Calculus of Variations and Geometric Measure Theory
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M. Focardi - P. M. Mariano - E. Spadaro

Multi-value microstructural descriptors for finer scale material complexity: analysis of ground states

created by focardi on 31 Jan 2013
modified on 26 Feb 2015


Accepted Paper

Inserted: 31 jan 2013
Last Updated: 26 feb 2015

Journal: Archive for Rational Mechanics and Analysis
Year: 2013


A multi-scale and multi-field description of material microstructures which distinguish at every point multiple microstructural individuals is analyzed paying attention to the determination of equilibrium configurations. Rigid bodies with microstructure represented by means of $Q$−valued maps from the reference place to the manifold of microstructural shapes are considered first. In that case, just microenergetics is considered and macroscopic motion neglected. Then, the stage is enlarged up to include deformable bodies suffering large strains, endowed with energies of Ginzburg-Landau type with respect to the microstructural descriptor fields. In both cases, conditions for semicontinuity of the relevant energies and the existence of ground states are provided.


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