Comparison of implicit and explicit numerical integration schemes for a bounding surface soil model without elastic range
Comparison of implicit and explicit numerical integration schemes for a bounding surface soil model without elastic range
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DOI：
10.1016/j.compgeo.2021.104206
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发表时间：
2021-09
影响因子：
5.3
通讯作者：
Christian Carow;F. Rackwitz
中科院分区：
文献类型：
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作者：
Christian Carow;F. Rackwitz
速率本构方程的标准积分方案是根据经典塑性理论设计的。因此，他们依赖于这样的假设：屈服准则定义了一系列纯弹性材料行为。许多非粘性土的本构模型放弃了这一假设。它们在不采用屈服准则的情况下解释非弹性变形。这简化了模型的制定，但提出了有关其数值实现的问题。特别是，尚不完全清楚哪种算法方法最适合无弹性范围的本构模型的数值积分。为了研究这一点，开发并实现了沙子临界状态边界面模型的两种不同应力点算法。显式方法采用子步自动控制局部误差。隐式方法通过局部牛顿迭代更新应力和状态变量，其雅可比行列式通过数值微分计算。通过积分点级计算以及边值问题对两种算法进行了比较。结果表明，对于给定的准确度水平，显式更新过程明显比隐式更新过程更有效。无论初始状态参数和输入应变增量大小如何，这都成立。
Standard integration schemes for rate constitutive equations were designed within the classical theory of plasticity. Consequently, they rely on the assumption that a yield criterion defines a range of purely elastic material behaviour. Many constitutive models for non-cohesive soils discard that assumption. They account for inelastic deformations without employing a yield criterion. This simplifies the formulation of the models but raises questions concerning their numerical implementation. In particular, it is not fully clear which algorithmic method is most appropriate for the numerical integration of constitutive models without elastic range. To investigate this, two different stress point algorithms for a critical state bounding surface model for sands were developed and implemented. The explicit method employs substepping to automatically control the local error. The implicit method updates stresses and state variables through a local Newton iteration, the Jacobian of which is computed by numerical differentiation. The two algorithms were compared by means of calculations at integration point level as well as with respect to a boundary value problem. The results show that for a given level of accuracy, the explicit update procedure is significantly more efficient than the implicit one. This holds regardless of initial state parameters and input strain increment magnitudes.