| 1. |
- Meyer, Knut Andreas, 1990, et al.
(författare)
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A distortional hardening model for finite plasticity
- 2021
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Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683. ; 232
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Tidskriftsartikel (refereegranskat)abstract
- Plastic anisotropy may strongly affect the stress and strain response in metals subjected to multiaxial cyclic loading. This anisotropy evolves due to various microstructural features. We first use simple models to study how such features result in evolving plastic anisotropy. A subsequent analysis of existing distortional hardening models highlights the difference between stress- and strain-driven models. Following this analysis, we conclude that the stress-driven approach is most suitable and propose an improved stress-driven model. It is thermodynamically consistent and guarantees yield surface convexity. Many distortional hardening models in the literature do not fulfill the latter. In contrast, the model proposed in this work has a convex yield surface independent of its parameter values. Experimental results, considering yield surface evolution after large shear strains, are used to assess the model's performance. We carefully analyze the experiments in the finite strain setting, showing how the numerical results can be compared with the experimental results. The new model fits the experimental results significantly better than its predecessor without introducing additional material parameters.
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| 2. |
- Kaliappan, Jayabal, et al.
(författare)
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Modelling of non-linear switching effects in piezoceramics: a three-dimensional polygonal finite-element-based approach applied to oligo-crystals
- 2015
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Ingår i: Journal of Intelligent Material Systems and Structures. - 1045-389X. ; 26:17, s. 2322-2337
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Tidskriftsartikel (refereegranskat)abstract
- A polygonal finite-element formulation is applied to solve electromechanically coupled inhomogeneous boundary value problems for polycrystalline materials. Each grain is discretised by one single polygonal finite element, which allows the efficient simulation of general boundary value problems which still resolves individual grains in space. The constitutive model proposed for switching in piezoceramics makes use of a volume-fraction-based framework, where the respective volume fractions refer to the respective crystallographic variants and take the interpretation as internal variables. Their evolution is combined with non-linear hardening-type functions which additionally account for grain-size dependencies. The computational model is shown to reproduce typical hysteresis and butterfly curves on the polycrystalline level under complex electromechanical loading conditions. The results are obtained by direct volume-averaging with respect to the discretised domain and are in good qualitative agreement with experimental data. Moreover, grain-size effects, such as an increase in the coercive electric field value with decreasing grain size, are also captured.
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| 3. |
- Kiefer, Bjoern, et al.
(författare)
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A gradient-enhanced damage model coupled to plasticity—multi-surface formulation and algorithmic concepts
- 2018
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Ingår i: International Journal of Damage Mechanics. - : SAGE Publications. - 1056-7895 .- 1530-7921. ; 27:2, s. 253-295
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Tidskriftsartikel (refereegranskat)abstract
- A non-local gradient-enhanced damage-plasticity formulation is proposed, which prevents the loss of well-posedness of the governing field equations in the post-critical damage regime. The non-locality of the formulation then manifests itself in terms of a non-local free energy contribution that penalizes the occurrence of damage gradients. A second penalty term is introduced to force the global damage field to coincide with the internal damage state variable at the Gauss point level. An enforcement of Karush–Kuhn–Tucker conditions on the global level can thus be avoided and classical local damage models may directly be incorporated and equipped with a non-local gradient enhancement. An important part of the present work is to investigate the efficiency and robustness of different algorithmic schemes to locally enforce the Karush–Kuhn–Tucker conditions in the multi-surface damage-plasticity setting. Response simulations for representative inhomogeneous boundary value problems are studied to assess the effectiveness of the gradient enhancement regarding stability and mesh objectivity.
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| 4. |
- Menzel, Andreas, et al.
