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Systematic design of 3D auxetic lattice materials with programmable Poisson's ratio for finite strains

机译:具有有限应变的可编程泊松比的3D膨胀晶格材料的系统设计

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This paper presents a systematic approach for designing 3D auxetic lattice materials, which exhibit constant negative Poisson’s ratios over large strain intervals. A unit cell model mimicking tensile tests is established and based on the proposed model, the secant Poisson’s ratio is defined as the negative ratio between the lateral and the longitudinal engineering strains. The optimization problem for designing a material unit cell with a target Poisson’s ratio is formulated to minimize the average lateral engineering stresses under the prescribed deformations. Numerical results demonstrate that 3D auxetic lattice materials with constant Poisson’s ratios can be achieved by the proposed optimization formulation and that two sets of material architectures are obtained by imposing different symmetry on the unit cell. Moreover, inspired by the topology-optimized material architecture, a subsequent shape optimization is proposed by parametrizing material architectures using super-ellipsoids. By designing two geometrical parameters, simple optimized material microstructures with different target Poisson’s ratios are obtained. By interpolating these two parameters as polynomial functions of Poisson’s ratios, material architectures for any Poisson’s ratio in the interval ofν∈[−0.78,0.00]are explicitly presented. Numerical evaluations show that interpolated auxetic lattice materials exhibit constant Poisson’s ratios in the target strain interval of [0.00, 0.20] and that 3D auxetic lattice material architectures with programmable Poisson’s ratio are achievable.
机译:本文提出了一种用于设计3D流变晶格材料的系统方法,该材料在较大的应变区间内呈现恒定的负泊松比。建立了模拟拉伸试验的晶胞模型,并基于该模型将割线泊松比定义为横向和纵向工程应变之间的负比。制定了设计具有目标泊松比的材料单元的优化问题,以最大程度地减少规定变形下的平均横向工程应力。数值结果表明,通过提出的优化公式可以实现具有恒定泊松比的3D流变晶格材料,并且通过在晶胞上施加不同的对称性来获得两组材料结构。此外,受拓扑优化的材料体系结构的启发,通过使用超级椭圆体对材料体系结构进行参数化,提出了后续的形状优化方案。通过设计两个几何参数,可以获得具有不同目标泊松比的简单优化的材料微观结构。通过将这两个参数作为泊松比的多项式函数进行插值,可以明确提出在νε[-0.78,0.00]区间内任何泊松比的材料结构。数值评估表明,内插的膨胀格子材料在目标应变区间[0.00,0.20]中显示恒定的泊松比,并且可以实现具有可编程泊松比的3D膨胀格子材料结构。

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