| 1. |
- Fredriksson, Per, et al.
(författare)
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Size-dependent yield strength of thin films
- 2005
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Ingår i: International journal of plasticity. - : Elsevier BV. - 0749-6419 .- 1879-2154. ; 21:9, s. 1834-1854
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Tidskriftsartikel (refereegranskat)abstract
- Biaxial strain and pure shear of a thin film are analysed using a strain gradient plasticity theory presented by Gudmundson [Gudmundson, P., 2004. A unified treatment of strain gradient plasticity. Journal of the Mechanics and Physics of Solids 52, 1379-1406]. Constitutive equations are formulated based on the assumption that the free energy only depends on the elastic strain and that the dissipation is influenced by the plastic strain gradients. The three material length scale parameters controlling the gradient effects in a general case are here represented by a single one. Boundary conditions for plastic strains are formulated in terms of a surface energy that represents dislocation buildup at an elastic/plastic interface. This implies constrained plastic flow at the interface and it enables the simulation of interfaces with different constitutive properties. The surface energy is also controlled by a single length scale parameter, which together with the material length scale defines a particular material. Numerical results reveal that a boundary layer is developed in the film for both biaxial and shear loading, giving rise to size effects. The size effects are strongly connected to the buildup of surface energy at the interface. If the interface length scale is small, the size effect vanishes. For a stiffer interface, corresponding to a non-vanishing surface energy at the interface, the yield strength is found to scale with the inverse of film thickness.
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| 2. |
- Hård af Segerstad, P., et al.
(författare)
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A constitutive equation for open-cell cellular solids, including viscoplasticity, damage and deformation induced anisotropy
- 2008
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Ingår i: International journal of plasticity. - : Elsevier BV. - 0749-6419 .- 1879-2154. ; 24:5, s. 896-914
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Tidskriftsartikel (refereegranskat)abstract
- A thermodynamically consistent approach is developed for modelling the response of an open-cell cellular solid at finite compressive strains. The cellular solid is considered as a network of struts, where each strut connects two vertex points. A hypothesis is proposed that the vertex points move affinely in the finite strain regime, where the struts buckle plastically. The strut deformation is assumed to be 1-dimensional and depend directly on the macroscopic deformation; thus the description of the strut response requires only a scalar valued response function. Owing to this simple ansatz it is possible to include multiple nonlinear mechanisms, such as hyperelasto-viscoplasticity and damage. The macrostress is obtained by averaging over a statistical ensemble of struts. The model has been implemented in the context of finite strains and damage coupled to viscoplastic Perzyna type behaviour. All model parameters may be determined by performing tests in simple compression. The model is well capable of reproducing data from compression experiments on various open-cell aluminium foams.
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| 3. |
- Hård af Segerstad, Per, 1977, et al.
(författare)
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Computational modelling of dissipative open-cell cellular solids at finite deformations
- 2009
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Ingår i: International Journal of Plasticity. - : Elsevier BV. - 0749-6419 .- 1879-2154. ; 25:5, s. 802-821
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Tidskriftsartikel (refereegranskat)abstract
- This study concerns the constitutive modelling of dissipative open-cell structural cellular solids under primarily finite compressive deformations and the corresponding non-linear finite element implementation. A thermodynamically consistent, mechanistic approach presented in Hard of Segerstad et al. [Hard of Segerstad, P., Larsson, R., Toll, S., 2008. A constitutive equation for open-cell cellular solids, including viscoplasticity, damage and deformation induced anisotropy. International Journal of Plasticity. 24, 896-914.] is adopted for modelling the initial linear-elastic response and the subsequent plateau behaviour. In these regions the cellular solid is considered as a network of struts, where each strut connects two vertex points. A hypothesis is proposed that the vertex points move affinely in the finite strain regime, where the struts buckle plastically. The strut deformation is further assumed to be one-dimensional and depend directly on the macroscopic deformation; thus the description of the strut response requires only a scalar valued response function. Owing to this simple ansatz, the introduction of multiple non-linear mechanisms, such as hyperelasto-viscoplasticity and damage becomes feasible for large scale computations. An additional hyperelastic volumetric response, activated near the point-of-compaction, is introduced for two reasons, (i) to capture the stiffness recovery at high compressive volumetric deformations, where the struts come into contact, and (ii) to prevent numerical instability. The model is implemented as a user defined constitutive driver in the implicit version of the finite element code ABAQUS and tested experimentally for an open-cell aluminium alloy foam (Duocel 6101-0,40 ppi). All material parameters are determined by a simple compression test, and subsequently used to simulate the indentation of a rigid sphere into a foam cylinder. The model accurately captures the experimental load-displacement relation and the deformed geometry. (C) 2008 Elsevier Ltd. All rights reserved.
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| 4. |
- Hallberg, Håkan, et al.
(författare)
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A constitutive model for the formation of martensite in austenitic steels under large strain plasticity
- 2007
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Ingår i: International Journal of Plasticity. - : Elsevier BV. - 0749-6419. ; 23:7, s. 1213-1239
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Tidskriftsartikel (refereegranskat)abstract
- A constitutive model for diffusionless phase transitions in elastoplastic materials undergoing large deformations is developed. The model takes basic thermodynamic relations as its starting point and the phase transition is treated through an internal variable (the phase fractions) approach. The usual yield potential is used together with a transformation potential to describe the evolution of the new phase. A numerical implementation of the model is presented, along with the derivation of a consistent algorithmic tangent modulus. Simulations based on the presented model are shown to agree well with experimental findings. The proposed model provides a robust tool suitable for large-scale simulations of phase transformations in austenitic steels undergoingz extensive deformations, as is demonstrated in simulations of the necking of a bar under tensile loading and also in simulations of a cup deep-drawing process.
