The viscosity of suspensions depends on the properties of the fluid, i.e., the matrix material as well as on the volume fraction and shape of embedded inclusions. Regarding this dependence, a micromechanics-based homogenization approach is presented, giving access to the resulting effective viscous properties, starting from well established homogenization schemes originally proposed for the linear-elastic material response. In order to incorporate nonlinear matrix behavior, i.e., non-Newtonian fluids, the secant method of nonlinear homogenization is employed. The effect of nonsphericity of inclusions is considered by substituting the Eshelby tensor by a replacement tensor (replacement Eshelby tensor) determined by linear-elastic finite element simulations in Traxl and Lackner [Mech. Mater. 126, 126–139 (2018)]. In total, suspensions consisting of four different types of matrix materials, namely, (i) Newtonian, (ii) shear thickening, (iii) shear thinning power-law fluids, and (iv) Bingham or Herschel–Bulkley yield-stress fluids are considered embedding spherical, cubical, and tetrahedral inclusions (rigid particles and pores). The performance of the model is assessed by finite element simulations of respective representative volume elements, showing good agreement between model predictions and numerical results for small and moderate inclusion volume fractions.

中文翻译：

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基于微力学的广义牛顿流体悬浮液有效粘度评估，嵌入非胶体角/球体孔和颗粒

悬浮液的粘度取决于流体的性质，即基质材料以及嵌入的夹杂物的体积分数和形状。关于这种依赖性，提出了一种基于微观力学的均质化方法，从最初为线弹性材料响应提出的完善的均质化方案开始，可以获得由此产生的有效粘性特性。为了结合非线性矩阵行为，即非牛顿流体，采用非线性均质化的割线方法。通过将 Eshelby 张量替换为由 Traxl 和 Lackner 中的线弹性有限元模拟确定的替换张量（替换 Eshelby 张量）来考虑夹杂物的非球形影响 [Mech. 母校。126, 126–139 (2018)]。总共，由四种不同类型的基体材料组成的悬浮液，即 (i) 牛顿流体、(ii) 剪切增稠、(iii) 剪切稀化幂律流体和 (iv) Bingham 或 Herschel-Bulkley 屈服应力流体被认为是嵌入球形、立方体和四面体包裹体（刚性颗粒和孔隙）。该模型的性能通过各自代表性体积元素的有限元模拟进行评估，表明模型预测与小和中等夹杂物体积分数的数值结果之间具有良好的一致性。