Institut für Mechanik

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Characterisation of damage by means of electrical measurements: numerical predictions
(2023-08-24) Güzel, Dilek; Kaiser, Tobias; Lücker, Lukas; Baak, Nikolas; Walther, Frank; Menzel, Andreas
Understanding damage mechanisms and quantifying damage is important in order to optimise structures and to increase their reliability. To achieve this goal, experimental- and simulation-based techniques are to be combined. Different methods exist for the analysis of damage phenomena such as fracture mechanics, phase field models, cohesive zone formulations and continuum damage modelling. Assuming a typical [1 – d]-type damage formulation, the governing equations of continua that account for gradient-enhanced ductile damage under mechanical and electrical loads are derived. The mechanical and electrical sub-problems give rise to the local form of the balance equation of linear momentum, the micromorphic balance relation and the continuity equation for the electric charge, respectively. Experimental investigations indicate that changes in electrical conductivity arise due to the evolution of the underlying microstructure, for example, of cracks and dislocations. Therefore, motivated by deformation-induced property changes, the effective electrical conductivity is assumed to be a function of the damage variable. This eventually allows the prediction of experimentally recorded changes in the electrical resistance due to mechanically-induced damage processes. Interpreting the resistivity as a fingerprint of the material microstructure, the simulation approach proposed in the present work contributes to the development of non-destructive electrical-resistance-based characterisation methods. To demonstrate the applicability of the proposed framework, different representative simulations are studied.
Isogeometric analysis of anisotropic mechanical and electromechanical higher-gradient continua
(2024) Witt, Carina Victoria; Menzel, Andreas; McBride, Andrew
This thesis deals with the modelling and numerical simulation of anisotropic materials whose mechanical, respectively electromechanical behaviour is significantly influenced by their microstructure. From a modelling point of view, generalised continuum approaches are adopted in order to account for these microstructural effects and isogeometric analysis is employed for their numerical treatment. Accordingly, isogeometric analysis is addressed in the first part of this work with special focus on the application to gradient continua. In the second part, a gradient elasticity approach for the modelling and simulation of fibre-reinforced composites is investigated in which the fibre bending stiffness is accounted for by incorporation of the gradient of the fibre vector in the underlying stored energy density function. An isogeometric analysis framework is established for a small strain as well as finite strain setting. In the last part of this thesis, a modelling approach for the gradient-based electromechanical phenomenon flexoelectricity is proposed for the simulation of flexoelectricity-induced bone remodelling processes and microcrack healing in cortical bone. Accordingly, chemo-electro-mechanical coupling is considered and a computational framework which captures flexoelectricity together with anisotropic cell diffusion processes and surface growth is established.
Rate-independent gradient-enhanced crystal plasticity theory—robust algorithmic formulations based on incremental energy minimization
(2023-12-16) Mosler, Jörn; Fohrmeister, Volker
Numerically robust algorithmic formulations suitable for rate-independent crystal plasticity are presented. They cover classic local models as well as gradient-enhanced theories in which the gradients of the plastic slips are incorporated by means of the micromorphic approach. The elaborated algorithmic formulations rely on the underlying variational structure of (associative) crystal plasticity. To be more precise and in line with socalled variational constitutive updates or incremental energy minimization principles, an incrementally defined energy derived from the underlying time-continuous constitutive model represents the starting point of the novel numerically robust algorithmic formulations. This incrementally defined potential allows to compute all variables jointly as minimizers of this energy. While such discrete variational constitutive updates are not new in general, they are considered here in order to employ powerful techniques from non-linear constrained optimization theory in order to compute robustly the aforementioned minimizers. The analyzed prototype models are based on (1) nonlinear complementarity problem (NCP) functions as well as on (2) the augmented Lagrangian formulation. Numerical experiments show the numerical robustness of the resulting algorithmic formulations. Furthermore, it is shown that the novel algorithmic ideas can also be integrated into classic, non-variational, return-mapping schemes.
