弹性固体材料中的空穴萌生与增长

Void Nucleation and Growth for Elastic Solid Materials

建立了描述弹性固体材料中空穴萌生与增长的非线性数学模型，获得了空穴萌生时控制参数临界值的精确计算公式和空穴半径增长的精确表达式．在大变形几何分析中采用了对数应变度量，并且应用了Ｈｏｏｋｅ弹性固体材料的本构关系．数值分析结果表明：当材料不可压时空穴萌生的临界载荷将略低于ｎｅｏ－Ｈｏｏｋｅ不可压超弹性材料的相应计算结果，并且在空穴萌生后空穴半径将迅速增大，这与细观损伤力学和超弹性材料的空穴分叉理论的结论相一致；空穴萌生时环向应力将成为无限大；如果材料是弹塑性（韧性）材料，则会使得空穴附近发生塑性变形，从而导致材料的局部损伤和破坏．

The nonlinear mathematical model is given to describe void nucleation and growth for elastic solid materials. Exact formulae to calculate the critical values of control parameters for cavitation and exact ex- pressions for growth of void radial are derived. For large deformation, finite logarithmic strain measure is used, and the constitutive relationship of materials is basic on Hookean elastic law. The numerical results show that the critical loads of cavitation for Hooke elastic solid in the case of uncompressible materials are slightly lower than the critical loads for uncompressible neo-Hookean hyperelastic materials. The cavity will be suddenly ra-pid growth after void nucleation. This conclusion is agreed with the corresponding conclusion from the damage micromechanics and the theory of cavitated bifurcation for hyperelastic materials. Also, the analysis shows that the loop stress will become infinite when void nucleation. Thus, the materials near the cavity will product plastic deformation if the materials are elastic-plastic. This leads to local failure and fracture of the materials.