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基于應變梯度理論的假設應變有限元方法

Assumed strain finite element method based on the theory of strain gradient

  • 摘要: 采用基于應變梯度理論的假設應變有限元方法研究了微尺度梁彎曲的尺寸效應.在假設應變單元設計中,非局部的應變梯度項通過圍繞高斯點的胞元進行數值積分得到.在本構方程中引入等效應變梯度項,在積分本構方程時就可以反映材料在微細變形時的尺寸效應.為了驗證本方法的正確性,對微尺度下的懸臂梁進行了模擬計算.計算結果與已發表的實驗結果比較吻合,表明可以模擬出材料微細變形的尺寸效應,具有較好的計算精度.

     

    Abstract: An assumed strain finite element method based on the theory of strain gradient was proposed to explore the size effect that frequently exhibited in micro-beam bending. In element design, strain gradient terms were obtained by using numerical integration of a cell constructing around a Gaussian point. An equivalent strain gradient term was incorporated into the constitutive model to reflect the effect of highly localized inhomogeneous deformation. In this way, an assumed strain finite element method program was developed. To validate the performance of the proposed method, a numerical simulation of micro-beam bending was carried out. Numerical resuits show a good agreement with the reported experimental data. It is concluded that the proposed approach is of good capability to reflect the response of microstructure.

     

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