Модифицированная Кэм-клэй модель. Основы теории и численный анализ
Автор: Гольдштейн Роберт Вениаминович, Кузнецов Сергей Владимирович
Журнал: Вычислительная механика сплошных сред @journal-icmm
Статья в выпуске: 2 т.9, 2016 года.
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Анализируются основные уравнения и допущения, принимаемые при конструировании модифицированной Кэм-клэй модели. Отмечается связь модифицированной Кэм-клэй модели с родственными моделями теории пластичности с изотропным упрочнением, описываемыми замкнутыми поверхностями пластичности. Дается оценка уравнений состояния модификаций Кэм-клэй моделей в упругой зоне; выделены работы, в которых упругое состояние представляется уравнениями гиперупругости с экспоненциальным потенциалом. Рассматриваются обобщения модифицированных Кэм-клэй моделей на случай больших деформаций. Подчеркивается, что впервые Кэм-клэй модель с логарифмической поверхностью пластичности в докритической зоне построена в работах Роску, Скофилда и Роса. Позже предложено логарифмическую поверхность пластичности заменить эллипсоидальной. Такая модель также именуется модифицированной Кэм-клэй моделью. Как Кэм-клэй модель с логарифмической поверхностью, так и ее модификация с эллипсоидальной поверхностью относятся к упругопластическим моделям с изотропным упрочнением. Выявлены аналоги модификации Кэм-клэй моделей, в которых учитывается возможность моделирования эффекта Баушингера за счет сдвига поверхности пластичности с помощью комбинации изотропного и кинематического упрочнений. Приводится значительное число работ по применению как Кэм-клэй модели, так и ее модификаций для исследования поведения различных гранулированных материалов с малой когезией в условиях монотонных и циклических воздействий. Большая часть этих работ посвящена либо одноосному, либо трехосному силовому нагружению. Исходя из обзора публикаций делается вывод, что исследования по кинематическим комбинированным нагружениям в шаровой и девиаторной областях на основе Кэм-клэй модели практически отсутствуют. Именно этой проблеме посвящена настоящая работа.
Кэм-клэй модель, пластичность, гиперупругость, упрочнение, размягчение, когезия, сam-clay model
Короткий адрес: https://sciup.org/14320802
IDR: 14320802 | УДК: 53.072.23:534.5 | DOI: 10.7242/1999-6691/2016.9.2.14
Modified Сam-clay model. Theoretical foundations and numerical analysis
State equations and principle assumptions of a modified cam-clay model are analyzed. It is assumed that the modified cam-clay model is related to the plasticity models described by the isotropic hardening rules and closed yield surfaces. Equations of state in the elastic zone, along with models related to the hyperelastic equations of state with the exponential potential, are considered. Some generalizations of the modified cam-clay model for finite strains are performed. Works associated with the problems regarding calibration of theoretical modified cam-clay models with experimental data are reviewed. The first Clay-clay model with logarithmic surface plasticity in the critical zone was constructed in [1, 2]. Later on, the logarithmic surface plasticity was replaced by ellipsoidal one. This model is also called a modified Cam-clay model. The Cam-clay model and its modified variant belong to a class of the elastic-plastic models with isotropic hardening. It should be noted that there are also some modifications of the Cam-clay models, which take into account the possibility of modeling the Bauschinger effect by shifting surface plasticity using a combination of isotropic and kinematic hardening rules. There are a considerable number of works, in which the Cam-clay model and its modifications are used to study the behavior of various granular materials with low cohesion under monotonic or cyclic force loadings. Most of these works are devoted to uniaxial or triaxial force loading. This paper deals with analyzing the behavior of the modified Cam-Clay model under combined kinematic loadings.
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