Uncertainty quantification is not yet widely adapted in the design process of engineering components despite its importance for achieving sustainable and resource-efficient structures. This is mainly due to two reasons: 1) Tracing the effect of uncertainty in engineering simulations is a computationally challenging task. This is especially true for inelastic simulations as the whole loading history influences the results. 2) Implementations of efficient schemes in standard finite element software are lacking. In this paper, we are tackling both problems. We are proposing a \rev{weakly}-intrusive implementation of the time-separated stochastic mechanics in the finite element software Abaqus. The time-separated stochastic mechanics is an efficient and accurate method for the uncertainty quantification of structures with inelastic material behavior. The method effectivly separates the stochastic but time-independent from the deterministic but time-dependent behavior. The resulting scheme consists only two deterministic finite element simulations for homogeneous material fluctuations in order to approximate the stochastic behavior. This brings down the computational cost compared to standard Monte Carlo simulations by at least two orders of magnitude while ensuring accurate solutions. In this paper, the implementation details in Abaqus and numerical comparisons are presented for the example of damage simulations.

翻译：尽管不确定性量化对于实现可持续和资源高效的结构设计至关重要，但其在工程构件设计过程中尚未得到广泛应用。这主要归因于两个原因：1）在工程模拟中追踪不确定性效应是一项计算上具有挑战性的任务，对于非弹性模拟尤其如此，因为整个加载历史都会影响结果。2）标准有限元软件中缺乏高效方案的实现。本文旨在同时解决这两个问题。我们提出了在有限元软件Abaqus中实现时间分离随机力学的弱侵入式实施方案。时间分离随机力学是一种针对具有非弹性材料行为的结构进行不确定性量化的高效精确方法。该方法有效地将随机但时间无关的行为与确定性但时间相关的行为分离开来。对于均匀材料波动，所得方案仅需两次确定性有限元模拟即可近似随机行为。与标准蒙特卡洛模拟相比，该方案在保证解的精度的同时，将计算成本降低了至少两个数量级。本文以损伤模拟为例，详细介绍了在Abaqus中的实现细节并进行了数值对比。