Simplified determination of elastic-plastic accumulated strain for analytical life assessment of structures by means of the Simplified Theory of Plastic Zones based on Zarka's method

超出弹性极限并承受不同载荷的结构的寿命取决于棘轮机制是否在连续的载荷循环中引起应力和应变的积累（渐进式变形），直到达到安定状态时该过程可能停止。此外，疲劳是要考虑的。因此，需要确定棘轮过程结束时积累的最大弹塑性应变，以便对寿命进行分析评估（与最大允许应变进行比较），以及随后循环中发生的有效应变范围（用于确定疲劳使用因子）。通常，这些量是通过对结构的有限元模型进行多次加载循环的增量弹塑性分析来获得的，直到至少近似地达到安定状态，通常伴随着巨大的计算负担。与此相反，塑性区简化理论（STPZ）利用了弹塑性本构方程的重新表述，包括从Zarkas方法中已知的硬化，允许以某种合适的方式估计一些特殊的量。因此，在安定状态下，可以在结构的每个位置获得累积应变和应变范围的近似。很少的线性弹性分析是足够的，与增量弹塑性分析相比，显著减少了计算负担。尽管到目前为止，在开发STPZ时，钢材是主要关注的材料，但STPZ的基础知识与特定材料无关。因此，潜在的应用领域是广泛的，包括，例如，土木工程，工厂设计和机械工程。第一次应用使人们希望STPZ，至少在确定应变范围方面，一方面是精确但昂贵的循环增量分析，另一方面是在发展循环塑性的结构的实际设计中广泛使用的简单且基于弱的击倒因子（例如因子Ke， Neuber方法）之间的合理折衷。本课题的目的是通过加速计算过程，扩大STPZ的适用范围，提高STPZ的性能，在较小的计算负担下，对STPZ进行扩展，以达到较好的逼近累积应变的目的。由于迄今为止还没有其他的简化方法来量化建立在良好力学背景下的累积应变，因此这一目标被认为是有很大价值的。

The lifetime of a structure, operated beyond elastic limits and subjected to varying loads, is dependent on whether a ratcheting mechanism causing an accumulation of stress and strain in successive cycles of loading is developing (progressive deformation) until this process possibly ceases when shakedown is attained. In addition, fatigue is to be considered. Accordingly, the maximum elastic-plastic strain accumulated at the end of a ratcheting process needs to be determined for an analytical assessment of life (for comparison with maximum admissible strains), as well as the effective strain range occurring in subsequent cycles (for determination of fatigue usage factors). Usually, these quantities are obtained by means of incremental elastic-plastic analyses of a finite element model of the structure for many cycles of loading until shakedown is at least approximately achieved, usually associated with a huge computational burden. In contrast to this, the Simplified Theory of Plastic Zones (STPZ) makes use of a reformulation of the elastic-plastic constitutive equations including hardening known from Zarkas method, allowing for estimating some special quantities in some suitable manner. Thus, an approximation of accumulated strains and of strain ranges may be obtained at each location in the structure in the condition of shakedown. Few linear elastic analyses are sufficient, reducing the computational burden remarkably compared to incremental elastic-plastic analyses. Although steel was the material of main focus when developing the STPZ up to now, the basics of the STPZ are independent of a particular material. Accordingly, the potential field of application is widespread, including, for example, civil engineering, plant design and mechanical engineering. First applications give rise to the hope that the STPZ, at least with respect to determining the strain range, is a reasonable compromise between exact but costly cyclic incremental analyses on one hand and the simple and thus weakly based knock-down factors widely used in practical design of structures developing cyclic plasticity (e.g. factor Ke, Neuber method) on the other hand. The object of the project applied is to expand the STPZ in order to achieve a good approximation to the accumulated strains at little computational burden as well, by accelerating the calculation process, expanding its range of applicability and increasing its performance. Since no other simplified methods quantifying accumulated strains founded on sound mechanical background are known so far, this aim is considered to be of great value.