A discrete Lagrangian based direct approach to macroscopic modelling

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• 作者：Saikat Sarkar ^{saikat@email.tamu.edu} ; Mohsen Nowruzpour ^{Nowruzpour@tamu.edu} ; J.N. Reddy ; ^{jnreddy@tamu.edu} ; A.R. Srinivasa ^{asrinivasa@tamu.edu}
• 关键词：Non-local continuum mechanics ; Peridynamics ; Euler&ndash ; Bernoulli beam theory ; Lagrangian ; Discrete model ; Microcracks
• 刊名：Journal of the Mechanics and Physics of Solids
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：98
• 期：Complete
• 页码：172-180
• 全文大小：828 K
• 卷排序：98

文摘

A direct discrete Lagrangian based approach, designed at a length scale of interest, to characterize the response of a body is proposed. The main idea is to understand the dynamics of a deformable body via a Lagrangian corresponding to a coupled interaction of rigid particles in the reduced dimension. We argue that the usual practice of describing the laws of a deformable body in the continuum limit is redundant, because for most of the practical problems, analytical solutions are not available. Since continuum limit is not taken, the framework automatically relaxes the requirement of differentiability of field variables. The discrete Lagrangian based approach is illustrated by deriving an equivalent of the Euler–Bernoulli beam model. A few test examples are solved, which demonstrate that the derived non-local model predicts lower deflections in comparison to classical Euler–Bernoulli beam solutions. We have also included crack propagation in thin structures for isotropic and anisotropic cases using the Lagrangian based approach.