On the localization properties of multiplicative hyperelasto-plastic continua with strong discontinuities
On the localization properties of multiplicative hyperelasto-plastic continua with strong discontinuities
复制标题
强间断乘法超弹塑性连续体的局域化性质
DOI：
10.1016/s0020-7683(96)00043-1
复制
发表时间：
1997
影响因子：
3.6
通讯作者：
K. Runesson
中科院分区：
文献类型：
--
作者：
P. Steinmann;R. Larsson;K. Runesson
本工作的目的是研究基于变形梯度乘法分解的超弹塑性材料的大应变局部化特性。由此，研究了强不连续的情况。为此，首先给出了空间切向算子的显式表达式，同时考虑了各向异性和非相关材料的行为。然后对正则化不连续速度梯度的结构进行了详细的阐述和讨论。在这两个结果的基础上，推导了定位条件，特别强调了预期定位带内外的载荷条件。因此，与几何线性理论的结构相似的正切算子的有趣的简单结构得到了广泛的利用。以各向同性材料为例，这种相似性延续到临界硬化模数的一般表示法。因此，在小弹性应变的假设下可以得到解析解，这对于金属来说是合理的。最后，给出了相关的von Mise流动规则的特例。为此，研究了在不同的均匀弹塑性变形模式下，临界局部化方向和临界硬化模数与有限弹性应变量的关系。
The objective of this work is to examine the large strain localization properties of hyperelasto-plastic materials which are based on the multiplicative decomposition of the deformation gradient. Thereby, the case of strong discontinuities is investigated. To this end, first an explicit expression for the spatial tangent operator is given, taking into account anisotropic as well as nonassociated material behaviour. Then the structure of a regularized discontinuous velocity gradient is elaborated and discussed in detail. Based on these two results, the localization condition is derived with special emphasis on the loading conditions inside and outside an anticipated localization band. Thereby, the intriguingly simple structure of the tangent operator, which resembles the structure of the geometrically linear theory, is extensively exploited. This similarity carries over to the general representation for the critical hardening modulus which is exemplified for isotropic materials. As a result, analytical solutions are available under the assumption of small elastic strains, which is justified for metals. Finally, examples are given for the special case of the associated von Mises flow rule. To this end, the critical localization direction and the critical hardening modulus are investigated with respect to the amount of finite elastic strain within different modes of homogeneous elasto-plastic deformations.