This work concerns mechanical systems known as “pantographic structures”, which are considered a family of beams connected by pivots. We propose a computationally efficient and predictive model capable of providing a plausible description of deformation, using a discrete two-dimensional (2D) “kinematic” model. This model assigns the displacements of certain points, called leaders, while the other points, called followers, are left free to rearrange themselves according to the lattice structure and assigned flocking rules. The advantages of the kinematic model include savings in calculation time and easier handling of complicated structures and fracture phenomena. Moreover, extending the model to encompass non-local interactions, as exemplified by second-gradient materials, is a more straightforward process than solving partial differential equations. The model has previously been employed to elucidate the behaviour of simple materials. The principal innovation of this paper is the essential delineation of the constraint between the pantograph beams, which is contingent upon the presence of the pivot. This was accomplished by imposing an ”average” displacement on the component points of the pivot belonging to two separate beams, thereby introducing an additional parameter into the model. This also necessitated a significant alteration to the calculation algorithm. The model is still constrained by several limitations, including the absence of a physical interpretation for its parameters and the necessity of connecting it to the CUDA (Compute Unified Device Architecture, by NVIDIA) architecture for the calculation of the developed algorithm. The principal limitation of the present approach, however, is the absence of a correlation between the parameters of the ’kinematic’ model and the constitutive parameters of the material. This aspect will be the subject of future research.
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