The current study proposes a computational-based method to employ the non-classical micropolar continuum for modelling plates with in-plane functionally graded porosities. Initially, a homogenisation method is developed to derive the micropolar parameters of porous heterogenous plates based on strain energy equivalence in various designed deformations simulated via finite element analysis. The modelling procedure is further augmented to accommodate structures with functionally graded porosities. The established method offers an effective framework for studying the mechanical behaviour of porous plates with various porosity distributions and a wide range of aspect ratios. Results indicate that the micropolar theory-based modelling surpasses traditional Cauchy theory in accurately predicting the stiffness and displacement distribution of the FG porous structures. The novelty of this study lies in the integration of micropolar theory with the homogenisation of graded porosity patterns, offering enhanced predictions for materials with microstructural features. Additionally, a custom finite element formulation is developed in COMSOL to implement micropolar elasticity, significantly improving the computational efficiency to account for complex geometry, loading, and boundary conditions. To show the applicability of the method, the modelling is used to design a dental implant with its functional property mimicking that of the natural bone to avoid stress-shielding while ensuring proper occlusivity.

中文翻译：

---

一种使用微极理论对功能梯度多孔平面介质进行建模的非经典计算方法


目前的研究提出了一种基于计算的方法，采用非经典微极连续体来模拟具有面内功能梯度孔隙率的板。最初，开发了一种均质化方法，以基于有限元分析模拟的各种设计变形中的应变能等效性推导多孔异质板的微极参数。建模程序进一步增强，以适应具有功能梯度孔隙率的结构。所建立的方法为研究具有不同孔隙率分布和宽纵横比的多孔板的机械行为提供了一个有效的框架。结果表明，基于微极理论的建模在准确预测 FG 多孔结构的刚度和位移分布方面超越了传统的柯西理论。这项研究的新颖之处在于将微极理论与分级孔隙率模式的均质化相结合，为具有微观结构特征的材料提供了增强的预测。此外，COMSOL 还开发了一种定制的有限元公式来实现微极弹性，显著提高了计算效率，以考虑复杂的几何、载荷和边界条件。为了显示该方法的适用性，该模型用于设计一种种植牙，其功能特性类似于天然骨骼，以避免应力屏蔽，同时确保适当的咬合性。