Abstract
We model and analyze the two-dimensional triangle-to-centred rectangle transformation of elastic crystals. By considering a Ginzburg–Landau type model, we compute the relaxation of the total energy both in the case of compressible and incompressible materials and construct some possible explicit microstructures as the approximate solutions of a non-convex minimization problem.
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Acknowledgments
The research of PC was partially supported by the ERC under the EU’s Seventh Framework Programme (FP7/2007–2013)/ERC grant agreement no. 291053.
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Cesana, P. (2017). Relaxation of an Energy Model for the Triangle-to-Centred Rectangle Transformation. In: Anderssen, B., et al. The Role and Importance of Mathematics in Innovation. Mathematics for Industry, vol 25. Springer, Singapore. https://doi.org/10.1007/978-981-10-0962-4_11
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DOI: https://doi.org/10.1007/978-981-10-0962-4_11
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