Revisiting strain localization analysis for elastoplastic constitutive models in geomechanics

IF 2.7 3区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY International Journal for Numerical Methods in Engineering Pub Date : 2024-08-21 DOI:10.1002/nme.7579
Paul Hofer, Matthias Neuner, Peter Gamnitzer, Günter Hofstetter
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Abstract

The localization of deformations plays a crucial role in the failure of granular materials. Concerning classical continuum constitutive models, the localization of deformations is considered to be connected to the loss of ellipticity of the governing rate equilibrium equations, and entails mesh sensitivity in finite element simulations. While previous studies are often limited to strain localization analyses of individual tests, the focus of the present contribution lies on studying the localization properties in general constitutive states. For this purpose, a staggered optimization algorithm for determining the loss of ellipticity, considering both extreme values, minimum and maximum, of the determinant of the acoustic tensor, is proposed. Part of this algorithm representing a novel application of spherical Fibonacci lattices for discretizing the feasible domain of the associated optimization problem. In the presented localization study of the widely recognized modified Cam‐clay model, special attention is paid to determining the influence of the individual model parameters. Specifically, three factors favoring strain localization are found, namely (i) a low value of the ratio of the primary compression index and the recompression index, (ii) a large value of the critical state frictional constant, as well as (iii) a large value of Poisson's ratio. Moreover, a structural finite element study is performed, confirming the results of localization analyses at the constitutive level.
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重新审视地质力学弹塑性构成模型的应变定位分析
变形的局部化在颗粒材料的失效中起着至关重要的作用。对于经典的连续构效模型,变形的局部化被认为与控制速率平衡方程的椭圆性丧失有关,并导致有限元模拟中的网格敏感性。以往的研究通常局限于单个试验的应变局部化分析,而本论文的重点在于研究一般构成状态下的局部化特性。为此,本文提出了一种交错优化算法,用于确定椭圆度损失,同时考虑声学张量行列式的极值(最小值和最大值)。该算法的一部分代表了球形斐波那契网格的新应用,用于离散相关优化问题的可行域。在对广受认可的改良卡姆粘土模型进行的定位研究中,特别注意确定各个模型参数的影响。具体而言,研究发现了三个有利于应变局部化的因素,即 (i) 初级压缩指数和再压缩指数之比值较低,(ii) 临界状态摩擦常数值较大,以及 (iii) 泊松比值较大。此外,还进行了结构有限元研究,证实了构成层面的局部分析结果。
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来源期刊
CiteScore
5.70
自引率
6.90%
发文量
276
审稿时长
5.3 months
期刊介绍: The International Journal for Numerical Methods in Engineering publishes original papers describing significant, novel developments in numerical methods that are applicable to engineering problems. The Journal is known for welcoming contributions in a wide range of areas in computational engineering, including computational issues in model reduction, uncertainty quantification, verification and validation, inverse analysis and stochastic methods, optimisation, element technology, solution techniques and parallel computing, damage and fracture, mechanics at micro and nano-scales, low-speed fluid dynamics, fluid-structure interaction, electromagnetics, coupled diffusion phenomena, and error estimation and mesh generation. It is emphasized that this is by no means an exhaustive list, and particularly papers on multi-scale, multi-physics or multi-disciplinary problems, and on new, emerging topics are welcome.
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