Computational design of two‐phase auxetic structures

In this paper, a novel three‐dimensional (3D) cellular structure with negative Poisson's ratio was designed by alternating cuboid surface indents on the vertical ribs of the unit cells. The Poisson's ratio and Young's modulus of structures with different geometric parameters were determined using the finite element method (FEM) as a function of these parameters. Samples with identical geometric variables were fabricated via 3D printing, and their through‐thickness direction Poisson's ratios were measured and compared with simulation results. Results showed that the Poisson's ratio of the 3D cellular structures can be tuned from positive to negative and can reach a minimal value of −0.958. Good agreement was found between the experimental results and the simulation. This lattice structure is considerably stiffer than re‐entrant negative Poisson's ratio foam with the same solid phase. The design concept developed here can be optimized for specific applications via geometric parameters manipulation.

Section: Introductionmentioning

confidence: 68%

Three‐Dimensional Stiff Cellular Structures With Negative Poisson's Ratio

Liu

Lakes

2017

“…To investigate the effect of changing the properties of the embedment on the indentation stiffness, the Poisson's ratio, the stiffness and thickness of the embedded layer were varied systematically. It is essential to assess the effect of the Poisson's ratio of the layer, as potentially the effect of the auxeticity may be associated with the mismatch of the Poisson's ratio, which has been observed in other systems, such as semi‐auxetic laminates or composites using a combination of materials with positive and negative Poisson's ratio . As shown in Figure , when the Poisson's ratio of the embedment changes, the indentation stiffness ratios of the materials show very limited change for a sample with a thin shell (0.1 mm thickness).…”

Section: Resultsmentioning

confidence: 99%

“…The material expands transversally upon being stretched and shrinks under compression. Many different mechanisms have been designed and explored, which has opened up more opportunities to develop negative Poisson's ratio materials at different length scales, in some cases, the material can be treated as a homogeneous system …”

Section: Introductionmentioning

confidence: 99%

The Effects of Poisson's Ratio on the Indentation Behavior of Materials With Embedded System in an Elastic Matrix

Al-Badani

et al. 2017

Soft materials with an embedded stiffer layer are increasingly used in medical and sports engineering. A detailed understanding of the mechanical behavior of such a material system under localised load and resistance to indentation is very important. In this work, the deformation of an isotropic soft matrix with a buried stiffer thin layer under a circular flat indenter was investigated through finite element (FE) modeling. A practical approach in simulating the indentation resistance of such a system (soft matrix with a buried thin stiffer layer) is evaluated. The numerical result is correlated with the data based on analytical approaches for both homogeneous materials and elastic half space with an embedded stiffer layer. The influence of Poisson's ratio and auxeticity of the matrix on the deformation and indentation stiffness of the material system under different conditions (indenter size, sheet thickness, and embedment depth) were established and main influences of the Poisson's ratio on the material deformation and stresses are discussed. The result shows that the influence of matrix auxeticity on indentation resistance is highly depth dependent, with over 30% enhancement of the indentation resistance being predicted for materials with matrix of a negative Poisson's ratio.

“…. The recently published paper by Strek et al deals with the minimization of the effective Poisson's ratio of the core in three‐layer sandwich two‐phase composite and shows that resultant composite structure exhibits a negative Poisson's ratio. This corollary is close to the interpretation of the numerical results obtained on the base of IMD method – Example 2 in Section 3.…”

Section: Introductionmentioning

confidence: 99%

Pareto Optimal Design of Non‐Homogeneous Isotropic Material Properties for the Multiple Loading Conditions

Czarnecki

Lewiński

2017

The present paper concerns two methods: IMD (isotropic material design) and YMD (Young modulus material design) concerning Pareto optimal distributions of the material and its isotropic properties. The merit function is the weighted sum of compliances corresponding to n independent loading conditions. The unit cost of the design is assumed as equal to the trace of the elastic moduli tensor C. In the IMD method, the design variables are the bulk and shear moduli. In the YMD method, the Poisson ratio is assumed as given, possibly non‐uniformly distributed in the design domain, the Young modulus being the only design variable. Both the methods reduce to the auxiliary minimization problem involving statically admissible stress fields corresponding to the subsequent loading conditions. The integrand is expressed by a norm of the collection of these stresses, hence has linear growth. The numerical method proposed refers to the primal formulation: it is based on piece‐wise polynomial approximation of the set of statically admissible stresses. The exemplary Pareto optimal solutions show that admitting negative values of Poisson's ratio may contribute to a decrease of the total compliances.