A large strain thermoplasticity model including recovery, recrystallisation and grain size effects
(2023-10-16) Böddecker, Merlin; Menzel, Andreas
In manufacturing, thermomechanical processes such as static annealing and hot working are commonly used to tailor the microstructure of metals to achieve favourable macroscopic material properties that meet specific application requirements. To improve sequential manufacturing processes and to accurately predict the microstructural changes of the material along the process chain, physically motivated constitutive models are required that simultaneously account for the effects of recovery and recrystallisation, as well as grain size dependencies. To this end, Cho et al. [Int. J. Plasticity 112, 123–157 (2019)] proposed a macroscopic hypo-elasticity based large strain thermoplasticity model that aims at the unification of the effects of static and dynamic recovery and recrystallisation, as well as grain growth and refinement. In the present contribution, the hypo-elasticity based large strain recrystallisation formulation proposed by Cho et al. is transferred to a hyper-elasticity based large strain thermoplasticity framework to overcome the limitations typically accompanied with hypo-elasticity based formulations. For this purpose, an isotropic temperature dependent hyper-elastic Hencky type formulation defined in logarithmic strains is combined with a temperature dependent von Mises yield criterion. The recrystallisation modelling approach by Cho et al. is adopted, assuming a non-associated temperature dependent proportional hardening rate in the form of an Armstrong-Frederick type hardening minus recovery format, wherein the proportional hardening related internal variable is interpreted as a measure of dislocation density. It is shown that the hyper-elasticity based format results in a thermodynamical consistency condition that effectively constrains the physically motivated evolutions of recrystallised volume fraction and average grain size. To investigate the capability of the model to predict the material response of unified recrystallisation thermodynamically consistently, representative thermomechanical sequential loading conditions including static annealing and hot working are studied.
Thermomechanical modelling and simulation of laser powder bed fusion processes
(2023) Noll, Isabelle Viktoria; Menzel, Andreas; Mergheim, Julia
Die vorliegende Arbeit behandelt einen neuartigen mikromechanisch motivierten Rahmen zur Modellierung und Simulation von Laser-Pulver-Bett-Fusion (LPBF) Prozessen. LPBF Verfahren gehören zur additiven Fertigung, welche die schichtweise Herstellung von Bauteilen ermöglicht. (Metallische) Partikel einer Pulverschicht werden durch einen Laserstrahl selektiv geschmolzen, um ein Bauteil zu fertigen. Dadurch ergeben sich innovative Möglichkeiten hinsichtlich Design, Struktur, Materialkombinationen und maßgeschneiderten Teilen. Aufgrund des hohen Temperatureintrags treten komplexe thermische, mechanische und metallurgische Phänomene auf, darunter auch Phasenumwandlungen von Pulver über geschmolzenes zu wieder erstarrtem Material. Diese Hochtemperaturzyklen mit schnellem Aufheizen und Abkühlen verursachen verschiedene Defekte, wie zum Beispiel Hohlräume, Verzug und Eigenspannungen. Um die verschiedenen Fehler eines mit LPBF hergestellten Werkstücks besser vorhersagen zu können, sind neue Ansätze erforderlich. Der erste Schwerpunkt dieser Arbeit liegt auf der Entwicklung eines physikalisch motivierten Materialmodells, das thermodynamisch konsistent ist und auf der Minimierung der freien Energiedichte basiert. Dieses Modell wird im kleinen Maßstab einer einzelnen Schmelzspur angewendet. Im zweiten Teil der Arbeit wird ein Multiskalen-Ansatz entwickelt, der das Phasentransformationsmodell mit der Methode der inhärenten Dehnung kombiniert, um ein vollständiges Teil simulieren zu können. Dieses stellt im Hinblick auf physikalische Genauigkeit und Rechenzeit einen vernünftigen Kompromiss dar. Hierfür wird ein vollständig thermomechanisch gekoppelter Framework verwendet, welcher mithilfe des kommerziellen Finite Elemente Programms Abaqus gelöst wird. Die Simulationen werden auf die α-β- Titanaluminiumlegierung Ti6Al4V angewendet, die je nach Abkühlgeschwindigkeit eine unterschiedliche Zusammensetzung der Mikrostruktur entwickelt. Daher wird im letzten Teil der Arbeit ein Festkörper-Phasentransformationsansatz mit einer neuartigen Dissipationsfunktion vorgestellt, um das entsprechende kontinuierliche Zeit-Temperatur-Umwandlungsschaubild modellieren zu können. Das thermodynamisch und physikalisch fundierte Modell wird anschließend auf LPBFTemperaturprofile auf lokaler Ebene angewendet.
