任意初始应力参考构型与无应力参考构型的响应
Responses of any arbitrary initially stressed reference and the stress-free reference
AI总结：
本文提出三种不依赖已知无应力状态的方法，从已知初始应力参考构型的响应出发，确定无应力或任意初始应力参考构型的本构关系，并发现即使已知状态为Green弹性，其他参考构型也可能表现出隐式弹性。
摘要：
初始应力参考构型的本构关系通常通过利用一个虚拟无应力参考构型的响应来确定。然而，在不进行破坏性试验的情况下，识别原始无应力体的本构关系可能具有挑战性。本文提出了三种方法，用于在已知某一特定初始应力参考构型的响应时，确定无应力参考构型——或任意初始应力参考构型——的响应。与标准做法不同，这些改变参考构型的方法并非从已知的无应力状态出发。第一种和第三种方法直接从一个受应力参考构型推导出另一个受应力参考构型的本构关系。第一种方法适用于已知初始应力状态的特定本构关系，而第三种方法扩展了第一种方法，适用于任何本构形式。第二种方法利用给定受应力参考构型的任意一般响应来识别无应力材料。进一步分析并处理无应力材料的响应，以确定任意受应力参考构型的响应。我们观察到，即使已知的初始应力状态是Green弹性，任意受应力或无应力参考构型也可能表现出隐式弹性。（完整摘要见已发表版本）
英文摘要：
The constitutive relation for an initially stressed reference is often determined by using the response of a virtual stress-free reference. However, identifying the constitutive relation of the original stress-free body can be challenging without conducting destructive tests. This paper presents three approaches for determining the response of a stress-free reference -- or any arbitrary initially stressed reference -- when the response of a particular initially stressed reference is known. Unlike standard practice, these approaches of changing reference configurations do not begin with a known stress-free state. The first and third approaches directly derive the constitutive relations of one stressed reference from another. {The first approach is applicable to a specific constitutive relation of the known initially stressed state,} while the third approach extends the first and is applicable to any constitutive form. The second approach uses any general response of a given stressed reference to identify the stress-free material. The response of the stress-free material is further analyzed and processed to determine the response of any stressed reference. We observe that even when the known initially stressed state is Green elastic, the arbitrarily stressed or stress-free references may exhibit implicit elasticity. (complete abstract is available in the published version)
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
