49 research outputs found
A multiscale damage model for composite materials using a FFT-Based method
Modeling failure and progressive damage of composite materials presents
a challenging task and is currently subject of many research activities in the field of
computational mechanics. Conventional methods which assume constant material coefficients
or global failure criteria, are in many cases not sufficient to predict the appropriate
mechanical material response. Composite failure occurs as a result of complex mesostructural
damage mechanisms and therefore it is preferable to capture these nonlinear
material effects directly on a finer scale. Hence, recent multiscale modeling and simulation
techniques were developed to consider the mesoscopic material behavior. In this contribution
we propose an alternative multiscale approach similar to FE2. Nonlinear material
effects caused by progressive damage behavior are captured on a finer length scale. The
constituents are modeled explicitly and simple isotropic damage laws are used to describe
the constitutive behavior. Hence, the resulting material response is based on genuine
physical effects and only a few material parameters are required which can be measured
directly in physical experiments. The fine scale problem (material level) is reformulated
into an integral equation of Lippmann-Schwinger type and solved efficiently using the
fast Fourier transformation (FFT). The calculation is carried out on a regular voxel grid
which can be obtained from 3D images like tomographies without using any complicated
mesh generation. Furthermore, the fine scale problem is integrated in a standard Finite
Element framework which is used to solve the macroscopic BVP (component level)
Fiber orientation interpolation for the multiscale analysis of short fiber reinforced composite parts
A space-time upscaling technique for modeling high-cycle fatigue-damage of short-fiber reinforced composites
A multiscale high-cycle fatigue-damage model for the stiffness degradation of fiber-reinforced materials based on a mixed variational framework
Under fatigue-loading, short-fiber reinforced thermoplastic materials typically show a progressive degradation of the stiffness tensor. The stiffness degradation prior to failure is of primary interest from an engineering perspective, as it determines when fatigue cracks nucleate. Efficient modeling of this fatigue stage allows the engineer to monitor the fatigue-process prior to failure and design criteria which ensure a safe application of the component under investigation.
We propose a multiscale model for the stiffness degradation in thermoplastic materials based on resolving the fiber microstructure. For a start, we propose a specific fatigue-damage model for the matrix, and the degradation of the thermoplastic composite arises from a rigorous homogenization procedure. The fatigue-damage model for the matrix is rather special, as its convex nature precludes localization, permits a well-defined upscaling, and is thus well-adapted to model the phase of stable stiffness degradation under fatigue loading. We demonstrate the capabilities of the full-field model by comparing the predictions on fully resolved fiber microstructures to experimental data.
Furthermore, we introduce an associated model-order reduction strategy to enable component-scale simulations of the local stiffness degradation under fatigue loading. With model-order reduction in mind and upon implicit discretization in time, we transform the minimization of the incremental potential into an equivalent mixed formulation, which combines two rather attractive features. More precisely, upon order reduction, this mixed formulation permits precomputing all necessary quantities in advance, yet, retains its well-posedness in the process. We study the characteristics of the model-order reduction technique, and demonstrate its capabilities on component scale. Compared to similar approaches, the proposed model leads to improvements in runtime by more than an order of magnitude
Accounting for viscoelastic effects in a multiscale fatigue model for the degradation of the dynamic stiffness of short-fiber reinforced thermoplastics
Under fatigue loading, the stiffness decrease in short-fiber reinforced polymers reflects the gradual degradation of the material. Thus, both measuring and modeling this stiffness is critical to investigate and understand the entire fatigue process. Besides evolving damage, viscoelastic effects within the polymer influence the measured dynamic stiffness. In this paper, we study the influence of a linear viscoelastic material model for the matrix on the obtained dynamic stiffness and extend an elastic multiscale fatigue-damage model to viscoelasticity. Our contribution is two-fold. First, we revisit the complex-valued elastic models known in the literature to predict the asymptotic periodic orbit of a viscoelastic material. For small phase shifts in an isotropic linear viscoelastic material, we show through numerical experiments that a real-valued computation of an âelasticâ material is sufficient to approximate the dynamic stiffness of a microstructure with a generalized Maxwell material and equal Poissonâs ratios in every element as matrix, reinforced by elastic inclusions. This makes standard solvers applicable to fiber-reinforced thermoplastics. Secondly, we propose a viscoelastic fatigue-damage model for the thermoplastic matrix based on decoupling of the time scales where viscoelastic and fatigue-damage effects manifest. We demonstrate the capability of the multiscale model to predict the dynamic stiffness evolution under fatigue loading of short-fiber reinforced polybutylene terephthalate (PBT) by a validation with experimental results
