Abstract Plastic deformations of metallic materials depend on the rate of loading or deformation, implying rate-independent constitutive theories cannot catch a realistic response of the material when the loading condition is not quasi-static. Considering the conventional rate-dependent algorithms, the description of irreversible deformations does not show a smooth transition of the so-called viscoplastic strain from the elastic domain to the viscoplastic domain. In fact, a sudden generation of irreversible deformation takes place whenever the stress state exceeds the macroscopic yield stress during loading. Moreover, some models that adopt the overstress concept are not suitable for the description of impact loadings, since they predict an unrealistic elastic response, implying that the material could bear an infinite load. The present paper adopted the overstress subloading surface theory, which overcame the previous drawbacks. The constitutive equations were modified to take into account the movement of the similarity centre with the viscoplastic deformations to extend the description of the rate-dependency of the material to cyclic loading conditions. Moreover, aspects of the finite step accuracy of the algorithm and the local convergence are discussed.

中文翻译：

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高/低循环应变率加载条件的过应力弹粘塑性模型：第 I 部分 - 公式和计算方面

摘要 金属材料的塑性变形取决于加载速率或变形速率，这意味着当加载条件不是准静态时，与速率无关的本构理论无法捕捉到材料的真实响应。考虑到传统的速率相关算法，不可逆变形的描述没有显示所谓的粘塑性应变从弹性域到粘塑性域的平滑过渡。事实上，在加载过程中，只要应力状态超过宏观屈服应力，就会突然产生不可逆变形。此外，一些采用过应力概念的模型不适合描述冲击载荷，因为它们预测了不切实际的弹性响应，这意味着材料可以承受无限载荷。本文采用超应力分载面理论，克服了以往的不足。修改本构方程以考虑相似中心随粘塑性变形的移动，以将材料的速率依赖性描述扩展到循环加载条件。此外，还讨论了算法的有限步精度和局部收敛性。