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A possible strain energy density, incorporating Cosserat's micro-rotations and Biot's change in porosity conferred by the microstructure geometry, is proposed in an elastic, two-dimensional, nonlinear context. The nonlinearities are taken into account both extracting the exact macro-rotations by the polar decomposition of the standard deformation gradient F and evaluating the change in the area at the macroscopic level of observation as J - 1 . Moreover, the bulk behavior of the material is assumed to be described by a compressible neo-Hookean model. Based on a variational formulation, finite element numerical simulations of static tests in some representative examples have been performed to illustrate the main features of the proposed model and the effect of the boundary conditions. [ABSTRACT FROM AUTHOR]

The present article is a rational report of the workshop Encounter of the third kind on Generalized continua and microstructures (Arpino, 3–7 April 2018). The main goal of the workshop was to gather together experts in the framework of generalized continuum theories and microstructured materials to discuss and analyse the recent advancements in the field. The interested reader will find in this article a general discussion of the motivations and of the main topics discussed during the workshop as well as a detailed report of the talks and the relative bibliography. All the talks have been recorded and it is possible to watch them on the M&MOCS YouTube channel at https://www.youtube.com/playlist?list=PLWzlK5oO41smkt5HtiDQJV7nsbz5wnD01 [ABSTRACT FROM AUTHOR]

In the last decade, the exotic properties of pantographic metamaterials have been investigated and different mathematical models (both discrete or continuous) have been introduced. In a previous publication, a large part of the already existing literature about pantographic metamaterials has been presented. In this paper, we give some details about the next generation of research in this field. We present an organic scheme of the whole process of design, fabrication, experiments, models and image analyses. [ABSTRACT FROM AUTHOR]