摘要
泡沫金属的力学性能强烈依赖于内部结构。当构件特征尺寸与胞孔特征尺寸d处于相同数量级时,表现出明显的尺度效应。为了揭示这种尺度效应的力学机理,研究了泡沫金属试件的剪切和纯弯曲试验。一方面,利用应变梯度弹性理论给出解析解,其中包含了材料内禀尺寸lc这一关键模型参数。另一方面,把每段胞壁视为铁木辛柯梁,从而建立梁链网作为泡沫金属的微观力学模型。通过应变能等效原理建立应变梯度连续体和基体金属材料弹性参数之间的关系。发现,边界层的约束条件对泡沫金属的力学响应有重要影响。弯曲问题中,只有对离散模型上下表面施加恰当的附加转角约束后,应变梯度理论解与链网模型数值解才能够吻合。这为理解应变梯度理论中的非传统边界条件提供了一个直观的实例。通过数据拟合,得到了内禀尺寸lc与胞孔特征尺寸d之间的关系,与文献结论相符。
The mechanical properties of the metal foam is strongly dependent on its internal structure. When the characteristic size of the specimen and the cell size d of the internal structure are of the same order of magnitude, there exist obvious size effects. In order to reveal the mechanical mechanism behind such size effects, simple shear and bending tests of metal foam specimens were performed. On one hand, the problems were solved analytically by using the strain gradient elasticity theory, which contains the key parameter lc, i.e., the material characteristic length scale. On the other hand, the beam lattice was established as the micromechanics model of metal foams by taking each cell wall as a Timoshenko beam. The relationship between the parameters of the generalized continuum and foam's matrix material was established according to the strain energy equivalence principle. It is found that boundary layer constraint conditions have an important impact on the mechanical response of metal foams. For the bending problem, the analytical solution based on strain gradient theory matches the result obtained by the lattice model only when the proper extra constraints are applied on the upper and lower surfaces of the lattice model. This provides an intuitive example for understanding non-classical boundary conditions in the strain gradient theory. By fitting the theoretical and numerical results, the relationship between the material length scale parameter lc and the cell size d is obtained, which agrees well with the conclusion from literature.
出处
《工程力学》
EI
CSCD
北大核心
2017年第10期35-43,共9页
Engineering Mechanics
基金
国家自然科学基金面上项目(11672119)
江苏省青年自然科学基金项目(BK20140520)
关键词
泡沫金属
尺度效应
梁链网模型
应变梯度弹性理论
边界层效应
metal foam
size effect
beam lattice model
strain gradient elasticity theory
boundary layer effect