非均匀分布孔洞材料的梯度本构关系  

Gradient Constitutive Relation of Non-homogeneous Perforated Material

作　　者：李辉[1] 匡震邦[1] 

机构地区：[1]上海交通大学工程力学系,上海200240

出　　处：《上海交通大学学报》2005年第2期309-313,共5页Journal of Shanghai Jiaotong University

摘　　要：提出了一种对非均匀分布孔洞材料的分层等效方法,宏观上可等效为材料参数随厚度变化的梯度材料.利用有限元方法建立代表单元体(RVU)的三维多层模型,并施加必要的边界条件,计算出各层的平均应力应变.将上述值代入多孔橡胶的本构方程(该方程由所选多孔橡胶的应变能函数推导),即可计算出描述等效梯度材料宏观力学性能的等效弹性参数,从而确定了非均匀分布孔洞材料的梯度本构关系.分析了2种典型的非均匀分布孔洞,从中可看出分布类型的影响.The material properties of the homogenized material are considered to be equivalent to the global properties of the perforated material based on the homogenization method. Considering the non-homogeneous voids, a method was proposed to simulate the mechanical behavior of non-homogeneous perforated material by dividing it into sequence of layers, and it can be equivalent to the gradient material whose material parameters vary with thickness. With the FEM, 3-D multiple-layer RVU (representative volume unit) model is established, a set of essential boundary conditions for the RVU is specified, and the homogenized stress and strain, the porosity of material in every layer can be computed. By introducing above values into the constitutive equation of porous rubber, which is derived from the selected strain energy function of porous rubber, the effective elastic parameters that describe the global mechanical properties of effective gradient material can be predicted through the least-squares method. The gradient constitutive relation of non-homogeneous perforated rubber material is established. Two sorts of typical structure with non-homogeneous voids were analyzed, from which the influence of non-homogeneous voids' distribution is present.

关 键 词：非均匀孔洞 非线性有限元 应变能函数 均匀化方法 代表单元体 

分 类 号：O343.5[理学—固体力学]