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Steen Krenk - One of the best experts on this subject based on the ideXlab platform.
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characteristic state Plasticity for granular materials part i basic theory
International Journal of Solids and Structures, 2000Co-Authors: Steen KrenkAbstract:A non-associated Plasticity theory is developed for granular materials based on the concept of a characteristic stress state of vanishing incremental dilation. The theory makes use of a common format for yield surface and flow potential, representing the surfaces in terms of stress invariants and a single shape function for each. The flow potential surface is determined by an approximate friction hypothesis. Plastic work hardening is introduced in a linear invariant form, that permits dilation before the ultimate state, by including the work associated with shape change in addition to the traditional contribution from volume change. The model is fully three-dimensional and is defined by only six parameters: two for elastic Stiffness, one for Plastic Stiffness, two for the shape of yield and Plastic potential surfaces, and one for the dilation at failure. Typical material response is illustrated, while model calibration and its ability to represent experimental data are discussed in Part II.
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characteristic state Plasticity for granular materials part ii model calibration and results
International Journal of Solids and Structures, 2000Co-Authors: Aylin Ahadi, Steen KrenkAbstract:A non-associated Plasticity theory for granular materials has been developed in Part 1 based on the concept of a characteristic stress state of vanishing incremental dilation. The model is fully three-dimensional and is defined by six material parameters: two for elastic Stiffness, one for Plastic Stiffness, two for the shapes of yield and Plastic potential surfaces and one for the dilation at failure. In this paper a calibration procedure is developed using test data only from a standard triaxial test. It is found that the shape parameter for the yield surface can be estimated from the Plastic how parameters, thus reducing the number of free parameters to five. Calibration examples are shown, as well as predictions made, for different confining stress levels and constant volume tests on sand. The model is found to represent stress-strain behaviour and development of volumetric strain in standard triaxial tests well. The model provides good predictions of constant volume behaviour of dense as well as loose sand on the basis of calibration by standard triaxial test data. A simple explicit formula is derived for the failure asymptote in constant volume testing, enabling explicit adjustment of the parameters, if incompressible-test data is available. (Less)
Peter I. Kattan - One of the best experts on this subject based on the ideXlab platform.
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a Plasticity damage theory for large deformation of solids i theoretical formulation
International Journal of Engineering Science, 1992Co-Authors: George Z. Voyiadjis, Peter I. KattanAbstract:Abstract A coupled theory of continuum damage mechanics and finite strain Plasticity (with small elastic strains) is formulated in the Eulerian reference system. The yield function used is of the von Mises type and incorporates both isotropic and kinematic hardening. An explicit matrix representation is derived for the damage effect tensor for a general state of deformation and damage. Although the theory is applicable to anisotropic damage, the matrix representation is restricted to isotropy. A linear transformation is shown to exist between the effective deviatoric Cauchy stress tensor and the total Cauchy stress tensor. It is also shown that a linear transformation between the deviatoric Cauchy stress tensor and its effective counterpart is not possible as this will lead to Plastic incompressibility in damaged materials. In addition, an effective elasto-Plastic Stiffness tensor is derived that includes the effects of damage. The proposed model is applied to void growth through the use of Gurson's yield function. It is also shown how a modified Gurson function can be related to the proposed model. Some interesting results are obtained in this case.
Aylin Ahadi - One of the best experts on this subject based on the ideXlab platform.
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characteristic state Plasticity for granular materials part ii model calibration and results
International Journal of Solids and Structures, 2000Co-Authors: Aylin Ahadi, Steen KrenkAbstract:A non-associated Plasticity theory for granular materials has been developed in Part 1 based on the concept of a characteristic stress state of vanishing incremental dilation. The model is fully three-dimensional and is defined by six material parameters: two for elastic Stiffness, one for Plastic Stiffness, two for the shapes of yield and Plastic potential surfaces and one for the dilation at failure. In this paper a calibration procedure is developed using test data only from a standard triaxial test. It is found that the shape parameter for the yield surface can be estimated from the Plastic how parameters, thus reducing the number of free parameters to five. Calibration examples are shown, as well as predictions made, for different confining stress levels and constant volume tests on sand. The model is found to represent stress-strain behaviour and development of volumetric strain in standard triaxial tests well. The model provides good predictions of constant volume behaviour of dense as well as loose sand on the basis of calibration by standard triaxial test data. A simple explicit formula is derived for the failure asymptote in constant volume testing, enabling explicit adjustment of the parameters, if incompressible-test data is available. (Less)
George Z. Voyiadjis - One of the best experts on this subject based on the ideXlab platform.
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a Plasticity damage theory for large deformation of solids i theoretical formulation
International Journal of Engineering Science, 1992Co-Authors: George Z. Voyiadjis, Peter I. KattanAbstract:Abstract A coupled theory of continuum damage mechanics and finite strain Plasticity (with small elastic strains) is formulated in the Eulerian reference system. The yield function used is of the von Mises type and incorporates both isotropic and kinematic hardening. An explicit matrix representation is derived for the damage effect tensor for a general state of deformation and damage. Although the theory is applicable to anisotropic damage, the matrix representation is restricted to isotropy. A linear transformation is shown to exist between the effective deviatoric Cauchy stress tensor and the total Cauchy stress tensor. It is also shown that a linear transformation between the deviatoric Cauchy stress tensor and its effective counterpart is not possible as this will lead to Plastic incompressibility in damaged materials. In addition, an effective elasto-Plastic Stiffness tensor is derived that includes the effects of damage. The proposed model is applied to void growth through the use of Gurson's yield function. It is also shown how a modified Gurson function can be related to the proposed model. Some interesting results are obtained in this case.
Marcial Gonzalez - One of the best experts on this subject based on the ideXlab platform.
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generalized loading unloading contact laws for elasto Plastic spheres with bonding strength
Journal of The Mechanics and Physics of Solids, 2019Co-Authors: Marcial GonzalezAbstract:Abstract We present generalized loading-unloading contact laws for elasto-Plastic spheres with bonding strength. The proposed mechanistic contact laws are continuous at the onset of unloading by means of a regularization term, in the spirit of a cohesive zone model, that introduces a small and controllable error in the conditions for interparticle breakage. This continuity property is in sharp contrast with the behavior of standard mechanistic loading and unloading contact theories, which exhibit a discontinuity at the onset of unloading when particles form solid bridges during Plastic deformation. The formulation depends on five material properties, namely two elastic properties (Young’s modulus and Poisson’s ratio), two Plastic properties (a Plastic Stiffness and a power-law hardening exponent) and one fracture mechanics property (fracture toughness), and its predictions are in agreement with detailed finite-element simulations. The numerical robustness and efficiency of the proposed formulation are borne out by performing three-dimensional particle mechanics static calculations of microstructure evolution during the three most important steps of powder die-compaction, namely during compaction, unloading, and ejection. These simulations reveal the evolution, up to relative densities close to one, of microstructural features, process variables and compact mechanical attributes which are quantitatively similar to those experimentally observed and in remarkable agreement with the (semi-)empirical formulae reported in the literature.