A novel, accurate, and computationally efficient integration approach is developed to integrate small strain viscoplastic constitutive equations involving nonlinear coupled first‐order ordinary differential equations. The developed integration scheme is achieved by a combination of the implicit backward Euler difference approximation and the implicit asymptotic integration. For the uniaxial loading case, the developed integration scheme produces accurate results irrespective of time steps. For the multiaxial loading case, the accuracy and computational efficiency of the developed integration scheme are better than those of either the implicit backward Euler difference approximation or the implicit asymptotic integration. The simplicity of the developed integration scheme is equivalent to that of the implicit backward Euler difference approximation since it also reduces the solution of integrated constitutive equations to the solution of a single nonlinear equation. The algorithm tangent constitutive matrix derived for the developed integration scheme is consistent with the integration algorithm and preserves the quadratic convergence of the Newton–Raphson method for global iterations.

中文翻译：

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粘塑性本构模型的一种新型精确且计算效率高的集成方法

开发了一种新颖，准确且计算高效的积分方法，以积分涉及非线性耦合一阶常微分方程的小应变粘塑性本构方程。通过将隐式后向欧拉差分近似和隐式渐近积分相结合，可以实现所开发的积分方案。对于单轴加载情况，无论时间步长如何，开发的积分方案都能产生准确的结果。对于多轴载荷情况，所开发积分方案的精度和计算效率均优于隐式后向欧拉差分逼近法或隐式渐近积分法。所开发积分方案的简单性等同于隐式向后欧拉差分逼近，因为它也将积分本构方程的解简化为单个非线性方程的解。为已开发的积分方案导出的算法切线本构矩阵与积分算法一致，并且保留了Newton-Raphson方法的二次收敛性用于全局迭代。