Modeling and Optimization of Layer-by-Layer Structures

• Published in: Journal of physics. Conference series Vol. 1009; no. 1; pp. 12014 - 12050
• Main Authors: Lychev, S A, Kostin, G V, Koifman, K G, Lycheva, T N
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.04.2018
• Subjects: Algorithms; Compensation; Deformation; Differential geometry; Euclidean geometry; Incompatibility; Modelling; Multilayers; Optimization; Physics; Residual stress; Thin films
• ISSN: 1742-6588; 1742-6596
• DOI: 10.1088/1742-6596/1009/1/012014

In the present paper a differential-geometric approach is developed to modeling of residual stresses in layered (LbL) structures obtained as a result of successive curing of thin layers of material. The objects of modeling are the structures obtained by sequential adsorption of a large number of thin layers. During this assembling, the internal (residual) stresses appear in the multilayered structure while local deformations turn out to be incompatible. This leads to accumulation of residual stresses and distortion of the final shape of the LbL structure. To reduce these factors, geometric compensation is used, the calculation of which is extremely laborious with a large number of layers. Geometric methods allow us to implement fast algorithms for obtaining the compensation. They are based on the "smoothing" of the multilayer LbL structure and its representation by introducing a smooth body-manifold with non-Euclidean connection that characterizes the incompatibility of deformations. Connection is determined from the solution of the evolutionary problem, which formalizes the course of the technological process. The classical fields of the mechanics of a continuous medium are put in correspondence with their non-Euclidean counterparts. As an example, model problems for cylindrical LbL elastic structures are considered. A model problem of structural optimization is solved to determine the optimal strategy of the technological process.