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| 5. |
- Håkansson, Paul, et al.
(författare)
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Comparison of isotropic hardening and kinematic hardening in thermoplasticity
- 2005
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Ingår i: International Journal of Plasticity. - : Elsevier BV. - 0749-6419. ; 21:7, s. 1435-1460
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Tidskriftsartikel (refereegranskat)abstract
- A coupled thermo-mechanical problem is presented in this paper. The constitutive model is based on thermoplastic model for large strains where both kinematic and isotropic hardening are included. It is shown that a non-associated plasticity formulation enables thermodynamic consistent heat generation to be modeled, which can be fitted accurately to experimental data. In the numerical examples the effect of heat generation is investigated and both thermal softening and temperature-dependent thermal material parameters are considered. The constitutive model is formulated such that pure isotropic and pure kinematic hardening yield identical uniaxial mechanical response and mechanical dissipation. Thus, differences in response due to hardening during non-proportional loading can be studied. Thermally triggered necking is studied, as well as cyclic loading of Cook's membrane. The numerical examples are solved using the finite element method, and the coupled problem that arises is solved using a staggered method where an isothermal split is adopted.
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| 6. |
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| 7. |
- Håkansson, Paul, et al.
(författare)
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Thermomechanical response of non-local porous material
- 2006
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Ingår i: International Journal of Plasticity. - : Elsevier BV. - 0749-6419. ; 22:11, s. 2066-2090
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Tidskriftsartikel (refereegranskat)abstract
- A thermomechanical model of a porous material is presented. The constitutive model is based on the Gurson model, formulated within a thermodynamic framework and adapted to large deformations. The thermodynamic framework yields a heat equation that naturally includes the mechanical dissipation. To introduce a length scale, the Gurson model was enhanced through non-local effects of the porosity being taken into account. A numerical integration scheme of the constitutive model and the algorithmic stiffness tensor are derived. The integration of the plastic part of the deformation gradient is based on an exponential update operator, an eigenvalue decomposition is also being used to reduce the number of equations that need to be solved. The coupled problem that arises is dealt with by employing a staggered solution method. To examine the capabilities of the model, shear band formation in a thick disc and crack growth in a thick notched disc were investigated. (c) 2006 Elsevier Ltd. All rights reserved.
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| 8. |
- Jansson, Mikael, et al.
(författare)
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On constitutive modeling of aluminum alloys for tube hydroforming applications
- 2005
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Ingår i: International Journal of Plasticity. - : Elsevier BV. - 0749-6419. ; 21:5, s. 1041-1058
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Tidskriftsartikel (refereegranskat)abstract
- The increased interest in lightweight materials for automotive structures has also lead to a search for efficient forming methods that suit these materials. One attractive concept is to use hydroforming of aluminum tubes. The advantages of this forming method includes better tolerances, decreased number of parts and an increased range of forming options. By using FE simulations, the process can be optimized to reduce the risk for failure, i.e. bursting or wrinkling. However, extruded aluminum is highly anisotropic and it is crucial that the material model used for simulations is able to accurately describe this behavior. Also, tube hydroforming occurs predominantly in a biaxial stress state which should be considered in the material testing, where uniaxial tests are used extensively in the industry today. The present study accentuates the need for improved constitutive models. It is shown that a material model, which accurately describes the anisotropic behavior of aluminum tubes, can be obtained from simple and robust experiments.
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| 9. |
- Wallin, Mathias, et al.
(författare)
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Deformation gradient based kinematic hardening model
- 2005
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Ingår i: International Journal of Plasticity. - : Elsevier BV. - 0749-6419. ; 21:10, s. 2025-2050
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Tidskriftsartikel (refereegranskat)abstract
- A kinematic hardening model applicable to finite strains is presented. The kinematic hardening concept is based on the residual stresses that evolve due to different obstacles that are present in a polycrystalline material, such as grain boundaries, cross slips, etc. Since these residual stresses are a manifestation of the distortion of the crystal lattice a corresponding deformation gradient is introduced to represent this distortion. The residual stresses are interpreted in terms of the form of a back-stress tensor, i.e. the kinematic hardening model is based on a deformation gradient which determines the back-stress tensor. A set of evolution equations is used to describe the evolution of the deforrnation gradient. Non-dissipative quantities are allowed in the model and the implications of these are discussed. Von Mises plasticity for which the uniaxial stress-strain relation can be obtained in closed form serves as a model problem. For uniaxial loading, this model yields: a kinematic hardening identical to the hardening produced by isotropic exponential hardening. The numerical implementation of the model is discussed. Finite element simulations showing the capabilities of the model are presented.
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| 10. |
- Yin, Z. Y., et al.
(författare)
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Micromechanical analysis of kinematic hardening in natural clay
- 2009
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Ingår i: International Journal of Plasticity. - : Elsevier BV. - 0749-6419. ; 25:8, s. 1413-1435
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a micromechanical analysis of the macroscopic behaviour of natural clay. A microstructural stress-strain model for clayey material has been developed which considers clay as a collection of clusters. The deformation of a representative volume of the material is generated by mobilizing and compressing all the clusters along their contact planes. Numerical simulations of multistage drained triaxial stress paths on Otaniemi clay have been performed and compared the numerical results to the experimental ones in order to validate the modelling approach. Then, the numerical results obtained at the microscopic level were analysed in order to explain the induced anisotropy observed in the clay behaviour at the macroscopic level. The evolution of the state variables at each contact plane during loading can explain the changes in shape and position in the stress space of the yield surface at the macroscopic level, as well as the rotation of the axes of anisotropy of the material.
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