Transition mechanism for a periodic bar-and-joint framework with limited degrees of freedom controlled by uniaxial load and internal stiffness

Abstract

A specific periodic bar-and-joint framework with limited degrees of freedom is shown to have a transition mechanism when subjected to an external force. The static nonlinear elasticity of this framework under a uniaxial load is modelled with the two angular variables specifying the rotation and distortion of the linked square components. Numerically exploring the equilibrium paths then reveals a transition state of the structure at a critical value of the internal stiffness. A simplified formulation of the model with weak nonlinear terms yields an exact solution of its transition state. Load–displacement behaviour and stability for the two systems with or without approximation are analysed and compared.

Auxetic vibration behaviours of periodic tetrahedral units with a shared edge

“…The two-dimensional corner-linked frameworks of polygons such as triangles and squares have been developed by employing several types of flexible mechanisms per unit cell [15][16][17][18]. In threedimensional frameworks, a tetrahedron unit is one possible geometrical component; indeed, a subgroup of synthesized tetrahedra may be designed and used at a microscopic scale in chemistry [19].…”

Spatial pseudo-rigid body model for the analysis of a tubular mechanical metamaterial

“…Current examples of rigid body mechanisms used to model mechanical metamaterials are either solely kinematic [25][26][27] or only consider planar structures [17,[28][29][30]. However, for spatial mechanical metamaterials, PRBMs have not yet been applied, while for these more complicated structures the resulting computational efficiency will be of significant benefit.…”

Macroscopic out-of-plane auxetic features of a laminated open-cell structure with in-plane negative Poisson’s ratios induced by bridging beam components

“…A variety of microstructured materials have been designed extensively and developed partially in recent years to achieve enhanced mechanical properties, such as specific stiffness and strength [3,4]. Some of these materials exhibit anomalous elastic behaviors with a negative nature regarding the Poisson's ratio [5-17] and thermal expansion coefficient [18][19][20], and with the related systems [21][22][23][24][25]; see also the relevant review papers and books [26][27][28][29][30]. These materials with a remarkable mechanical functionality, as provided by their microstructures, are termed mechanical metamaterials [31][32][33][34].…”