On the determination of thermal boundary conditions for parameter identifications of thermo-mechanically coupled material models
(2022-05-24) Rose, Lars; Menzel, Andreas
Identifiability and sensitivity of thermal boundary coefficients identified alongside thermal material parameters by means of full field measurements during a simple tension test are shown empirically using a simple tension test with self heating as a proof of concept. The identification is started for 10 different initial guesses, all of which converge toward the same optimum. The solution appears to be locally unique and parameters therefore independent, but a comparison against a reference solution indicates high correlation between three model parameters and the prescribed external temperatures required to model heat exchange with either air or clamping jaws. This sensitivity is further analyzed by rerunning the identification with different prescribed external temperatures and by comparing the obtained optimal parameter values. Although the model parameters are independent, optimal values for heat conduction and the heat transfer coefficients are highly correlated as well as sensitive with respect to a change, respectively, measurement error of the external temperatures. A precise fit on the basis of a simple tension test therefore requires precise measurements and a suitable material model which is able to accurately predict dissipated energy.
Parameter identification approaches with application to different classes of materials
(2023) Schulte, Robin; Menzel, Andreas; Kiefer, Björn
Die vorliegende Arbeit befasst sich mit verschiedenen Strategien der Parameteridentifikation bezüglich der multi-objektiven Optimierung unter Berücksichtigung von integralen Größen und Feldgrößen, um effizient Parameter von komplexen Materialmodellen zu identifizieren, wie beispielsweise Gradienten-erweiterte Schädigungsmodelle. Außerdem wird eine hybride Strategie entwickelt, um die Problematik der Bestimmung von adequaten Startwerten zu überwinden. Zu diesem Zweck wird ein künstliches neuronales Netz mit den simulierten Materialverhalten von diversen Parameterkombinationen trainiert. Anschließend wird die experimentell gemessene Materialantwort in das Netz eingegeben um eine Vorhersage der Parameter zu erhalten, die im Anschluss als qualitativ hochwertiger Startwert für eine multi-objektive Parameteridentifikation verwendet wird. In dieser Arbeit werden die hybride und die weiteren Strategien untersucht unter der Verwendung von verschiedener komplexer Materialmodelle und diverser Gruppen von Materialien. Zusätzlich wird ein Gradienten-erweitertes, mit Viskoelastizität unter finiter Dehnung gekoppeltes Schädigungsmodel entwickelt um effizient Schädigungseffekte in ratenabhängigen Materialien abzudecken. Des Weiteren wird im Kontext eines Laminat-basierenden Modells für ferroelektrische Materialien eine numerische Untersuchung bezüglich numerisch effizienter Fischer-Burmeister Ansätze durchgeführt, um die häufig auftretenden Karush-Kuhn-Tucker Konditionen zu lösen.