Zur Simulation von Klebeverbindungen fĂŒr Scheibenbauteile mit Level-Set-Funktionen und erweiterter Finite-Elemente-Methode
Das Kleben ist noch eine relativ neue Art der Verbindung von Betonbauteilen. Bei der iterativen Optimierung der Fugengestalt wird eine Folge von unterschiedlichen FugenverlĂ€ufen analysiert. Um eine Neuvernetzung fĂŒr jede einzelne Fugengestalt zu vermeiden und gleichzeitig die Verzerrungen und Spannungen an der GrenzflĂ€che zwischen HPC-Platte und Klebefuge effizient und genau zu berechnen, wird in dieser Arbeit eine Variante der erweiterten Finite-Elemente-Methode (XFEM) als Strukturanalyseverfahren vorgeschlagen. Es wird gezeigt, dass die Methode sehr gut zur Strukturanalyse bei der Optimierung der Fugengestalt, die implizit ĂŒber eine Level-Set-Funktion beschrieben wird, geeignet ist. Die Ergebnisse der Gestaltoptimierung werden diskutiert
Zur Simulation von Klebeverbindungen fĂŒr Scheibenbauteile mit Level-Set-Funktionen und erweiterter Finite-Elemente-Methode
Das Kleben ist noch eine relativ neue Art der Verbindung von Betonbauteilen. Bei der iterativen Optimierung der Fugengestalt wird eine Folge von unterschiedlichen FugenverlĂ€ufen analysiert. Um eine Neuvernetzung fĂŒr jede einzelne Fugengestalt zu vermeiden und gleichzeitig die Verzerrungen und Spannungen an der GrenzflĂ€che zwischen HPC-Platte und Klebefuge effizient und genau zu berechnen, wird in dieser Arbeit eine Variante der erweiterten Finite-Elemente-Methode (XFEM) als Strukturanalyseverfahren vorgeschlagen. Es wird gezeigt, dass die Methode sehr gut zur Strukturanalyse bei der Optimierung der Fugengestalt, die implizit ĂŒber eine Level-Set-Funktion beschrieben wird, geeignet ist. Die Ergebnisse der Gestaltoptimierung werden diskutiert
Mikrostruktursimulation der mechanischen Deformation von Fasermaterialien
Die Deformation von porösen Natur- und Kunstfasermaterialien unter Zug-, Druck- oder Biegebelastung hĂ€ngt sehr stark von den geometrischen und mechanischen Eigenschaften der verwendeten Fasern und den Eigenschaften der Faser-Faser-Kontaktstellen ab. In den betrachteten Materialien besitzen die Fasern hĂ€ufig eine Orientierung, die zu elastisch anisotropen Eigenschaften fĂŒhrt. Um das Materialverhalten beim Herstellungsprozess und im Einsatz vorherzusagen werden in dieser Arbeit Fasernetzwerkmodelle zur Beschreibung der Mikrostruktur verwendet.
Im Vergleich zu Ă€hnlichen Verfahren werden sehr komplizierte dreidimensionale Fasernetzwerke mit einem effizienten numerischen Verfahren gelöst. Das Lösungsverfahren basiert auf einer Formulierung der ElastizitĂ€tsgleichungen als Integralgleichung vom Lippmann-Schwinger-Typ. Diese Integralgleichungen werden iterativ mit Hilfe der schnellen Fourier-Transformation (FFT) gelöst. Die Anwendung dieser Lösungstechnik auf poröse Medien ist neu. Im Vortrag werden Simulationsergebnisse fĂŒr verschiedene Fasermaterialien erlĂ€utert und diese mit entsprechenden Messungen verglichen. Dabei werden geometrisch und physikalisch nichtlineare Verformungen betrachtet.
Mit Hilfe der entwickelten Mikrostruktursimulationstechnik (Softwarepaket FeelMath) lĂ€sst sich die AbhĂ€ngigkeit der makroskopischen Deformationseigenschaften von den Eigenschaften der Einzelfasern und der Faserorientierung analysieren. Damit kann die Anzahl der notwendigen Messungen reduziert werden und die Eigenschaften der Materialien lassen sich fĂŒr den speziellen Einsatzzweck optimieren. Das vorgestellte Lösungsverfahren ist ebenfalls fĂŒr nichtporöse Verbundwerkstoffe und zur Lösung von WĂ€rmeleitproblemen in Fasernetzwerken geeignet
Dataâbased prediction of the viscoelastic behavior of short fiber reinforced composites
The viscoelastic behavior of short fiber reinforced polymers (SFRPs) partly depends on different microstructural parameters such as the local fiber orientation distribution. To account for this by simulation on component level, twoâscale methods couple simulations on the microâ and macroscale, which involve considerable computational costs. To circumvent this problem, the generation of a viscoelastic surrogate model is presented here. For that purpose, an adaptive sampling technique is investigated and data are obtained by creep simulations of representative volume elements (RVEs) using a fast Fourier transform (FFT) based homogenization method. Numerical tests confirm the high accuracy of the surrogate model. The possibility of using that model for efficient material optimization is shown
Factors influencing the dynamic stiffness in shortâfiber reinforced polymers
In shortâfiber reinforced polymers, fatigue damage is typically characterized by measuring the dynamic stiffness and its degradation under cyclic loading. Computational homogenization methods may be used to characterize the fatigue behavior of the composite via numerical predictions. Such an approach may reduce the experimental effort significantly. In the previous works, the authors proposed an elastic fatigue damage model for predicting the relative stiffness degradation of shortâfiber reinforced materials. However, the absolute value of the dynamic stiffness within the first cycle showed deviations from the expected elastic material behavior. Thus, the effect of viscoelastic polymer behavior as well as different microstructure descriptors on the dynamic stiffness is studied in the work at hand