(författare)
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Continuum Damage Mechanics—Modelling and Simulation
- 2020
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Ingår i: Constitutive Modelling of Solid Continua. - Cham : Springer International Publishing. - 0925-0042 .- 2214-7764. ; 262, s. 231-256
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Bokkapitel (refereegranskat)abstract
- Continuum damage mechanics elaborates the continuum mechanics-based modelling and simulation of mechanical degradation effects. The objective of this contribution is to briefly review different aspects of continuum damage mechanics of solid continua with a focus on general modelling concepts and application to isotropic as well as anisotropic damage approaches on the one hand, and to discuss possible solution strategies in the context of finite element simulations on the other. In particular, viscous regularisation and gradient-enhanced regularisation—as a reduced form of general non-local theories—are considered. Several numerical examples including ductile damage, i.e. the coupling of damage with plasticity related phenomena, are addressed which show the applicability of the particular modelling and simulation frameworks highlighted.
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| 5. |
- Wcisło, Balbina, et al.
(författare)
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Numerical analysis of ellipticity condition for large strain plasticity
- 2018
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Ingår i: Computer Methods in Mechanics, CMM 2017 : Proceedings of the 22nd International Conference on Computer Methods in Mechanics - Proceedings of the 22nd International Conference on Computer Methods in Mechanics. - : Author(s). - 9780735416147 ; 1922
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Konferensbidrag (refereegranskat)abstract
- This paper deals with the numerical investigation of ellipticity of the boundary value problem for isothermal finite strain elasto-plasticity. Ellipticity can be lost when softening occurs. A discontinuity surface then appears in the considered material body and this is associated with the ill-posedness of the boundary value problem. In the paper the condition for ellipticity loss is derived using the deformation gradient and the first Piola-Kirchhoff stress tensor. Next, the obtained condition is implemented and numerically tested within symbolic-numerical tools AceGen and AceFEM using the benchmark of an elongated rectangular plate with imperfection in plane stress and plane strain conditions.
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| 6. |
- Alastrue, V, et al.
(författare)
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Anisotropic micro-sphere-based finite elasticity applied to blood vessel modelling
- 2009
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Ingår i: Journal of the Mechanics and Physics of Solids. - : Elsevier BV. - 1873-4782 .- 0022-5096. ; 57:1, s. 178-203
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Tidskriftsartikel (refereegranskat)abstract
- A fully three-dimensional anisotropic elastic model for vascular tissue modelling is here presented. The underlying strain energy density function is assumed to additively decouple into volumetric and deviatoric contributions. A straightforward isotropic neo-Hooke-type law is used to model the deviatoric response of the ground substance, whereas a micro-structurally or rather micro-sphere-based approach will be employed to model the contribution and distribution of fibres within the biological tissue of interest. Anisotropy was introduced by means of the use of von Mises orientation distribution functions. Two different micro-mechanical approaches -- a, say phenomenological, exponential ansatz and a worm-like-chain-based formulation -- are applied to the micro-fibres and illustratively compared. The passage from micro-structural contributions to the macroscopic response is obtained by a computational homogenisation scheme, namely numerical integration over the surface of the individual micro-spheres. The algorithmic treatment of this integration is discussed in detail for the anisotropic problem at hand, so that several cubatures of the micro-sphere are tested in order to optimise the accuracy at reasonable computational cost. Moreover, the introduced material parameters are identified from simple tension tests on human coronary arterial tissue for the two micro-mechanical models investigated. Both approaches are able to recapture the experimental data. Based on the identified sets of parameters, we first discuss a homogeneous deformation in simple shear to evaluate the models' response at the micro-structural level. Later on, an artery-like two-layered tube subjected to internal pressure is simulated by making use of a non-linear finite element setting. This enables to obtain the micro- and macroscopic responses in an inhomogeneous deformation problem, namely a blood-vessel-representative boundary value problem. The effect of residual stresses is additionally included in the model by means of a multiplicative decomposition of the deformation gradient tensor which turns out to crucially affect the simulation results.
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| 7. |
- Alastrue, V., et al.
