Using the Kröner–Lee elastic and plastic decomposition of the deformation gradient, a differential-algebraic system is obtained (in the so-called semi-explicit form). The system is composed by a smooth nonlinear differential equation and a non-smooth algebraic equation. The development of an efficient one-step constitutive integrator is the goal of this work. The integration procedure makes use of an explicit Runge–Kutta method for the differential equation and a smooth replacement of the algebraic equation. The resulting scalar equation is solved by the Newton–Raphson method to obtain the plastic multiplier. We make use of the elastic Mandel stress construction, which is power-consistent with the plastic strain rate. Iso-error maps are presented for a combination of Neo-Hookean material using the Hill yield criterion and a associative flow law. A variation of the pressurized plate is presented. The exact Jacobian for the constitutive system is presented and the steps for use within a structural finite element formulation are described .

使用变形梯度的Kröner-Lee弹性和塑性分解，可以得到微分-代数系统（所谓的半显式形式）。该系统由一个光滑的非线性微分方程和一个非光滑的代数方程组成。高效的一步式本构积分器的开发是这项工作的目标。积分程序对微分方程采用了明确的Runge-Kutta方法，并平稳地替换了代数方程。所得的标量方程通过牛顿-拉夫森方法求解，以得到塑性乘数。我们利用弹性的Mandel应力构造，该构造与塑性应变率一致。给出了使用Hill屈服准则和关联流定律的新胡克材料组合的等差图。提出了加压板的变化形式。给出了本构系统的精确雅可比公式，并描述了结构有限元公式中使用的步骤。