能量非局部模型和新的应变梯度理论

Energy non-local model and new strain gradient theory

摘要: 提出一种新的基于能量非局部模型的应变梯度理论，并应用此理论对多晶铜以及薄膜基底的微压痕硬度进行理论预测和数值分析. 首先，提出了能量非局部模型，并由此模型，得出新应变梯度理论的本构关系；其次，由变分原理，得出相应的有限元公式；再次，给出了微压痕硬度的有限元分析方法；最后，将该理论预测结果与经典理论预测结果以及实验结果进行了对比. 结果表明，计算结果与实验结果相符；而经典理论的预测结果远低于实验结果.

Abstract: A new strain gradient theory based on energy non-localmodel is proposed in the paper, and applied to predict the micro-indentationhardness of polycrystalline copper and the thin film--substrate system.First, an energy non-local model is presented to derive the constitutiveequation of a new strain gradient theory. Second, the finite element formulaof the new strain gradient theory is obtained with the case of theprediction of micro-indentation hardness. It is found that the predictedresults by the new strain gradient theory agree well with the experimentaldata, while the hardness values predicted by classic plasticity theory areremarkably lower than the experimental data.