| 1. |
- Cedergren, Joakim, et al.
(författare)
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Numerical investigation of powder compaction of gear wheels
- 2003
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Ingår i: International Journal of Solids and Structures. - 0020-7683. ; 40:19, s. 4989-5000
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Tidskriftsartikel (refereegranskat)abstract
- A method to judge the porosity distribution within complex powder compacted 3D structures using a dynamic 3D dilatant finite strain finite element program is presented. The method is demonstrated for a gear wheel, using a combined FKM Gurson model with parameters calibrated from experiments to model a ferrous powder. Compaction is pursued until a final average porosity of 3% in the gear. The method is shown successful in judging the influence on local as well as average properties from change in geometrical parameters and compaction speed. (C) 2003 Elsevier Ltd. All rights reserved.
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| 2. |
- Grassl, Peter, 1974, et al.
(författare)
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Concrete in compression: A plasticity theory with a novel hardening law
- 2002
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Ingår i: International Journal of Solids and Structures. - 0020-7683. ; 39:20, s. 5205-5223
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Tidskriftsartikel (refereegranskat)abstract
- This paper deals with the modelling of the behaviour of plain concrete in triaxial compression using the theory of plasticity. The aim is to model the load resistance and the deformation capacity in uniaxial, biaxial and triaxial compression by means of few parameters, which can be determined easily.A novel hardening law based on a non-associated flow rule and the volumetric plastic strain as hardening parameter is combined with a yield surface proposed by Menetrey and William (1995). The novel hardening and softening law differs from a classic strain-hardening law, as instead of the length of the plastic strain vector only the volumetric component of the latter is used as a hardening parameter. Thus, the non-linearity of the plastic potential is utilized to describe the influence of multiaxial compression on the deformation capacity and no additional ductility measure is required.The implementation and calibration of the novel hardening law are discussed. The prediction of the model is compared to results of uniaxial, biaxial and triaxial compression tests. It is shown that with one set of calibration parameters a good prediction of the load resistance and the deformation capacity for all three types of compression tests can be achieved.
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| 3. |
- magnusson, Anders, et al.
(författare)
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Behaviour of the extensible elastica solution
- 2001
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Ingår i: International Journal of Solids and Structures. - 0020-7683. ; 38:46-47, s. 8441-8457
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Tidskriftsartikel (refereegranskat)abstract
- The general form of the virtual work expression for the large strain Euler–Bernoulli beam theory is derived using the nominal strain (Biot's) tensor. From the equilibrium equations, derived from the virtual work expression, it turns out that a linear relation between Biot's stress tensor and the (Biot) nominal strain tensor forms the differential equation used to derive the elastica solution. Moreover, in the differential equation one additional term enters which is related to the extensibility of the beam axis. As a special application, the well-known problem of an axially loaded beam is analysed. Due to the extensibility of the beam axis, it is shown that the buckling load of the extensible elastica solution depends on the slenderness, and it is of interest that for small slenderness the bifurcation point becomes unstable. This means the bifurcation point changes from being supercritical, which always hold for the inextensible case, i.e. the classical elastica solution, to being a subcritical point. In addition, higher order singularities are found as well as nonbifurcating (isolated) branches.
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| 4. |
- Ottosen, Niels Saabye, et al.
(författare)
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Acceleration Waves in Elasto-Plasticity
- 1991
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Ingår i: International Journal of Solids and Structures. - 0020-7683. ; 28:2, s. 135-159
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Tidskriftsartikel (refereegranskat)abstract
- A spectral analysis of the acceleration wave problem in general elasto-plastic materials is carried out, whereby explicit expressions for the eigenvalues and eigenvectors are obtained. In case of nonassociated plasticity, all eigenvectors become nonorthogonal and one eigenvalue always remains unchanged and equal to the shear modulus. For a very broad class of nonassociated plasticity models, it is shown that the eigenvalues are always real, implying that so-called “divergence” instability can occur, while “flutter” instability can never occur. It is found that a certain value of the hardening modulus exists for which specific propagation directions will always imply that all wave speeds are identical and equal to the elastic distortion wave speed. Moreover, in this situation the eigenvectors are arbitrary, corresponding to a state of diffuse wave modes. The criteria of von Mises and Rankine are used to illustrate some of the findings.
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| 5. |
- Ottosen, Niels Saabye
(författare)
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Behaviour of Viscoelastic-Viscoplastic Spheres and Cylinders-Partly Plastic Vessels walls
- 1985
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Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683. ; 21:6, s. 573-595
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Tidskriftsartikel (refereegranskat)abstract
- The material model consists of a viscoelastic Burgers element and an additional viscoplastic Bingham element when the effective stress exceeds the yield stress. For partly plastic vessel walls, expressions are derived for the stress and strain state in pressurised or relaxation loaded thick-walled cylinders in plane strain and spheres. For the spherical problem, the material compressibility is accounted for. The influence of the different material parameters on the behaviour of the vessels is evaluated. It is shown that the magnitude of the Maxwell viscosity is of major importance for the long-term behaviour of thick-walled partly plastic vessels.
