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Auxetic materials with negative Poisson's ratio have potential applications across a broad range of engineering fields. Several FE based design techniques have been developed to achieve auxetic materials with targeted effective properties, mostly in linear deformation regime. In this paper, an isogeometric shape optimization framework for designing 2D auxetic materials with prescribed deformation over large strain intervals is presented. Taking into account practical manufacturing considerations, a minimum thickness for each member is imposed via a spline-based geometric constraint. The capability of the framework is demonstrated through two examples. First, the paper considers shape optimization of smoothed hexa-petals in plane strain condition to achieve constant Poisson's ratios ranging from a null value to -0.5 to an effective tensile strain of 50%. The second example showcases the shape optimization of smoothed tri- and hexa-petals in plane stress condition for targeted nonlinear deformation behaviour of cat's skin up to 90% tensile strain. • Shape optimization with IGA for smoothed petals with targeted deformation. • Minimum member thickness enforced with a spline based constraint. • Constant negative Poisson's ratio achieved for up till 50% effective tensile strain in plane strain. • Replicated nonlinear deformation of cat's skin up to 90% tensile strain. [ABSTRACT FROM AUTHOR]

In this paper, an effective and efficient topology optimization method, termed as Isogeometric Topology Optimization (ITO), is proposed for systematic design of both 2D and 3D auxetic metamaterials based on isogeometric analysis (IGA). Firstly, a density distribution function (DDF) with the desired smoothness and continuity, to represent the topological changes of structures, is constructed using the Shepard function and non-uniform rational B-splines (NURBS) basis functions. Secondly, an energy-based homogenization method (EBHM) to evaluate material effective properties is numerically implemented by IGA, with the imposing of the periodic boundary formulation on material microstructure. Thirdly, a topology optimization formulation for 2D and 3D auxetic metamaterials is developed based on the DDF, where the objective function is defined as a combination of the homogenized elastic tensor and the IGA is applied to solve the structural responses. A relaxed optimality criteria (OC) method is used to update the design variables, due to the non-monotonic property of the problem. Finally, several numerical examples are used to demonstrate the effectiveness and efficiency of the proposed method. A series of auxetic microstructures with different deformation mechanisms (e.g. the re-entrant and chiral) can be obtained. The auxetic behavior of material microstructures are numerically validated using ANSYS, and the optimized designs are prototyped using the Selective Laser Sintering (SLS) technique. • Development of a more efficient and effective topology optimization (ITO) method. • Application of ITO to the design of auxetic metamaterials, a first study with many desirable features. • Presentation of a series of new and interesting 3D auxetic metamaterials. [ABSTRACT FROM AUTHOR]

The application of auxetic composites in practice often relies on a compromise between properties as auxetics are mostly too porous (not dense enough or not stiff enough) to bear structural loads. Hence, the focus of this paper is topological design optimization of new functionally graded cellular composites with auxetics using a level set method. Firstly, a new hierarchical multi-scale formulation is developed to account for both the auxetic behavior of the microstructure and the stiffness of the macrostructure. The composite, comprising multiple layers of periodic microstructures, is tailored to have functionally graded properties for stiffness and auxetic behaviors, subject to volumetric gradient constraints. Secondly, the microstructures underpinning composite layers are topologically designed under the consideration of boundary and loading conditions of the macrostructure. Finally, a level set method is applied to evolve the shape and topology of the microstructure for each layer, with the numerical homogenization method to evaluate the effective properties of the microstructures. Several numerical examples are used to demonstrate the effectiveness of the proposed method. It can be seen that such composites systematically gear together the features of the functionally graded materials, cellular composites, and metamaterials towards a new kind of man-made composites. [ABSTRACT FROM AUTHOR]

