• Computers and Concrete
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• v.1 no.4
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• pp.433-455
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• 2004

The paper presents results of FE-calculations on shear localizations in quasi-brittle materials during both an uniaxial plane strain compression and uniaxial plane strain extension. An elasto-plastic model with a linear Drucker-Prager type criterion using isotropic hardening and softening and non-associated flow rule was used. A non-local extension was applied in a softening regime to capture realistically shear localization and to obtain a well-posed boundary value problem. A characteristic length was incorporated via a weighting function. Attention was focused on the effect of mesh size, mesh alignment, non-local parameter and imperfections on the thickness and inclination of shear localization. Different methods to calculate plastic strain rates were carefully discussed.

• Geomechanics and Engineering
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• v.12 no.3
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• pp.347-360
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• 2017

The problem of cylindrical cavity expansion incorporating deformation dependent of intermediate principal stress in rock or soil mass is investigated in the paper. Assumptions that the initial axial total strain is a non-zero constant and the axial plastic strain is not zero are defined to obtain the numerical solution of strain which incorporates deformation-dependent intermediate principal stress. The numerical solution of plastic strains are achieved by the 3-D plastic potential functions based on the M-C and generalized H-B failure criteria, respectively. The intermediate principal stress is derived with the Hook's law and plastic strains. Solution of limited expansion pressure, stress and strain during cylindrical cavity expanding are given and the corresponding calculation approaches are also presented, which the axial stress and strain are incorporated. Validation of the proposed approach is conducted by the published results.

• Computers and Concrete
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• v.7 no.4
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• pp.317-329
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• 2010

The paper describes localization of deformation in a bar under tensile loading. The material of the bar is considered as non-linear viscous elastic and the bar consists of two symmetric halves. It is assumed that the model represents behavior of the quasi-brittle viscous material under uniaxial tension with different loading rates. Besides that, the bar could represent uniaxial stress-strain law on a single plane of a microplane material model. Non-linear material property is taken from the microplane material model and it is coupled with the viscous damper producing non-linear Maxwell material model. Mathematically, the problem is described with a system of two partial differential equations with a non-linear algebraic constraint. In order to obtain solution, the system of differential algebraic equations is transformed into a system of three partial differential equations. System is subjected to loadings of different rate and it is shown that localization occurs only for high loading rates. Mathematically, in such a case two solutions are possible: one without the localization (unstable) and one with the localization (stable one). Furthermore, mass is added to the bar and in that case the problem is described with a system of four differential equations. It is demonstrated that for high enough loading rates, it is the added mass that dominates the response, in contrast to the viscous and elastic material parameters that dominated in the case without mass. This is demonstrated by several numerical examples.