多孔材料塑性极限载荷及其破坏模式分析

Plastic limit load and failure analyses of perforated materials

运用塑性力学中的机动极限分析理论,研究韧性基体多孔材料的塑性极限承载能力和破坏模式。以多孔材料的细观结构为研究对象,将细观力学中的均匀化理论引入到塑性极限分析中,并结合有限元技术,建立细观结构极限载荷的一般计算格式,并提出相应的求解算法。数值算例表明:细观孔洞对材料的宏观强度影响明显;在单向拉伸作用下,孔洞呈现膨胀扩大规律;多孔材料破坏源于基体塑性区的贯通。

A numerical method is presented for determining the load-bearing capacities and failure modes of the perforated materials with ductile matrix by means of the kinematic limit theorem. Based on a representative volume element reflecting the microstructure of a perforated material, the plastic limit loads can be calculated by introducing the homogenization theory into the kinematic limit theorem. The finite element modeling of the kinematic limit analysis is formulated as a nonlinear mathematical programming with equality-constraint conditions, which can be solved by a direct iterative algorithm. Numerical examples show that the effect of microscopic holes on the macroscopic strength of materials is intensive, the microscopic holes will expand under uniaxial loads and the failure of materials is due to the linking of plastic areas.