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| 6. |
- Ottosen, Niels Saabye
(författare)
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Behaviour of viscoelastic-viscoplastic spheres and cylinders—Fully plastic vessel walls
- 1985
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Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683. ; 21:6, s. 561-595
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Tidskriftsartikel (refereegranskat)abstract
- The material model consists of a viscoelastic Burgers element and an additional viscoplastic Bingham element when the effective stress exceeds the yield stress. For fully plastic vessel walls, exact closed-form expressions arc derived for the stress and strain state in pressurised or relaxation loaded thick-walled cylinders in plane strain and spheres. For the spherical problem, the material compressibility is accounted for. The influence of the different material parameters on the behaviour of the vessels is evaluated. It is shown that the magnitude of the Maxwell viscosity is of major importance for the long-term behaviour of thick-walled fully plastic vessels.
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| 7. |
- Ottosen, Niels Saabye, et al.
(författare)
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Corners in Plasticity - Koiter's Theory Revisited
- 1996
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Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683. ; 33:25, s. 3697-3721
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Tidskriftsartikel (refereegranskat)abstract
- A general theory for plastic loading at corners is presented that includes Koiter's theory as a special case. This theory is derived within a thermodynamic framework and includes non-associated as well as associated theory. The non-associated theory even allows the number of potential functions to differ from the number of yield functions. The properties of the matrix of plastic moduli as well as of another important matrix are discussed in detail and hardening, perfect and softening plasticity are concisely defined. The existence of limit points is also discussed. The strain driven format turns out to be the most general. Moreover, consistent loading and unloading criteria are established for general non-associated plasticity. An explicit criterion for uniqueness is derived, and finally, some of the general findings are illustrated by means of specific plasticity formulations often encountered in practice.
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| 8. |
- Ottosen, Niels Saabye, et al.
(författare)
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Properties of Discontinuous Bifurcations Solutions in Elasto-Plasticity
- 1991
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Ingår i: International Journal of Solids and Structures. - 0020-7683. ; 27:4, s. 401-421
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Tidskriftsartikel (refereegranskat)abstract
- Explicit expressions for the spectral properties of the bifurcation problem involving discontinuities for general elastic-plastic materials are presented. It then follows that the classical value of the critical hardening modulus derived by Rice (1976. Proc. 14th IUTAM Congr., Delft, The Netherlands, pp. 207–220, North Holland, Amsterdam.) is, in fact, the only possible one. Furthermore, from the spectral analysis it follows in a very straightforward fashion that bifurcation displaying elastic unloading on one side of the singular surface can never precede bifurcation with plastic loading on both sides of this surface. Explicit analytical results for the critical bifurcation directions and the corresponding hardening modulus are derived for non-associated volumetric flow rules while the devialoric portion is associated. The considered yield and potential functions may depend on all three stress invariants and may involve mixed isotropic and kinematic hardening. The result obtained by Rudnicki and Rice (1975, J. Mech. Phys. Solids 23, 371–394) for a Drucker-Pruger material appear as a special case. Other criteria that are investigated arc those of Coulomb and Rankine.
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| 9. |
- Ottosen, Niels Saabye
(författare)
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Theoretical Framework for Modelling the Behaviour of Frictional Materials
- 1986
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Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683. ; 22:11, s. 1325-1342
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Tidskriftsartikel (refereegranskat)abstract
- A constitutive theory is proposed, which possesses the possibilities of modelling all the important features or the behaviour or frictional materials such as: influence of all three stress invariants, coupling between deviatoric and volumetric response, dilatancy, softening, and different behaviour in loading and unloading. The basic constitutive assumptions are relations between properly defined stress and strain rate invariants, from which the component equations are derived by means of a suitable reformulation. After the incremental stress-strain relations have been derived, they are augmented by consistent loading/unloading criteria. Emphasis is given to a fundamental discussion of the general properties of the theory proposed and it is shown to fulfil all the formal requirements (causality, determinism, admissibility, form-invariance, continuity) that a properly formulated constitutive theory must obey. Moreover, the theory contains a surprisingly large number of classical as well as nonclassical theories as special cases. In particular, it contains formulations ranging from nonassociated plasticity theory, associated plasticity theory, hypoelasticity to elasticfracturing theory.
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| 10. |
- Ristinmaa, Matti, et al.
(författare)
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Consequences of Dynamic Yield Surface in Viscoplasticity
- 2000
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Ingår i: International Journal of Solids and Structures. - 0020-7683. ; 37:33, s. 4601-4622
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Tidskriftsartikel (refereegranskat)abstract
- A theory of viscoplasticity is formulated within a thermodynamic concept. The key point is the postulate of a dynamic yield surface, which allows us to take advantage of the postulate of maximum dissipation to derive an associated formulation of the evolutions laws for the internal variables without using penalty techniques that only hold in the limit it when viscoplasticity degenerates to inviscid plasticity. Even a non-associated formulation is presented. Within this general formulation, a particular format of the dynamic yield function enables us to derive the static yield function in a consistent manner. Hardening, perfect and softening viscoplasticity is also defined in a consistent manner. The approach even includes associated and non-associated viscoplasticity where corners exist on the yield and potential surfaces.
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