Multiscale multiphysics material modelling
(2023) Kaiser, Tobias
Die vorliegende Arbeit befasst sich mit der skalenübergreifenden Modellierung von Materialien und ist in fünf Abschnitte gegliedert. Der erste Abschnitt beschäftigt sich mit der Entwicklung von computergestützten Mehrskalenansätzen für elektro-mechanisch gekoppelte Probleme elektrisch leitfähiger Materialien bei infinitesimalen und finiten Deformationen. Die Anwendbarkeit dieser Verfahren wird im zweiten Abschnitt unter Berücksichtigung experimenteller Ergebnisse untersucht. Angesichts der Komplexität realer Mikrostrukturen liegt der Schwerpunkt im dritten Abschnitt auf der Entwicklung einer Grenzschichtformulierung, um den Einfluss von materiellen Grenzflächen und von Versagensprozessen in diesen auf die effektiven elektrischen Eigenschaften der betrachteten Mikrostruktur in Simulationen abbilden zu können. Die signifikanten Rechenzeit- und Speicheranforderungen, die insbesondere bei Mehrskalenmethoden für gekoppelte Probleme vorliegen, motivieren die Behandlung effizienter Lösungsverfahren unter besonderer Berücksichtigung wavelet- und FFT-basierter Ansätze im vierten Abschnitt der vorliegenden Arbeit. Im abschließenden fünften Abschnitt wird die Spannungs-Gradienten-Theorie als alternativer Ansatz zur Berücksichtigung mikrostruktureller Eigenschaften in makroskopischen Simulationen betrachtet, wobei insbesondere der Einfluss von spannungsfreien Randschichten und damit verbundene Größeneffekte untersucht werden.
Optimizing artificial neural networks for mechanical problems by physics-based Rao-Blackwellization: example of a hyperelastic microsphere model
(2023-03-24) Geuken, Gian-Luca; Mosler, Jörn; Kurzeja, Patrick
The Rao-Blackwell scheme provides an algorithm on how to implement sufficient information into statistical models and is adopted here to deterministic material modeling. Even crude initial predictions are improved significantly by Rao-Blackwellization, which is proven by an error inequality. This is first illustrated by an analytical example of hyperelasticity utilizing knowledge on principal stretches. Rao-Blackwellization improves a 1-d uniaxial strain-energy relation into a 3-d relation that resembles the classical micro-sphere approach. The presented scheme is moreover ideal for data-based approaches, because it supplements existing predictions with additional physical information. A second example hence illustrates the application of Rao-Blackwellization to an artificial neural network to improve its prediction on load paths, which were absent in the original training process.
Application of the Coupled Eulerian Lagrangian method to the prediction of single-grain cutting forces in grinding
(2023-03-24) Furlan, Tim; Tsagkir Dereli, Tountzer; Schmidt, Nils; Biermann, Dirk; Menzel, Andreas
Continuous technological advancements in the field of grinding technology and improved grinding tools have contributed to the development of high performance grinding processes. One example of such a process is internal traverse grinding (ITG) with electroplated cBN grinding wheels, where the tool consists of a conical roughing zone and a cylindrical finishing zone. Since the tool is fed in axial direction into a revolving workpiece, spindle deflections induced by varying process forces can lead to contour errors along the bore. Numerical simulations are a valuable tool to overcome the challenges associated with such high performance processes. Whenever spindle deflections need to be considered, accurate prediction of the process forces is paramount. Finite Element (FE) simulations have been widely used for the prediction of forces in cutting processes such as turning and milling, where only a small number of active cutting edges is considered, and where the geometry of these cutting edges is clearly defined. Grinding tools, on the other hand, contain a large number of grains with varying geometric characteristics. We recently proposed a multi-scale simulation system for the simulation of ITG processes, where a geometric kinematic grinding simulation, based on a database of digitalised grains of a real grinding wheel, was used to determine the grain engagements [1]. The process forces were obtained from summation of the contributions of all active grains at any given time, based on a force model on the individual grain level. The force model takes the material removal rate and an approximation of the rake angle into account, and was calibrated via finite element simulations. In recent years, the Coupled Eulerian Lagrangian method (CEL), which is part of the commercial finite element software Abaqus, has been applied to simulate various cutting processes. No remeshing is necessary in this framework, and separation of chips from the workpiece can be modelled without element deletion. The application of CEL to the simulation of single grain cutting is therefore a promising approach to further improve the force model included in the process simulation of ITG. In this work, the kinematics of ITG are incorporated into a single grain cutting simulation, and the suitability of the CEL method for the problem is evaluated with a focus on the chip formation, separation and self-contact between the chip and the workpiece.
