , e e , and e p , respectively), e tot = e t + e e + e p = a ·DT + s + ep.
7b. Note the von Mises stress stays at 200 MPa once yielding commences. 1). This again implies a “false” strain hardening behavior which will be measured in actual experiments. The change in sxx after yielding is larger for a thicker polyimide substrate. Additionally, a lateral tensile stress syy also exists. 34). Upon yielding, this lateral stress component starts to develop and its magnitude can become quite significant if the substrate is sufficiently thick. ) Therefore, care must be taken when interpreting experimentally obtained information, since a true macroscopic uniaxial stress state may not exist even with a compliant substrate.