An alternative difference scheme for solving problems of deformation of geomaterials with internal structure

For solving plane problems, two nested difference grids are introduced. In each grid, a field of displacements and individual stresses are set. The difference of the displacement fields allows describing nonuniformity (non-affinity) of strains in structural elements of the medium. The governing equa...

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Bibliographic Details
Main Authors: Revuzhenko, A. F., Lavrikov, S. V., Mikenina, O. A.
Format: Conference Proceeding
Language:English
Subjects:
Deformation
Difference equations
Dilatancy
Elasticity
Geomaterials
Internal friction
Mathematical analysis
Nonuniformity
Problem solving
Sliding
Structural members
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Summary:For solving plane problems, two nested difference grids are introduced. In each grid, a field of displacements and individual stresses are set. The difference of the displacement fields allows describing nonuniformity (non-affinity) of strains in structural elements of the medium. The governing equations are divided into two groups. The first group describes deformation of structural elements, and the second group describes internal friction, dilatancy and sliding between the elements. In the limiting case when sliding is absent and the size of the structural element tends to zero, the equations transform to classical equations of linear elasticity. The difference equations of the two nested grids represent an alternative to the equations constructed for a single difference grid approximating elasticity equations. Examples of solutions to boundary problems are discussed.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0073263