Aspects of accuracy and uniqueness of solutions in data-driven mechanics
(2023-03-24) Bartel, Thorsten; Harnisch, Marius; Menzel, Andreas; Schweizer, Ben
Data-driven methods provide great potential for future applications in engineering, for example in terms of more efficient simulations. Conventional material models and the associated constitutive equations are substituted by a minimization of a distance between so-called material and mechanical states, which, however, leads to non-unique solutions. The aim of this paper is to analyze the influence of the chosen initial values on the accuracy of the obtained results. Furthermore, Mixed Integer Quadratic Programming (MIQP) is implemented and its applicability to data-driven mechanics is assessed.
How regularization concepts interfere with (quasi-)brittle damage: a comparison based on a unified variational framework
(2022-09-05) Langenfeld, K.; Kurzeja, P.; Mosler, J.
Three regularization concepts are assessed regarding their variational structure and interference with the predicted physics of (quasi-)brittle damage: the fracture energy concept, viscous regularization and micromorphic regularization. They are first introduced in a unified variational framework, depicting how they distinctively evolve from incremental energy minimization. The analysis of a certain time interval of a one-dimensional example is used to show how viscous and micromorphic regularization retains well-posedness within the softening regime. By way of contrast, the fracture energy concept is characterized by ill-posedness—as known from previous non-variational analyses. Numerical examples finally demonstrate the limitations and capabilities of each concept. The ill-posed local fracture energy concept leads by its design to a spatially constant fracture energy—in line with Griffith’s theory. The viscous regularization, in turn, yields a well-posed problem but artificial viscosity can add a bias to unloading and fracture thickness. Furthermore, and even more important, a viscous regularization does not predict a spatially constant fracture energy due to locally heterogeneous loading rates. The well-posed micromorphic regularization is in line with the underlying physics and does not show this undesired dependency. However, it requires the largest numerical efforts, since it is based on a coupled two-field formulation.
An adaptive wavelet-based collocation method for solving multiscale problems in continuum mechanics
(2022-09-27) Kaiser, Tobias; Remmers, Joris J. C.; Geers, Marc G. D.
Computational multiscale methods are highly sophisticated numerical approaches to predict the constitutive response of heterogeneous materials from their underlying microstructures. However, the quality of the prediction intrinsically relies on an accurate representation of the microscale morphology and its individual constituents, which makes these formulations computationally demanding. Against this background, the applicability of an adaptive wavelet-based collocation approach is studied in this contribution. It is shown that the Hill–Mandel energy equivalence condition can naturally be accounted for in the wavelet basis, (discrete) wavelet-based scale-bridging relations are derived, and a wavelet-based mapping algorithm for internal variables is proposed. The characteristic properties of the formulation are then discussed by an in-depth analysis of elementary one-dimensional problems in multiscale mechanics. In particular, the microscale fields and their macroscopic analogues are studied for microstructures that feature material interfaces and material interphases. Analytical solutions are provided to assess the accuracy of the simulation results.
