Contact interactions in complex fibrous metamaterials

Abstract

In this work, an extension of the strain energy for fibrous metamaterials composed of two families of parallel fibers lying on parallel planes and joined by connective elements is proposed. The suggested extension concerns the possibility that the constituent fibers come into contact and eventually scroll one with respect to the other with consequent dissipation due to friction. The fibers interact with each other in at least three different ways: indirectly, through microstructural connections that could allow a relative sliding between the two families of fibers; directly, as the fibers of a family can touch each other and can scroll introducing dissipation. From a mathematical point of view, these effects are modeled first by introducing two placement fields for the two fiber families and adding a coupling term to the strain energy and secondly by adding two other terms that take into account the interdistance between the parallel fibers and the Rayleigh dissipation potential (to account for friction).

Second-gradient continua: From Lagrangian to Eulerian and back

“…[10,29]), the non-conservative part of the internal work functional can be calculated from a so-called Rayleigh dissipation functional. An interesting physical system in which a phase transition occurs (similar to what has been described by Javanbakht et al [30]) in large deformations is given by Spagnuolo and Cazzani [31]: Pantographic metamaterials may behave as a second-gradient continua until a certain threshold is reached, beyond which, because of friction phenomena, they behave as standard first-gradient continuum.…”

Third-gradient continua: nonstandard equilibrium equations and selection of work conjugate variables

“…Moreover, we expect that also the phase field theory, aiming to regularize the fracture propagation problems, will soon include second- and third-gradient modelling to properly describe the elastic part of the deformation [75]. This opinion is motivated by the need to properly accommodate edge and point contact forces [76], in the presence of fracture processes with geometric nonlinearity.…”

Shear rupture mechanism and dissipation phenomena in bias-extension test of pantographic sheets: Numerical modeling and experiments

“…Pantographic structures have been intensively studied in recent years [1][2][3][4][5][6] because of their peculiar behavior, consisting of two main features within the family of lightweight structures: (1) the capability to exploit large deformations in the elastic regime; (2) hierarchical behavior in the damage mechanisms. The research lines can be roughly classified into those devoted to the analysis of theoretical aspects [7][8][9][10][11][12], to the formulation of computational methods in discrete [13][14][15][16] and continuum framework [17][18][19][20], as well as to the investigations of experimental evidence [21][22][23][24][25][26][27].…”