| 1. |
- Svendsen, Bob, et al.
(författare)
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On constitutive and configurational aspects of models for gradient continua with microstructure
- 2009
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Ingår i: ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik. - : Wiley. - 0044-2267. ; 89:8, s. 687-697
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Tidskriftsartikel (refereegranskat)abstract
- The purpose of this work is the investigation of some constitutive and configurational aspects of phenomenological model formulations for a class of materials with history-dependent gradient microstructure. The assumption that the behavior of a material point is affected by history-dependent processes in a finite neighbor of this point yields an extended continuum characterized by non-simple material behavior and by additional degrees-of-freedom. This includes both standard micromorphic materials as well as inelastic gradient materials as special cases. As in the case of simple materials, the corresponding constitutive relations are subject to restrictions imposed by material frame-indifference and material symmetry. In the latter case, both direct and differential restrictions are obtained in the case of assuming that the free energy density is an isotropic function of its arguments. In addtion, the concept of material isomorphism is shown to extend to inelastic gradient continua, resulting in a gradient generalization of the well-known elastoplastic multiplicative decomposition of the deformation gradient. Finally, we examine the consequences of gradient extension for the formulation of configurational field and balance relations, and in particular for the Eshelby stress. This is carried out with the help of an incremental stress potential formulation as based on a continuum thermodynamic approach to the coupled field problem involved.
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| 2. |
- Bartel, Thorsten, et al.
(författare)
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Enhanced Micromechanical Modelling of Martensitic Phase-Transitions Considering Plastic Deformations
- 2009
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Ingår i: [Host publication title missing]. - Les Ulis, France : EDP Sciences. ; , s. 03002-03002
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Konferensbidrag (refereegranskat)abstract
- The purpose of this contribution is the presentation of a micromechanical model for martensitic phase transformations which can be applied to a wide range of materials like shape memory alloys (SMA), TRIP-steels (TRansformation Induced Plasticity) and piezoceramics. One of the key-features of the model is the consideration of several martensitic variants in addition to the parent phase austenite based on crystallographic theories. According to a specifically chosen microstructure, a fluctuation field is superimposed to the local, homogeneous deformations. These fluctuations implicate several additional internal variables which are partially supposed to minimize the microscopic energy density. Furthermore, the variables assumed to be ’dissipative’, like the volume fractions of martensite, are determined by evolution laws. Another focal point of our work is the combination of martensitic phase transformations and plasticity. As a first step towards a complete micromechanical description of this problem, we make use of a phenomenological approach for plasticity here. The results of our computations reveal significant differences of the single-crystalline behavior to the well-known macroscopic material response, which is indeed verified by experimental studies.
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| 3. |
- Dusthakar, Dinesh K., et al.
(författare)
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A laminate-based modelling approach for rate-dependent switching in ferroelectric materials
- 2015
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Ingår i: PAMM - Proceedings in Applied Mathematics and Mechanics. - : Wiley. - 1617-7061. ; 15, s. 3-6
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Tidskriftsartikel (refereegranskat)abstract
- This contribution focuses on the sequential laminate-based modelling approach for the numerical simulation of the complex electromechanical material behaviour of ferroelectric single crystals. The construction of engineered domain configurations by using the method of sequential lamination in order to study the domain evolution and polarisation switching in ferroelectric single crystals has recently been carried out in the works of [1–4]. By fulfilling the kinematic and polarisation compatibility conditions between the domain structures in a crystal, the proposed laminate-based formulation is governed by an energy-enthalpy function and by a dissipation potential. The mixed energy-enthalpy, written in terms of the total strains, electric field and a set of internal variables, here the multi-rank laminate volume fractions, governs the dissipative electromechanical response of the ferroelectric crystal, whereas the rate-dependent dissipation potential formulated in terms of the flux of the internal variables describes the time-dependent evolution of the multi-rank laminate volume fractions, subjected to inequality constraints. The model reproduces experimentally observed hysteresis and butterfly curves, characteristic for single crystal ferroelectric materials, when subjected to homogeneous electromechanical loading conditions.
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| 4. |
- Dusthakar, Dinesh Kumar, et al.
(författare)
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Comparison of phenomenological and laminate-based models for rate-dependent switching in ferroelectric continua
- 2015
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Ingår i: GAMM-Mitteilungen. - : Wiley. - 1522-2608 .- 0936-7195. ; 38:1, s. 147-170
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Tidskriftsartikel (refereegranskat)abstract
- The purpose of the current work is the comparison of a phenomenological and a laminate-based model for rate-dependent switching in ferroelectric single crystals. To this end, the phenomenological model formulation of [1] is considered. In this model, the polarization vector is treated as an internal variable. The evolution of the polarization determines the remanent strain; dependence of energy storage on its direction results in generally transverse isotropic material behavior. This is compared here with a laminate-based model in which the volume fractions of ferroelectric variants are treated as internal variables. The evolution of these volume fractions determines in turn the remanent strain and polarization as volume averages of corresponding ferroelectric variant quantities. Besides a comparison of the respective model formulations, the phenomenological and laminate models are compared in the context of numerical simulation examples. It turns out that both modeling frameworks nicely recapture the underlying dissipative and rate-dependent effects, which is represented by means of simulated butterfly curves and hysteresis loops under homogeneous loading conditions as well as by finite element simulations.
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| 5. |
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| 6. |
- Menzel, Andreas, et al.
(författare)
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Two configurational approaches on the modelling of continuum dislocation inelasticity
- 2009
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Ingår i: International Journal of Structural Changes in Solids. - 2163-8160. ; 1:1, s. 61-72
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Tidskriftsartikel (refereegranskat)abstract
- The main focus of this contribution consists in the elaboration of a continuum modelling approach accounting for dislocation-based quantities. Related deformation dependent history-variables are attached to individual material points and, moreover, are extended by means of gradients thereof so that so-called weak non-localities are captured. These gradients of internal variables may be further specified and in this regard are here reduced to particular representations of dislocation density tensors. While in this work we will make use of the concept of a material isomorphism—similarly present in the kinematic framework denoted as multiplicative decomposition—the approach itself can also be generalised, for instance with application to micromorphic continua. Apart from the non-simple kinematic framework, special emphasis is placed on the configurational mechanics perspective of the problem at hand. First, a variational strategy is discussed in detail, whereby the underlying stored energy density is assumed as an isotropic function in terms of its arguments. Later on, the configurational framework derived is compared with the configurational balance of linear momentum as based on straightforward transformation relations of its standard spatial representation. As a result, similar forms of the configurational Eshelby stresses are obtained for the two different approaches, and the related volume forces additionally incorporate contributions related to the material’s hereogeneities and inhomogeneities.
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