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Lagrangian stress tensor | Alloy Wiki
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Lagrangian stress tensor
Posted by: steel world2023-10-17Comments Off on Lagrangian stress tensor Notice: Undefined variable: lang_edit in /www/sites/alloy.wiki/index/wp-content/themes/likegoogle/includes/single-meta.php on line 22
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The asymmetric stress tensor described by the initial configuration (see elastic-plastic finite element method) when studying large deformations. Before solving deformation mechanics problems, it is necessary to determine the configuration of an object (a configuration of an object refers to the area occupied by the object in space at a certain moment composed of continuous media) and list the boundary conditions on it. However, the current configuration (see elastic-plastic finite element method) and its boundary conditions need to be determined by the solution of the problem, so these are unknown before solving the problem. If Lagrangian stress tensor is used, the initial configuration of the object before deformation and the boundary conditions on it are determined, thus avoiding the difficulty of using Cauchy stress tensor. By using the Lagrangian correspondence rule, which assumes that the magnitude and direction of the corresponding surface forces on the initial and current configurations are identical, and by using the relationship between the initial and current configuration surface elements, the Lagrangian stress tensor Tmi and the Cauchy stress tensor can be obtained σ The relationship between ji Tmi=JX M, J σ In formula ji, J is the Jacobian determinant of coordinate transformation,; XM is the initial coordinate of the particle before deformation; Xj is the instantaneous coordinate of the deformed particle.
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