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Finite strain expansion/contraction of a hollow sphere made of strain- and rate- hardening material
Continuum Mechanics and Thermodynamics ( IF 1.9 ) Pub Date : 2022-05-05 , DOI: 10.1007/s00161-022-01103-w
Sergei Alexandrov , Yeau-Ren Jeng

This paper presents a semi-analytic rigid/plastic solution for the expansion/contraction of a hollow sphere at large strains. The yield stress depends on the equivalent strain rate and the equivalent strain. No restriction is imposed on this dependence. The solution reduces to a single ordinary differential equation for determining the radial stress. The independent variable in this equation is the equivalent strain. Moreover, the equivalent strain rate is expressed in terms of elementary functions of the equivalent strain, which allows for representing the yield stress as a function of the equivalent strain and a time-like independent variable. In the course of deriving the equations above, the transformation between Eulerian and Lagrangian coordinates is used. A numerical example illustrates the solution for a material model available in the literature. The motivation of this research is that solutions for the expansion/contraction of a hollow sphere are widely used at the micro-level to calculate some material properties at the macro-level. To this end, it is necessary to specify constitutive equations for micromechanical modeling. The accuracy of these equations is questionable. An advantage of the solution found is that it is practically analytic for quite a general material model that accounts for both strain- and rate-hardening. Therefore, it is straightforward to generate a large amount of theoretical data for comparing with measurable quantities at the macro-level.



中文翻译:

由应变和速率硬化材料制成的空心球的有限应变膨胀/收缩

本文提出了空心球在大应变下膨胀/收缩的半解析刚性/塑性解。屈服应力取决于等效应变率和等效应变。对这种依赖没有任何限制。该解决方案简化为用于确定径向应力的单个常微分方程。该方程中的自变量是等效应变。此外,等效应变率用等效应变的初等函数表示,这允许将屈服应力表示为等效应变和类时间自变量的函数。在推导上述方程的过程中,使用了欧拉坐标和拉格朗日坐标之间的变换。一个数值示例说明了文献中可用的材料模型的解决方案。这项研究的动机是空心球体膨胀/收缩的解决方案在微观层面被广泛用于计算宏观层面的一些材料特性。为此,有必要为微机械建模指定本构方程。这些方程的准确性值得怀疑。所发现的解决方案的一个优点是它实际上是对一个相当通用的材料模型进行分析的,该模型同时考虑了应变硬化和速率硬化。因此,很容易产生大量的理论数据,用于与宏观层面的可测量量进行比较。这项研究的动机是空心球体膨胀/收缩的解决方案在微观层面被广泛用于计算宏观层面的一些材料特性。为此,有必要为微机械建模指定本构方程。这些方程的准确性值得怀疑。所发现的解决方案的一个优点是它实际上是对一个相当通用的材料模型进行分析的,该模型同时考虑了应变硬化和速率硬化。因此,很容易产生大量的理论数据,用于与宏观层面的可测量量进行比较。这项研究的动机是空心球体膨胀/收缩的解决方案在微观层面被广泛用于计算宏观层面的一些材料特性。为此,有必要为微机械建模指定本构方程。这些方程的准确性值得怀疑。所发现的解决方案的一个优点是它实际上是对一个相当通用的材料模型进行分析的,该模型同时考虑了应变硬化和速率硬化。因此,很容易产生大量的理论数据,用于与宏观层面的可测量量进行比较。所发现的解决方案的一个优点是它实际上是对一个相当通用的材料模型进行分析的,该模型同时考虑了应变硬化和速率硬化。因此,很容易产生大量的理论数据,用于与宏观层面的可测量量进行比较。所发现的解决方案的一个优点是它实际上是对一个相当通用的材料模型进行分析的,该模型同时考虑了应变硬化和速率硬化。因此,很容易产生大量的理论数据,用于与宏观层面的可测量量进行比较。

更新日期:2022-05-06
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