Continuum modeling of brittle and ductile damage: theory and computational frameworks
(2023) Langenfeld, Kai; Mosler, Jörn; Balzani, Daniel
Das Ziel der vorliegenden Arbeit ist es im Rahmen des Sonderforschungsbereichs TRR188 einen Modellierungsansatz auf kontinuumsmechanischer Basis zur Bewertung von Schädigungszuständen zu entwickeln. Die Bewertung der Strukturen erfolgt mittels Finite-Elemente-Simulationen. Dabei kann der zugrundeliegende Schädigungsmechanismus in Abhängigkeit der aufgeprägten Lastamplitude duktilen (im Kurzzeitfestigkeitsbereich) oder spröden (im Langzeitfestigkeitsbereich) Ursprungs sein. Aus diesem Grund werden in der vorliegenden Arbeit sowohl kontinuumsmechanische Materialmodelle für spröde als auch für duktile Sch ̈adigung ausgearbeitet. Bei der Modellierung der spröden Schädigung ist ein Schwerpunkt und im Kontext der Finite-Elemente-Methode die Berechnung netzunabhängiger und somit objektiver Simulationsergebnisse. Beim Vergleich verschiedener Regularisierungsverfahren wird eine Krümmungsabhängigkeit gradientenbasierter Modelle aufgezeigt, die sowohl analytisch als auch numerisch untersucht wird. Anschließend werden zwei Methoden zur gezielten Kontrolle dieser Krümmungseffekte erarbeitet. Für eine objektive Modellierung anisotroper, duktiler Schädigungsevolution wird ein aus der Literatur bekanntes, lokales Materialmodell mikromorph gradientenerweitert. Da der Standardansatz der mikromorphen Regularisierung sich als ungeeignet erweist, wird eine Erweiterung vorgeschlagen. Anschließend wird das Modell auf Basis experimenteller Daten erweitert und kalibriert. Diese Modellerweiterungen beinhalten überlagerte lineare und nicht-lineare isotrope und kinematische Verfestigung, thermomechanische Kopplungseffekte sowie ein neues Kriterium zur Vorhersage der Schädigungsinitiierung unter zyklischer Belastung.
Electrical and mechanical behaviour of metal thin films with deformation-induced cracks predicted by computational homogenisation
(2021-10-05) Kaiser, Tobias; Cordill, Megan J.; Kirchlechner, Christoph; Menzel, Andreas
Motivated by advances in flexible electronic technologies and by the endeavour to develop non-destructive testing methods, this article analyses the capability of computational multiscale formulations to predict the influence of microscale cracks on effective macroscopic electrical and mechanical material properties. To this end, thin metal films under mechanical load are experimentally analysed by using in-situ confocal laser scanning microscopy (CLSM) and in-situ four point probe resistance measurements. Image processing techniques are then used to generate representative volume elements from the laser intensity images. These discrete representations of the crack pattern at the microscale serve as the basis for the calculation of effective macroscopic electrical conductivity and mechanical stiffness tensors by means of computational homogenisation approaches. A comparison of simulation results with experimental electrical resistance measurements and a detailed study of fundamental numerical properties demonstrates the applicability of the proposed approach. In particular, the (numerical) errors that are induced by the representative volume element size and by the finite element discretisation are studied, and the influence of the filter that is used in the generation process of the representative volume element is analysed.
A finite deformation electro-mechanically coupled computational multiscale formulation for electrical conductors
(2021-08-05) Kaiser, Tobias; Menzel, Andreas
Motivated by the influence of deformation-induced microcracks on the effective electrical properties at the macroscale, an electro-mechanically coupled computational multiscale formulation for electrical conductors is proposed. The formulation accounts for finite deformation processes and is a direct extension of the fundamental theoretical developments presented by Kaiser and Menzel (Arch Appl Mech 91:1509–1526, 2021) who assume a geometrically linearised setting. More specifically speaking, averaging theorems for the electric field quantities are proposed and boundary conditions that a priori fulfil the extended Hill–Mandel condition of the electro-mechanically coupled problem are discussed. A study of representative boundary value problems in two- and three-dimensional settings eventually shows the applicability of the proposed formulation and reveals the severe influence of microscale deformation processes on the effective electrical properties at the macroscale.
