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首页> 外文期刊>International journal of non-linear mechanics >On the dynamic dilatation of a compressible Rivlin cube beyond its elastic limit
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On the dynamic dilatation of a compressible Rivlin cube beyond its elastic limit

机译：关于可压缩Rivlin立方体超出其弹性极限的动态膨胀

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摘要

When an isotropic hyperelastic unit cube subjected to dynamic tri-axial extension/compression dilates successfully beyond its elastic limit, namely into its work-hardening deformation regime, plastic flow transforms any kind of induced into permanent anisotropy. If, for instance, two pairs of forces are identical while the third pair is different, then the initially isotropic material properties will transform permanently into those of transverse isotropy. For this problem, a plasticity model is presented that enables the energy stored during the work-hardening deformation stage of the resulting cuboid to be influenced not only by a tensorial measure of the observed deformation, but also by a measure of the plastic flow that takes place simultaneously. The model considers that plastic flow still obeys conventional plastic yield criteria, but does not postulate a-priory a rule that splits the observed deformation into elastic and plastic parts. Derivation of constitutive equations is based instead on the postulate that the strain energy density of the material is a function of the deformation gradient tensor and either the rate-of-plastic-deformation tensor encountered during loading within the work-hardening deformation regime or the residual strain tensor encountered after unloading is completed from some relevant offset yield point. An example application presents a complete analytical solution to the deformation problem of a dynamically loaded Rivlin cube which is made initially of a compressible Rivlin-Mooney material.
机译：当经受了动态三轴拉伸/压缩的各向同性超弹性单元立方成功地膨胀超过其弹性极限（即进入其工作硬化变形状态）时，塑性流动将任何一种诱导形式转变为永久各向异性。例如，如果两对力相同而第三对不同，则最初各向同性的材料特性将永久转变为横向各向同性。针对此问题，提出了一种可塑性模型，该模型不仅使所观测到的长方体在加工硬化变形阶段存储的能量受到张紧量的观测到的变形的影响，而且还受到所采取的塑性流动的影响。同时放置。该模型认为塑性流仍然符合常规塑性屈服准则，但没有假定先有规则将观察到的变形分为弹性和塑性部分。本构方程的推导基于以下假设：材料的应变能密度是变形梯度张量和在工作硬化变形区域内加载过程中遇到的塑性变形率张量的函数，或者是残余量的函数。从某个相关的偏移屈服点完成卸载后遇到的应变张量。一个示例应用程序为动态加载的Rivlin立方体的变形问题提供了完整的解析解决方案，该立方体最初由可压缩的Rivlin-Mooney材料制成。

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