基于C2阶连续函数的广义Hoek-Brown强度准则屈服面与塑性势面棱角圆化方法

C2 continuous approximation to generalized Hoek-Brown strength criterion yield surface and plastic potential surface

Hoek-Brown强度准则的屈服面与塑性势面在棱角处导数无定义,具有数值奇异性,采用圆角进行光滑过渡只能满足一阶导数连续性,而二阶导数仍然无定义,使得棱边上一致切线模量矩阵无法正确计算,导致有限元总体平衡方程组Newton-Raphson隐式迭代二阶收敛性丧失。提出基于C2阶连续函数的广义Hoek-Brown准则屈服面与塑性势面棱角圆化方法,使得棱角处函数曲面二阶连续可导,棱边上一致切线模量矩阵可精确计算。基于ABAQUS数值开发平台,采用FORTRAN语言编制Hoek-Brown准则理想弹塑性UMAT用户子程序,通过数值算例验证所提方法的正确性。

Derivative is not defined at the edge corners of yield and plastic potential surfaces based on the generalized Hoek-Brown strength criterion and numerical singularity has been caused there. Smooth transitions with circular surface only satisfy the first derivative continuity; the second derivative is still undefined on the edges; so that the consistent tangent modulus can not be calculated correctly there. The implicit solution of nonlinear equilibrium equations in finite element method(FEM) with Newton-Raphson method is unable to achieve full quadratic convergence. C2 continuous rounding of yield and plastic potential surfaces in the π-plane has been introduced; so that the surfaces can be second-order continuous derivative on the edges; and the consistent tangent modulus matrix can be calculated accurately. Subroutine UMAT for the generalized Hoek-Brown linear elastic-perfectly plastic constitutive model has been coded with FORTRAN in ABAQUS software. Numerical examples are used to verify the correctness of the proposed method.