This paper proposes a level set-based robust topology optimization (RTO) method for computational design of metamaterials under hybrid uncertainties, e.g. auxetics with negative Poisson’s ratio, where the Young’s modulus of the solid is described as a random variable while the Poisson’s ratio is regarded as an interval variable. Firstly, the robust objective function is formulated by a combination of interval mean and interval variance of the deterministic objective function. Secondly, the interval mean and interval variance are computed by a hybrid uncertain analysis approach, termed as Polynomial Chaos-Chebyshev Interval (PCCI) method. Thirdly, the design sensitivities of the robust objective function are obtained after the implementation of the PCCI method. Finally, a powerful parametric level set method (PLSM) in conjunction with the numerical homogenization method is applied to achieve the robust topological design for the auxetic microstructure. Several numerical cases are used to demonstrate the effectiveness of the proposed method for the robust topology optimization problems. This method is non-intrusive and general, and can be easily extended to a range of design problems of micro-structured metamaterials. [ABSTRACT FROM AUTHOR]

Auxetic materials have recently emerged as new types of advanced materials with unique material properties that conventional materials do not possess. In this paper, we examine the effect of in-plane negative Poisson's ratio (NPR) on the thermal postbuckling behavior of graphene-reinforced metal matrix composite (GRMMC) laminated cylindrical shells. The shell consists of GRMMC layers arranged in a piece-wise functionally graded (FG) pattern and is subjected to a uniform thermal load surrounded by an elastic medium. Based on the molecular dynamics simulation results, it is noted that the temperature-dependent material properties of GRMMCs can be expressed as a nonlinear function of temperature. The thermal postbuckling problem of shells is modeled under the framework of the Reddy's third order shear deformation theory and solved by using a singular perturbation technique in conjunction with a two-step perturbation approach. Numerical investigations are carried out for the postbuckling of (10/-10/10/-10/10) S and (10/-10/10) S shells with in-plane NPR. It is found that the FG-X pattern can enhance the buckling temperature and the thermal postbuckling strength of the shells. The anomaly is that the thermal buckling load and postbuckling strength of UD (10/-10/10) S shell are slightly higher than those of UD (10/-10/10/-10/10) S GRMMC laminated cylindrical shell. • Both piece-wise FG configurations and in-plane NPRs are considered. • Temperature dependent material properties for both graphene reinforcements and metal matrix are considered. • Buckling temperatures of UD (10/-10/10) S shell are slightly higher than those of UD (10/-10/10/-10/10) S shell. • Thermal postbuckling load–deflection curves of UD (10/-10/10) S shell are higher than those of UD (10/-10/10/-10/10) S shell. [ABSTRACT FROM AUTHOR]

This paper presents an investigation on the nonlinear flexural vibrations of carbon nanotube-reinforced composite (CNTRC) laminated cylindrical shells with negative Poisson's ratios in thermal environments. The material properties of the CNTRCs are temperature-dependent and the functionally graded (FG) in a piece-wise pattern in the thickness direction of the shell. An extended Voigt (rule of mixture) model is employed to estimate the CNTRC material properties. The motion equations for the nonlinear flexural vibration of FG-CNTRC laminated cylindrical shells are based on the Reddy's third order shear deformation theory and the von Kármán-type kinematic nonlinearity, and the effects of thermal environmental conditions are included. The nonlinear vibration solutions for the FG-CNTRC laminated cylindrical shells can be obtained by applying a singular perturbation technique along with a two-step perturbation approach. The effects of material property gradient, the temperature variation, shell geometric parameter, stacking sequence as well as the end conditions on the vibration characteristics of CNTRC laminated cylindrical shells are discussed in detail through a parametric study. The results show that negative Poisson's ratio has a significant effect on the linear and nonlinear vibration characteristics of CNTRC laminated cylindrical shells. • Both piece-wise FG configurations and NPRs are considered. • A multi-scale approach is proposed for nonlinear vibration of auxetic CNTRC shells. • NPR has a significant effect on the nonlinear vibration behavior of FG-CNTRC shells. [ABSTRACT FROM AUTHOR]