An approximated theoretical model for linear hyperelastic materials with orthotropic inclusions is presented based on a mixture approach and orientation averaging of mechanical properties. In many modern composites, particle inclusions are used to achieve the desired properties. The properties of the resulting composite depend on the material, inclusion-density and also the shape and orientation of the particles. This paper discusses different methods to describe the orientation of the particles and formulate an orientation density distribution function. In particular, the use of quaternions is compared to Cardan angles for orientation averaging. The proposed approximating material model can be applicable to a composite made of a matrix material that contains biaxial particles or a material that is composed of particles of an orthotropic material. An example for the former could be fiber concrete with hooked-end fibers and an example for the latter could be particle boards, as wood is an orthotropic material.

基于混合方法和力学性能的定向平均，提出了具有正交各向异性夹杂物的线性超弹性材料的近似理论模型。在许多现代复合材料中，颗粒夹杂物用于实现所需的性能。所得复合材料的性能取决于材料，夹杂物密度以及颗粒的形状和方向。本文讨论了描述粒子取向并制定取向密度分布函数的不同方法。具体而言，将四元数的使用与Cardan角进行了比较，以求平均方向。提出的近似材料模型可以适用于由包含双轴颗粒的基质材料或由正交各向异性材料的颗粒组成的材料制成的复合材料。