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IUGG XXIV General Assembly July 2-13, 2007 Perugia, Italy
(S) - IASPEI - International Association of Seismology and Physics of the Earth's
Interior
JSS001 Oral Presentation 1718
Plane strain and axisymmetric models to simulate the mechanical behavior
of a rock sample
Mr. Shervin Mizani
Electrical and Computer Engineering School of Electrical and Computer Engineering IASPEI
In this study a finite element program is developed for the analysis of static instability and consequent
flow of an elasto-plastic solid in the cases of plane strain and axisymmetric by using correspondence
principle in the theory of rheological mechanics. The steps are as follows: firstly, declarations of the
quantities for the finite element mesh, the finite element calculations and the constitutive models are
specified. Then the necessary files which are used in the calculation procedures are opened. After that
the geometrical data as generated by the mesh generator is read from a file to specify the geometry of
the problem. Then the material parameters and the applied boundary conditions are read in. Next the
nodal freedom matrix is composed by considering restraint nodes or restraint freedoms of nodes along
restraint sections of the boundary. The numerical implementation concerns three main processes,
namely: (i)-The check of the initial stress state, which involves the calculation of the initial load vector.
(ii)-The specification of the global stiffness matrix, by considering the corresponding solution
procedures. (iii)-Application of displacement increment steps, which involves a Newton-Raphson
iteration method for the equilibrium equation solution in each iteration. With respect to the point that in
the finite element calculation the estimated stress distribution must be in equilibrium with the external
load, this is achieved by calculating the stress distribution for any set of nodal displacements. The
program deals with plane strain and axisymmetric deformation using eight-node rectangular elements
for the elastic, elasto-plastic and viscous behavior of a rock sample. The finite element mesh has been
kept regular to simplify the presentation and to minimize the volume of data required. The simple
geometries enable the nodal co-ordinates and freedom numbers to be generated automatically. The
program is quite capable of analyzing geometrically more complex problems, by simply replacing the
mesh file generated by another program, a so-called mesh generator. The starting geometry, the initial
boundary conditions and material properties which are used as inputs to the numerical models are
obtained from experimental deformation. In general there are three output files for this program which
are used for storage of basic and necessary results, commonly include the calculation results of the
program for the latest step in terms of nodal displacements and invariants of stress and strain. Some
calculated results are demonstrated in relevant figures as displacement-force, nodal displacement
vectors, deformed mesh, contours of deviatoric stresses and strains at integration points for various
cases.
Keywords: plane strain, axisymmetric, rock behavior