Gedanken experiments for the determination of two-dimensional linear second gradient elasticity coefficients

In the present paper, a two-dimensional solid consisting of a linear elastic isotropic material, for which the deformation energy depends on the second gradient of the displacement, is considered. The strain energy is demonstrated to depend on 6 constitutive parameters: the 2 Lam´e constants (λ and μ) and 4 more parameters (instead of 5 as it is in the 3D-case). Analytical solutions for classical problems such as heavy sheet, bending and flexure are provided. The idea is very simple: The solutions of the corresponding problem of first gradient classical case are imposed, and the corresponding forces, double forces and wedge forces are found. On the basis of such solutions, a method is outlined, which is able to identify the six constitutive parameters. Ideal (or Gedanken) experiments are designed in order to write equations having as unknowns the six constants and as known terms the values of suitable experimental measurements

Designing a light fabric metamaterial being highly macroscopically tough under directional extensio. First experimental evidence

In this paper, we study a metamaterial constructed with an isotropic material organized following a geometric structure which we call pantographic lattice. This relatively complex fabric was studied using a continuous model (which we call pantographic sheet) by Rivlin and Pipkin and includes two families of flexible fibers connected by internal pivots which are, in the reference configuration, orthogonal. A rectangular specimen having one side three times longer than the other is cut at 45° with respect to the fibers in reference configuration, and it is subjected to large-deformation plane-extension bias tests imposing a relative displacement of shorter sides. The continuum model used, the presented numerical models and the extraordinary advancements of the technology of 3D printing allowed for the design of some first experiments, whose preliminary results are shown and seem to be rather promising. Experimental evidence shows three distinct deformation regimes. In the first regime, the equilibrium total deformation energy depends quadratically on the relative displacement of terminal specimen sides: Applied resultant force depends linearly on relative displacement. In the second regime, the applied force varies nonlinearly on relative displacement, but the behavior remains elastic. In the third regime, damage phenomena start to occur until total failure, but the exerted resultant force continues to be increasing and reaches a value up to several times larger than the maximum shown in the linear regime before failure actually occurs. Moreover, the total energy needed to reach structural failure is larger than the maximum stored elastic energy. Finally, the volume occupied by the material in the fabric is a small fraction of the total volume, so that the ratio weight/resistance to extension is very advantageous. The results seem to require a refinement of the used theoretical and numerical methods to transform the presented concept into a promising technological prototype

SHEARING TESTS APPLIED TO PANTOGRAPHIC STRUCTURES

With the advancements in 3D printing technology, rapid manufacturing of fabric materials with complex geometries became possible. By exploiting this technique, different materials with different structures have been developed in the recent past with the objective of making generalized continuum theories useful for technological applications. So-called pantographic structures are introduced: Inextensible fibers are printed in two arrays orthogonal to each other in parallel planes. These superimposed planes are inter-connected by elastic cylinders. Five differently-sized samples were subjected to shear-like loading while their deformation response was analyzed. Results show that deformation behavior is strong non-linear for all samples. Furthermore, all samples were capable to resist considerable external shear loads without leading to complete failure of the whole structure. This extraordinary behavior makes these structures attractive to serve as an extremely tough metamaterial

3D-measurements of 3D-deformations of pantographic structures

Samples of differently sized so-called pantographic structures are subjected to large deformation loading tests up to rupture, while their response to the deformation is recorded by an optical 3D-measurement system. Digital image correlation is used to calculate the deformation that took place perpendicular to the reference plane by the help of a four-camera system. Results show that the deformation behavior is strongly non-linear and that the structures are capable to perform large (elastic) deformations without leading to complete failure

A Ritz approach for the static analysis of planar pantographic structures modeled with nonlinear Euler–Bernoulli beams

We present a finite element discrete model for pantographic lattices, based on a continuous Euler–Bernoulli beam for modeling the fibers composing the pantographic sheet. This model takes into account large displacements, rotations and deformations; the Euler–Bernoulli beam is described by using nonlinear interpolation functions, a Green–Lagrange strain for elongation and a curvature depending on elongation. On the basis of the introduced discrete model of a pantographic lattice, we perform some numerical simulations. We then compare the obtained results to an experimental BIAS extension test on a pantograph printed with polyamide PA2200. The pantographic structures involved in the numerical as well as in the experimental investigations are not proper fabrics: They are composed by just a few fibers for theoretically allowing the use of the Euler–Bernoulli beam theory in the description of the fibers. We compare the experiments to numerical simulations in which we allow the fibers to elastically slide one with respect to the other in correspondence of the interconnecting pivot. We present as result a very good agreement between the numerical simulation, based on the introduced model, and the experimental measures

The influence of different geometries of matrix/scaffold on the remodeling process of a bone and bioresorbable material mixture with voids

Since internal architecture greatly influences crucial factors for tissue regeneration, such as nutrient diffusion, cell adhesion and matrix deposition, scaffolds have to be carefully designed, keeping in mind case-specific mechanical, mass transport and biological requirements. However, customizing scaffold architecture to better suit conflicting requirements, such as biological and mechanical ones, remains a challenging issue. Recent advances in printing technologies, together with the synthesis of novel composite biomaterials, have enabled the fabrication of various scaffolds with defined shape and controlled in vitro behavior. Thus, the influence of different geometries of the assemblage of the matrix and scaffold on the remodeling processes of living bone and artificial material should be investigated. To this end, two implant shapes are considered in this paper, namely a circular inclusion and a rectangular groove of different aspect ratios. A model of a mixture of bone tissue and bioresorbable material with voids was used to numerically analyze the physiological balance between the processes of bone growth and resorption and artificial material resorption in a plate-like sample. The adopted model was derived from a theory for the behavior of porous solids in which the matrix material is elastic and the interstices are void of material

Viscous second gradient porous materials for bones reconstructed with bio-resorbable grafts

International audienceIt is well known that size effects play an important role in the mechanical behavior of bone tissues at different scales. In this paper we propose a second gradient model for accounting these effects in a visco-poro-elastic material and present some sample applications where bone is coupled with bioresorbable artificial materials of the kind used in reconstructing surgery

Modelling and analysis of lower limb joint loads during the Naeryo chagi technique in taekwondo

Study aim: estimate reaction forces and muscle torque in lower limb joints during the Naeryo chagi technique in taekwondo