Using an unified approach based on the local material symmetry group introduced for general first- and second-order strain gradient elastic media, we analyze the constitutive equations of strain gradient fluids. For the strain gradient medium there exists a strain energy density dependent on first- and higher-order gradients of placement vector, whereas for fluids a strain energy depends on a current mass density and its gradients. Both models found applications to modeling of materials with complex inner structure such as beam-lattice metamaterials and fluids at small scales. The local material symmetry group is formed through such transformations of a reference placement which cannot be experimentally detected within the considered material model. We show that considering maximal symmetry group, i.e. material with strain energy that is independent of the choice of a reference placement, one comes to the constitutive equations of gradient fluids introduced independently on general strain gradient continua.

使用基于为一般一阶和二阶应变梯度弹性介质引入的局部材料对称群的统一方法，我们分析了应变梯度流体的本构方程。对于应变梯度介质，应变能密度取决于放置矢量的一阶和更高阶梯度，而对于流体，应变能取决于电流质量密度及其梯度。这两种模型都应用于具有复杂内部结构的材料建模，例如小尺度的梁-晶格超材料和流体。局部材料对称组是通过参考位置的这种转换形成的，在所考虑的材料模型中无法通过实验检测到。我们证明考虑最大对称群，即