Micropolar continuum modeling of 2-D periodic cellular materials and a fast mapping algorithm for the micro-stress

作者：Niu Bin^*; Yan Jun; Cheng Gengdong

来源：Chinese Journal of Solid Mechanics, 2008, 29(2): 109-120.

• Analysis results
• Boundary layer effects
• Cell lengths
• Cellular materials
• Characteristic lengths
• Constitutive relations
• Discrete simulations
• Elastic indentation
• Equivalent continuum model
• Fast algorithms
• Fast mapping
• Lateral loads
• Local properties
• Local stresses
• Micro-stress distribution
• Micropolar
• Micropolar continuum
• Numerical simulations
• Point force
• Reliable method
• Size effects
• Square cell
• Volume averaging

Micropolar equivalent continuum model is established in this paper to capture the non-local properties of cellular materials and to explain the size effects and boundary layer effects observed experimentally. After comment on a few relative equivalent methods of microplolar continuum for 2-D periodic cellular materials, including energy approaches, homogenization of volume averaging technique and others, we present a united approach to formulate the equivalent micropolar constitutive relation. Taking the square cell structure as an example, the solutions from the standard continuum and three kinds of micropolar continua are compared with the exact discrete simulations of same structures under different ratio of cell length to characteristic length of structures. Three different kinds of loading examples are investigated which are elastic indentation by a point force, distributed pressure and distributed lateral load, respectively. Based on the numerical simulation, micropolar continuum can give much better agreement than those from Cauchy-type continuum under elastic indentation and distributed shear-like load, especially around regions with loading applied and near boundary layer of structures. At last, a fast mapping algorithm for detailed micro-stress distribution in components of cellular materials is developed based on the analysis results with micropolar continuum representation. And the fast algorithm is found to be a reliable method to obtain the detailed local stress information of structures composed of cellular materials by numerical simulation.

• 出版日期2008