基于能量密度等效的超弹性压入模型与双压试验方法

针对超弹性材料压入问题, 本文基于能量密度中值等效原理, 提出了描述球、平面、锥3类压头独立压入下载荷、深度、压头几何尺寸和Mooney-Rivlin本构关系参数之间关系的半解析超弹性压入模型(semi-theoretical hyperelastic-material indentation model, SHIM), 进而提出了球、平面、锥压入组合的双压试验方法(indentation method due to dual indenters, IMDI). 正向验证表明, 基于系列超弹性材料的本构关系参数, 由SHIM分别预测的球、平面、锥3类压入下的载荷-位移曲线与有限元分析(finite element analysis, FEA)结果之间密切吻合; 反向验证表明, 基于系列超弹性材料的FEA条件本构关系下3类压入的载荷-位移曲线, 由双压试验方法预测的Mooney-Rivlin本构关系与FEA条件本构关系密切吻合. 针对3种超弹性橡胶, 完成了球、平面、锥压入试验, 应用双压试验方法获得的3组Mooney-Rivlin本构关系均与单轴拉伸试验结果吻合良好. 

HYPERELASTIC INDENTATION MODELS AND THE DUAL-INDENTATION METHOD BASED ON ENERGY DENSITY EQUIVALENCE1)

For the hyperelastic problems of materials under indentation conditions, based on the mean-value energy density equivalence principle, semi-theoretical hyperelastic-material indentation models(SHIM) are proposed to describe the relationship among load, depth, indenter dimension and Mooney-Rivlin constitutive parameters under independent indentation with spherical indenter, flat indenter and conical indenter, respectively, and then the indentation method due to dual indenters(IMDI) is presented. The forward verification shows that, based on a series constitutive relation parameters of hyperelastic materials, the force-depth curves of spherical, conical and flat indentation respectively predicted by SHIM are closely consistent with the FEA results; and the reverse verification shows that, based on the force-depth curves under FEA conditional constitutive relation of a series of hyperelastic materials, the Mooney-Rivlin constitutive relations predicted by the dual indentation experimental method are closely consistent with the FEA conditional constitutive relations. For three hyperelastic rubbers, the spherical, flat and conical indentation tests were carried out, three constitutive relationships of the hyperelastic rubbers obtained by IMDI are all in good agreement with the uniaxial tensile results.