Recovery of the Auxetic Microstructures Appearing in the Least Compliant Continuum Two‐Dimensional Bodies,Physica Status Solidi (B) - Basic Solid State Physics

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Recovery of the Auxetic Microstructures Appearing in the Least Compliant Continuum Two‐Dimensional Bodies
Physica Status Solidi (B) - Basic Solid State Physics ( IF 1.5 ) Pub Date : 2020-08-11 , DOI: 10.1002/pssb.201900676
Sławomir Czarnecki ₁ , Tomasz Łukasiak ₁

Affiliation

The article discusses the 2D problem of manufacturability of the minimum compliance designs of the structural elements made of inhomogeneous materials of local isotropic or square symmetry properties. The available isotropic material design (IMD) and cubic material design (CMD) methods deliver the optimal distribution of the elastic moduli within the design domain. Within the 2D setting, the cubic symmetry reduces to the symmetry of a square. The varying underlying microstructures corresponding to the optimal designs are recovered by matching the values of the optimal moduli with the values of the effective moduli of the representative volume elements (RVEs) computed by the asymptotic homogenization method for periodic media. The shape of the RVE and its internal symmetries are properly selected providing assumed isotropy or symmetry of a square of the homogenized constitutive tensor. The microstructure topology is described by parametric description of single (or several) fibers in RVE. The periodicity of the structure and the final topology of the material within RVE is ensured by multiplication of a single fiber in accordance with the symmetries adopted for RVE. The ability to model an auxetic behavior within the subdomains where the optimal Poisson's ratio assumes negative values is shown.

中文翻译：

恢复最少的连续体二维实体中出现的辅助微结构

本文讨论了由局部各向同性或方形对称特性的不均匀材料制成的结构元件的最小顺应性设计的二维可制造性问题。可用的各向同性材料设计（IMD）和立方材料设计（CMD）方法可在设计域内提供弹性模量的最佳分布。在2D设置中，三次对称减小为正方形的对称。通过将最佳模的值与通过周期性介质的渐近均质化方法计算的代表性体积元素（RVE）的有效模的值进行匹配，可以恢复与最佳设计相对应的各种底层微观结构。的RVE和形状及其内部对称性被适当地选择提供所述匀浆组成张量的平方的假定各向同性或对称。通过RVE中单根（或多根）光纤的参数描述来描述微观结构拓扑。RVE中材料的结构周期性和最终拓扑结构是通过根据RVE采用的对称性乘以单根光纤来确保的。显示了在最佳泊松比为负值的子域内建模举止行为的能力。RVE中材料的结构周期性和最终拓扑结构是通过根据RVE采用的对称性乘以单根光纤来确保的。显示了在最佳泊松比为负值的子域内建模举止行为的能力。RVE中材料的结构周期性和最终拓扑结构是通过根据RVE采用的对称性乘以单根光纤来确保的。显示了在最佳泊松比假设为负值的子域内建模举止行为的能力。

更新日期：2020-10-11

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