The popularity of the elasto-plastic Hardening Soil (HS) model is based on simple parameter identification from standard testing and empirical formulas. The HS model is implemented in many commercial FE codes designed to analyse geotechnical problems. In its basic version, the stress–strain behaviour within the elastic range is subject to the hypoelastic power law, which assures the barotropy of the elastic stiffness. However, a proper modelling within the small strain range, i.e. strain-induced stiffness degradation and correct reproduction of the hysteretic behaviour, was one of the most important drawbacks in the HS formulation. The first small strain stiffness extension to the HS model was proposed by Benz (Small strain stiffness of soils and its numerical consequences, 2007), and the new model was called Hardening Soil Small (HSS). Despite the simple isotropic formulation, its applicability was proved in various numerical simulations in geotechnics. However, the HSS formulation exhibits a serious fault known in the literature as overshooting, i.e. uncontrolled reset of the loading memory after tiny unloading–reloading cycles. The authors' main aim was to retain the set of material parameters for the HSS formulation and to propose a new small strain extension to the HS model without overshooting. The new proposal is based on the Brick model which represents the concept of nested yield surfaces in strain space. The implementation aspects of the new HS-Brick model are described, and its performance is presented in some element tests and selected boundary value problems by comparisons with the HSS formulation.

中文翻译：

---

在较小应变范围内完善硬化土模型

弹塑性硬化土（HS）模型的流行是基于标准测试和经验公式的简单参数识别。HS模型在许多旨在分析岩土问题的商业FE代码中实现。在其基本版本中，弹性范围内的应力-应变行为服从次弹性幂定律，该定律可确保弹性刚度的正压性。但是，在小应变范围内进行适当的建模，即应变引起的刚度降低和滞后行为的正确再现，是HS配方中最重要的缺点之一。苯提出了对HS模型的第一个小应变刚度扩展（土壤的小应变刚度及其数值结果，2007年），新模型称为“硬化小土壤”（HSS）。尽管有简单的各向同性公式，但其适用性已在岩土工程的各种数值模拟中得到了证明。但是，HSS公式表现出严重的故障，在文献中称为过冲，即在微小的装卸循环之后，装填存储器的不受控制的复位。作者的主要目的是保留用于HSS配方的材料参数集，并为HS模型提出新的小应变扩展而不会出现过冲。新提案基于 主要目的是保留用于HSS配方的材料参数集，并为HS模型提出新的小应变扩展而不会发生过冲。新提案基于 主要目的是保留用于HSS配方的材料参数集，并为HS模型提出新的小应变扩展而不会发生过冲。新提案基于砖模型代表了应变空间中嵌套屈服面的概念。描述了新HS-Brick模型的实现方面，并通过与HSS公式的比较，在一些元素测试和选定的边值问题中展示了其性能。