Mesoscale modeling and experimental analyses for pantographic cells: Effect of hinge deformation

In this paper, we represent second-gradient internal work functionals in Lagrangian (referential) and Eulerian (spatial) descriptions, and we deduce the corresponding expressions for the Piola transformations of stress and double-stress tensors and of external forces and double-forces. We also derive, in both the Eulerian and Lagrangian description, the expression of surface and edge contact interactions (which include forces and double-forces) for second-gradient continua in terms of the normal and the curvature of contact boundary surfaces and edge shapes.

“…We recall that (see equation (56) in Appendix 1) the symbols ðÞ 6 denote the limits on the curves constituting ∂∂O from the faces 6 of the quantities in the brackets.…”

Section: Boundary Value Problem In Second-gradient Continuamentioning

confidence: 99%

Section: The Eulerian Virtual Work Principle For Second-gradient Cont...mentioning

confidence: 99%

Second-gradient continua: From Lagrangian to Eulerian and back

Dell’Isola

Eugster

Fedele

et al. 2022

“…The parameters q 1 , q 2 , q 3 , and q 4 in equation ( 32) are calculated using equations ( 27), ( 28), (30), and (31).…”

Section: Discussionmentioning

confidence: 99%

“…Generalized mechanics has been widely investigated in the literature. 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.…”

Section: Introductionmentioning

confidence: 99%

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

Shekarchizadeh

Abali

Bersani

2022

In elasticity, microstructure-related deviations may be modeled by strain gradient elasticity. For so-called metamaterials, different implementations are possible for solving strain gradient elasticity problems numerically. Analytical solutions of simple problems are used to verify the numerical approach. We demonstrate such a case in a two-dimensional continuum as a benchmark case for computations. As strain gradient enforces higher regularity conditions in displacements, in the finite element method (FEM), the use of standard elements is often seen as inadequate. For such piecewise or elementwise continuous elements, we examine a possible remedy to correctly simulate strain gradient elasticity problems by implementing two techniques. First, we enforce continuity of displacement gradient across elements; second, we employ a mixed finite element method where displacement and its gradient are solved both as unknowns. The results show the pros and cons of each numerical technique. All methods converge monotonically, but the mixed method is more reliable than the other one.

“…Pantographic fabrics were designed and then realized physically by arranging the two families of beams onto two different parallel planes. The design and realization of connections between two beams have been accomplished by means of cylindrical pivots acting ideally as in-plane elastic hinges, i.e., hinges with torsional springs [4,5], and by means of actual hinges which, however, are prone to suffering significant non-elastic phenomena and hence pose complex challenges in manufacturing engineering. While the realization of cylindrical pivots is less challenging from the manufacturing point of view—there are, however, issues related to the plane in which scanning tracks lie and heat treatments for metallic specimens—it has been proved by experimental and computational investigations that the behavior of cylindrical pivots involves complex deformation modes and, particularly, significant non-torsional deformation modes in large deformation.…”

Section: Introductionmentioning

confidence: 99%

Experimental analysis, discrete modeling and parameter optimization of SLS-printed bi-pantographic structures

Harsch

Ganzosch

Barchiesi

et al. 2022

Making use of experimental data for bias extension, shearing, and point-load tests in large deformation regime for rectangular and square bi-pantographic specimens, we perform a numerical identification to fit the a priori parameters of a planar discrete spring model. The main objective of the work is to develop an automatized optimization process based on the Nelder–Mead simplex algorithm for identifying the constitutive parameters of discrete modeling of bi-pantographic structures, as well as assessing its descriptiveness and predictive capacity. The analysis allows to conclude that there exists a single set of parameters for the adopted discrete modeling such that it is descriptive and predictive for several different tests and for a wide range of deformations.