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- Bartel, Thorsten, et al.
(author)
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A data-driven approach for plasticity using history surrogates : Theory and application in the context of truss structures
- 2023
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In: Computer Methods in Applied Mechanics and Engineering. - 0045-7825. ; 414
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Journal article (peer-reviewed)abstract
- Data-driven methods and algorithms show immense potential for future advancements in the modeling and simulation of complex mechanical systems. However, in order to actually exploit this potential, the methods must be extended to consider inelastic and path-dependent material behavior—a step that appears more complex than in conventional material modeling, where this can be achieved with the help of additional, mostly internal, history variables. The effect of such history variables must thereby be transferred to the data-driven framework. This is achieved in the present paper by defining an appropriate history surrogate as well as a so-called propagator. The history surrogate contains tangible quantities that represent the backward path–uniquely in the ideal case–and enrich the conventional database entries of matching pairs of stresses and strains. The propagator defines the update of the history surrogate from one discrete time step to another. As a major advantage, the newly developed method retains the structures of the data-driven algorithm for elastic material behavior and therefore allows a rather straightforward extension of preexisting program codes. Thus, for instance, heterogeneous problems in which purely elastic and elastoplastic materials are present can be solved without further significant coding effort. Furthermore, several material classes covering different inelastic phenomena such as plasticity with isotropic and kinematic hardening as well as phase transformations in shape memory alloys can be considered in our framework.
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| 3. |
- Bartel, Thorsten, et al.
(author)
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A thermodynamically consistent modelling framework for strongly time-dependent bainitic phase transitions
- 2021
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In: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683. ; 232
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Journal article (peer-reviewed)abstract
- In this work, a thermodynamically consistent constitutive framework is introduced that is capable of reproducing the significant time-dependent behaviour of austenite-to-bainite phase transformations. In particular, the aim is to incorporate the effect of these diffusion-controlled processes by plasticity-like evolution equations instead of incorporating related global diffusion equations. To this end, a variational principle for inelastic solids is adopted and enhanced by an additional term. This term essentially contributes to the evolution equations for the phase volume fractions of several crystallography-based bainite variants. Due to the specific modifications, special attention has to be paid with respect to the fulfilment of thermodynamical consistency, which can be shown to be unconditionally satisfied for the newly proposed modelling framework. The phase transformation model itself is based on the convexification of a multi-well energy density landscape in order to provide the effective material response for possible phase mixtures. Several material parameters are determined via parameter identification based on available experimental results for 51CrV4, which also allow the quantitative evaluation of the predicted results.
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| 4. |
- Bartel, Thorsten, et al.
(author)
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An energy-relaxation-based framework for the modeling of magnetic shape memory alloys—Simulation of three-dimensional effects under homogeneous loading conditions
- 2021
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In: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683. ; 208-209, s. 221-234
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Journal article (peer-reviewed)abstract
- It is known from experimental findings that three-dimensional effects can have a strong influence on magnetic shape memory behavior. Such phenomena are, however, often neglected in MSMA constitutive models, as they only become meaningful under complex loading conditions. The extensions of our original modeling framework, cf. Bartel et al. (2020), to include 3D-effects is threefold: (i) vector-valued microstructural variables are now elements in R3, i.e. no longer parameterizable in polar coordinates, (ii) a third tetragonal martensite variant may form/vanish by switching from/back into both other variants, and (iii) a more general and robust algorithmic treatment is necessary. The latter includes the implementation of a staggered Augmented Lagrangian scheme to handle the now much larger and numerically more advanced sets of equality and inequality constraints. In this context, two extended model formulations are presented. The first considers a first-order, two-variant laminate approach (rank-one convexification), in which domain magnetizations, interface orientations etc. are now three-dimensional vectors. The second model is based on a convexification approach, for which the incorporation of the third martensitic variant is quite natural. Numerical examples are investigated to test the generalized modeling framework. Firstly, it is confirmed that both extended models recover the solution of the previously established two-dimensional model for a simple loading case. Secondly, response predictions for more complex loading scenarios (non-proportional bi-axial stresses, orthogonal magnetic field), motivated by experiments, are investigated. It is found that capturing the formation, elimination and mutual interaction of all martensitic variants as well as general three-dimensional magnetization vector orientations is of key importance under these conditions. The extended convexification model and modified algorithmic formulation are shown to reliably handle even such general cases.
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| 5. |
- Bartel, Thorsten, et al.
(author)
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An energy-relaxation-based framework for the modelling of magnetic shape memory alloys—Simulation of key response features under homogeneous loading conditions
- 2020
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In: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683. ; 182-183, s. 162-178
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Journal article (peer-reviewed)abstract
- In this contribution we present a constitutive modelling framework for magnetic shape memory alloys (MSMA) that builds on a global variational principle. The approach relies on concepts of energy relaxation and generalised notions of convexity to compute effective energy hulls to the non-convex energy landscape associated with the underlying multi-phase solid, from which the prediction of microstructure evolution results. In this sense it fundamentally distinguishes itself from MSMA models that essentially follow phenomenological concepts of classical plasticity (Kiefer and Lagoudas, 2005; 2009). The microstructure is not spatially resolved, but micro-scale quantities are taken into account in an effective sense by additional state variables—such as volume fractions or interface orientations—and appropriate mixture rules. The model allows all mechanisms central to MSMA behaviour—i.e. variant switching, magnetisation rotation away from easy axes, and magnetic domain evolution—to occur simultaneously. The authors have previously been able to demonstrate that such a modelling approach can quantitatively capture the key characteristics of single-crystalline MSMA response under standard loading scenarios (Kiefer et al., 2015). The modelling framework presented here is now further able to predict much more general response features, such as variant switching diagrams, magnetic field-biased pseudo-elasticity and the influence of specimen shape anisotropy. Moreover, the global variational framework is formulated in a manner that lends itself to finite element implementation. In this work, however, numerical examples are considered in which the nonlocal nature of the demagnetisation field is taken into account in an approximate sense through appropriate shape factors.
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| 6. |
- Bartel, Thorsten, et al.
(author)
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Enhanced Micromechanical Modelling of Martensitic Phase-Transitions Considering Plastic Deformations
- 2009
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In: [Host publication title missing]. - Les Ulis, France : EDP Sciences. ; , s. 03002-03002
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Conference paper (peer-reviewed)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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| 7. |
- Bartel, Thorsten, et al.
(author)
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Partially relaxed energy potentials for the modelling of microstructures - application to shape memory alloys
- 2012
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In: GAMM-Mitteilungen. - : Wiley. - 1522-2608 .- 0936-7195. ; 35:1, s. 57-72
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Journal article (peer-reviewed)abstract
- Energy relaxation is well-established by several researchers – especially in the field of the modelling of solid-solid phase transformations. Nevertheless, critics still counter this concept by considering it as a purely mathematical tool with poor physical significance. In this contribution we aim at emphasising the significance of energy relaxation methods for the modelling of dissipative solids and especially microstructure formation and its further evolution. In particular, we shall point out aspects and advantages of this concept which are not straight forward to achieve within alternative schemes
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