(författare)
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On the use of non-linear transformations for the evaluation of anisotropic rotationally symmetric directional integrals. Application to the stress analysis in fibred soft tissues
- 2009
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 1097-0207 .- 0029-5981. ; 79:4, s. 474-504
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Tidskriftsartikel (refereegranskat)abstract
- Microsphere-based constitutive models are a helpful tool in the modelling of materials with a microstructure composed of contributing elements directionally arranged. This is the case, for instance, for fibred soft tissues. In these models, the macroscopic mechanical behaviour is obtained from the integration of the micro-structural contribution of each component (e.g. each fibre) over the surface of an underlying microsphere, which allows incorporating the mechanical features of the micro-constituents to the macroscopic response. The combination of this sort of models and the associated numerical techniques constitutes a powerful modelling tool for which an efficient integration scheme is required. In this regard, the unit sphere discretizations proposed by Bazant and Oh (ZAMM-J Appl Math Mech Z Angew Math Mech 1986; 66(1):37-49) have been used for the integration of the microscopic contributions in isotropic materials. Nevertheless, the inclusion of anisotropy has important implications with regard to the integration scheme, since very fine discretizations are needed to perform the integration accurately, causing the integration process to be very costly. In addition, the storage of internal variables at each integration direction of every integration point is required for constitutive models based on the use of internal variables at the micro-structural level, which renders this approach rather complex and memory demanding. In order to reduce the number of necessary integration directions, several non-linear transformations for the integration of rotationally symmetric functions over the Surface of the unit sphere are here presented. Their accuracy in the integration of the von Mises orientation distribution function is evaluated. Furthermore, a hyperelastic microsphere-based constitutive law for the modelling of soft biological tissues is used in order to check the accuracy and computational efficiency of the proposed transformations within a Finite Element context in inhomogeneous deformation problems. Simulation results show the suitability of the proposed methodology in order to accurately approximate the Value of the integrals within reasonable computational costs. Copyright (C) 2009 John Wiley & Sons, Ltd.
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| 8. |
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| 9. |
- Ask, Anna, et al.
(författare)
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Electromechanics of polyurethane elastomers
- 2011
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Konferensbidrag (refereegranskat)abstract
- It is well known that electroactive polymers (EAP) deform under electric fields. An advantage of EAP is that it may undergo deformations much larger than those capable by electroactive ceramics, however at comparatively low forces. As common for polymers, EAP exhibit time-dependent material behavior, i.e. an electro-viscoelastic effect. In the modeling the deformation as well as the electric potential are introduced as global degrees of freedom, the internal variables accounting for the viscous response are incorporated at the so-called constitutive level. The proposed model is calibrated against experimental data, and a simple coupled finite element example is studied to show the applicability of the finite deformation electro-viscoelastic formulation proposed.
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| 10. |
- Ask, Anna, et al.
(författare)
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Electrostriction in electro-viscoelastic polymers
- 2012
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Ingår i: Mechanics of Materials. - : Elsevier BV. - 0167-6636. ; 50, s. 9-21
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Tidskriftsartikel (refereegranskat)abstract
- Electrostrictive polyurethane (PU) elastomers belong to the class of materials commonly referred to as electroactive polymers (EAP). These materials have their use in a variety of applications, including biomimetics and microrobotics where traditional engineering components may fall short. PU is one of the materials considered for so called dielectric actuators, where the electromechanical response is generally due to Coulomb forces on the actuator electrodes, giving rise to a compressive pressure and thereby large deformations of the polymer. On the other hand, for more moderate electric fields, which may be more attractive in certain applications, a large part of the electroactive response for PU elastomers is due to inherent electrostriction. The latter phenomena is the focus of this work. As is common in elastomers, PU elastomers are viscoelastic. A coupled electro-viscoelastic phenomenological constitutive model for electrostrictive PU is proposed and fitted to experimental data available in the literature. The possibility of performing simulations of EAP is of interest as the number of applications grow. Considering this, the computational model is embedded in a coupled finite element formulation and, based on this, representative simulations of inhomogeneous boundary value problems are presented.
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