A computationally efficient numerical strategy called as variational differential quadrature-finite element method (VDQFEM) is developed herein for the nonlinear analysis of hyperelastic micromorphic continua. To this end, a novel formulation including microstructure effects is proposed in which high-order tensors are written in equivalent matrix or vector forms, and is then discretized in an efficient way. This feature is utilized in the coding process of numerical method. For the solution purpose, the domain is first transformed into a number of finite elements. Thereafter, a variational discretization technique called as VDQ is applied within each element. In order to employ the VDQ method, the irregular domain of the element is transformed into the regular one using the mapping technique. Finally, the assemblage procedure is performed. This approach can be used for the analysis of bodies with arbitrary geometries. By considering several numerical examples, it is revealed that the presented size-dependent formulation and numerical solution approach have a good performance to study the large deformations of hyperelastic micromorphic bodies with complex geometries.

中文翻译：

---

一种有效的微形态超弹性数值方法

本文开发了一种计算有效的数值策略，称为变分差分正交有限元方法（VDQFEM），用于非线性超弹性微晶连续体分析。为此，提出了一种包含微观结构效应的新颖配方，其中将高阶张量以等效矩阵或矢量形式编写，然后以有效方式离散化。此功能在数值方法的编码过程中得到利用。为了解决问题，首先将域转换为多个有限元。此后，在每个元素内应用称为VDQ的变分离散化技术。为了采用VDQ方法，使用映射技术将元素的不规则域转换为规则域。最后，执行组装过程。该方法可用于分析具有任意几何形状的物体。通过考虑几个数值实例，发现所提出的尺寸依赖公式和数值求解方法对于研究具有复杂几何形状的超弹性微晶体的大变形具有良好的性能。