A finite deformation isogeometric finite element approach to fibre-reinforced composites with fibre bending stiffness
(2021-05-28) Witt, Carina; Kaiser, Tobias; Menzel, Andreas
It is a common technique in many fields of engineering to reinforce materials with certain types of fibres in order to enhance the mechanical properties of the overall material. Specific simulation methods help to predict the behaviour of these composites in advance. In this regard, a widely established approach is the incorporation of the fibre direction vector as an additional argument of the energy function in order to capture the specific material properties in the fibre direction. While this model represents the transverse isotropy of a material, it cannot capture effects that result from a bending of the fibres and does not include any length scale that might allow the simulation of size effects. In this contribution, an enhanced approach is considered which relies on the introduction of higher-gradient contributions of the deformation map in the stored energy density function and which eventually allows accounting for fibre bending stiffness in simulations. The respective gradient fields are approximated by NURBS basis functions within an isogeometric finite element framework by taking advantage of their characteristic continuity properties. The isogeometric finite element approach that is presented in this contribution for fibre-reinforced composites with fibre bending stiffness accounts for finite deformations. It is shown that the proposed method is in accordance with semi-analytical solutions for a representative boundary value problem. In an additional example it is observed that the initial fibre orientation and the particular bending stiffness of the fibres influence the deformation as well as the stress response of the material.
On the incorporation of curvature effects into the isogeometric analysis of fibre-reinforced solids
(2021-12-14) Witt, Carina; Kaiser, Tobias; Menzel, Andreas
In the context of engineering on the micro- and nanoscale, size-dependency is an important characteristic of material behaviour. In order to avoid complex experiments and predict size effects in simulations instead, classic continuum approaches are extended by the introduction of a length scale, e.g. through the consideration of gradient contributions. For the particular case of fibre-reinforced materials, such a gradient-enhanced approach can be achieved by introducing the fibre curvature as an additional kinematic quantity. This implies that basis functions with a global continuity higher than C0 are required for a finite element-based approach which accounts for these fibre curvature effects. The present contribution shows that the isogeometric finite element method can provide a framework for the simulation of the respective higher-gradient continua.
On the incorporation of a micromechanical material model into the inherent strain method - application to the modeling of selective laser melting
(2021-09-09) Noll, Isabelle; Bartel, Thorsten; Menzel, Andreas
When developing reliable and useful models for selective laser melting processes of large parts, various simplifications are necessary to achieve computationally efficient simulations. Due to the complex processes taking place during the manufacturing of such parts, especially the material and heat source models influence the simulation results. If accurate predictions of residual stresses and deformation are desired, both complete temperature history and mechanical behavior have to be included in a thermomechanical model. In this article, we combine a multiscale approach using the inherent strain method with a newly developed phase transformation model. With the help of this model, which is based on energy densities and energy minimization, the three states of the material, namely, powder, molten, and resolidified material, are explicitly incorporated into the thermomechanically fully coupled finite-element-based process model of the micromechanically motivated laser heat source model and the simplified layer hatch model.
Numerical simulation of low cycle fatigue behavior, combining the phase-field method and the Armstrong-Frederick model
(2021-12-14) Wiegold, Tillmann; Aygün, Serhat; Klinge, Sandra
The present work couples the phase field method of fracture to the Armstrong-Frederick model of plasticity with the kinematic hardening. The chosen approach inherits the advantages of both techniques and is aimed at the study of low cycle fatigue effects in ductile materials. However, the numerical implementation of this promising concept brings with it several challenges, such as the definition of a unique framework for both setups, the derivation of coupled evolution equations, the distinction between tension and compression mode and the development of a computationally efficient algorithm. In the approach developed, the derivation of evolution equations uses the minimum principle of the dissipation potential. This step requires the expression of the dissipation potential of the classic Armstrong-Frederick model in terms of the internal variable rates by using the Legendre transformation. The model is eventually implemented in the FE-program and applied in order to investigate the life-time of the cold-formed carbon steel and the cold-formed stainless steel.

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