Parameter identification of a second-gradient model for the description of pantographic structures in dynamic regime

Abstract

Pantographic structures are examples of metamaterials with such a microstructure that higher-gradient terms’ role is increased in the mechanical response. In this work, we aim for validating parameters of a reduced-order model for a pantographic structure. Experimental tests are carried out by applying forced oscillation to 3D-printed specimens for a range of frequencies. A second-gradient coarse-grained nonlinear model is utilized for obtaining a homogenized 2D description of the pantographic structure. By inverse analysis and through an automatized optimization algorithm, the parameters of the model are identified for the corresponding pantographic structure. By comparing the displacement plots, the performance of the model and the identified parameters are assessed for dynamic regime. Qualitative and quantitative analyses for different frequency ranges are performed. A good agreement is present far away from the eigenfrequencies. The discrepancies near the eigenfrequencies are a possible indication of the significance of higher-order inertia in the model.

Improved mechanical performance of quasi-cubic lattice metamaterials with asymmetric joints

“…In the present paper, we focus on the strut-based artificial cellular structures -hereafter referred to as lattice metamaterials 4 . Modern 3d-printing technologies allow to produce the lattice metamaterials with complex geometry of the unit cells that provides their unique mechanical properties such as the ultra-high and tailorable specific stiffness and strength 5,6 , high impact strength [7][8][9] and wide band gaps in the dynamic response [10][11][12] , negative Poisson's ratio, thermal expansion or stiffness [13][14][15] , pronounced non-classical Cosserat-type and Mindlin-type macroscale behavoir [16][17][18][19] , etc. The design of the unit cells in the lattice structures are usually defines the position, size and orientation of the struts to provide some desired topology and related macroscopic response such that the stretch-dominated behavior [20][21][22] , the quasi-isotropic averaged properties 23,24 , the prescribed anisotropy and the symmetric groups 25,26 or the functionally graded structure 27,28 .…”

A benchmark strain gradient elasticity solution in two-dimensions for verifying computational approaches by means of the finite element method

“…A reliable numerical computation of such equations requires suitable techniques and element type selection that ensure the monotonous convergence. For this purpose, different numerical approaches have been proposed for the strain gradient theories such as isogeometric analysis [47–50], C 1 continuous elements [52,53], and mixed finite element formulation [54–56]. It is beneficial to verify the computations by analytical solutions.…”

“…It has been implemented for problems of elasticity [9][10][11][12][13]; plasticity [14][15][16][17][18][19]; damage modeling [20][21][22][23][24][25]; modeling metamaterials [26][27][28] such as pantographic structures [29][30][31], network materials [32], viscoelastic truss structures [33], bipantographic structures [34], second gradient fluids [35]; gradient-enhanced homogenization [36][37][38][39]; micropolar continua [40]; fracture mechanics [41]; biomechanics [42][43][44]; and anisotropic systems [45]. Parameter determination of generalized mechanics models has been studied for static and dynamic regimes in Shekarchizadeh et al [46,47], respectively.…”

The «materialization» of forces: Why confounding mathematical concept and physical entity makes the design of metamaterials arduous

“…Indeed, the microstructure of such materials allows for the combination of «simpler forces» to produce, at macro-level, more complex ones. For instance, the microscopically homogeneous materials described by Cauchy continua cannot support distributed couples or double-forces [9][10][11][12] which, instead, can be supported by strain-gradient continua describing, at macro-level, microscopically heterogeneous materials [13][14][15][16][17][18][19]. The description of the mental process, which produced the materialization of forces, is also relevant when one wants to firmly found (especially if he needs to avoid ambiguities and contradictions in their formulation) the mathematical models suitable to describe and predict nonstandard generalized and desired exotic mechanical properties [20][21][22][23][24][25].…”