![]() The predictive capability of the micromorphic approach is next demonstrated with a flat punch indentation problem in a regime without a clear separation of length scales. Considering an axial loading problem, it is shown that the proposed micromorphic framework accurately captures the coupling between internal ring rotation and stretching of tangential ligaments. The predictive capability of the micromorphic CH framework is demonstrated through three benchmark problems in plane strain condition. These two kinematic fields, each characterizing a particular aspect of the unit cell deformation, enable the micromorphic framework to adequately characterize the underlying dominant deformation modes. Together with the standard macro-distortion tensor, an additional kinematic variable is introduced to characterize the deformation and rotation of the central ring. (2019), is reformulated for 2D tetra-chiral solids to address these limitations. In this contribution, the micromorphic CH framework developed in Biswas and Poh (2017), Biswas et al. Moreover, a size effect arising from the interactions between micro and macro length scales cannot be accounted for. ![]() ![]() The standard first-order Computational Homogenization (CH) approach is inadequate in capturing this coupling effect. Lastly we show that defect measures of pion fields description of the Skyrmions are related to the defect measures of the micropolar continua via correspondences between its underlying symmetries and compatibility conditions of vanishing curvature.Īuxetic chiral structures exhibit many unique and enhanced mechanical properties, which emerge from the coupling of stretching and rotational mechanisms within the underlying unit cell. Micropolar continua are shown to be the general case of nematic liquid crystals in projective geometry, and in formulations of the order parameter, which is also the generalisation of the Higgs isovectors. #ECLEAR ELASTY FREE#Order parameters are carefully defined to be used both in homotopic considerations and free energy expansion in the language of microcontinua. Nematic liquid crystals are identified as a projective plane from a sphere hinted by the discrete symmetry in its directors. ![]() This further leads to a notion of topologically stable defects determined by invariant winding numbers for a given solution classification. We show that associated charges can be written as integers under a finite energy requirement in connection with homotopic considerations. Then we consider position-dependent axial configurations of the microrotations to construct intrinsically conserved currents. Classical compatibility conditions are re-interpreted leading to a universal process to derive a distinct set of compatibility conditions signifying a geometrical role of the Einstein tensor in Riemann-Cartan manifolds. We show various deformational measures, used in deriving the soliton solutions, can be written when both curvature and torsion are allowed, especially by means of microrotations and its derivatives. Then criteria in constructing the chiral energy functional is specified to be included to obtain soliton-like solutions. We derive equations of motion and its solutions in the form of solitons from deformational energy functionals of a coupled system of microscopic and macroscopic deformations. ![]()
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