1,174 research outputs found
Data Sets for a Fractional Moisture-Dependent Viscoelasticity Model for Thermoplastic Polymers
No full textThis dataset contains Dynamical Mechanical Thermal Analysis (DMTA) results, including the determination of the complex Young’s modulus and complex shear modulus from torsion and tension measurements. The dataset is associated with the publication Fauser et al. (2025) and complements the dataset “A Modular Framework for Non-Linear Optimization of Linear Viscoelastic Model Parameters Using a Second-Order Fractional Approach”.
Frequency-dependent measurements were performed using a rheometer (MCR 702, linear motor, Anton Paar, Graz, Austria) over a frequency range of 0.1 s⁻¹ to 10 s⁻¹. The applied strain amplitudes were ε = 0.01 % (axial) and γ = 0.01 % (shear). Measurements were conducted at constant temperatures within the glass transition range of the respective polymers.
Master curves were generated from frequency sweeps of the complex Young’s and shear moduli for cylindrical samples (BASF, Ludwigshafen, Germany) of:
Poly-l-actic acid (PLA)
Poly-ethylene terephthalate (PET)
Poly-amid (PA)
and for rectangular samples of:
Thermoplastic poly-urethane (TPU, SMP Technologies Inc., Tokyo, Japan)
TPU samples were analyzed at varying moisture contents (in 10 % RH increments). The corresponding state-dependent shift factors used for master curve generation are also provided in the dataset.</p
Direct and Indirect Measurement of Complex Poisson's Ratio - Direct Measurement in Tension
No full textThis data set contains directly determined complex Poisson's ratio from axial and transversal strain measurements. Here, the axial and transverse strains were measured locally with strain gauges (K-CXY3-0015-3-350-O, HBK, Darmstadt, Germany) on cylindric polymethyl methacrylate (PMMA, EH-Design, Wörrstadt, Germany) samples with a diameter of d = 5 mm.
Frequency measurements were performed with a rheometer (MCR 702, linear motor, Anton-Paar, Graz, Austria) in the range of 1 Hz to 100 Hz with an axial strain of 0.01 % at constant temperatures in the range of 15 °C to 105 °C. 500 periods were measured per frequency and recorded using a measuring amplifier (Universal Amplifier MX1615B, HBK, Darmstadt, Germany).
Transversal and axial strain is then measured on the PMMA sample with strain gauges in tension mode.
The material response in the time domain is transformed to the frequency domain using the Fast Fourier Transform. This gives the axial and transverse amplitude as well as the axial and transverse phase shift. With the variable from the frequency domain, the complex Poisson's ratio is calculated in post-processing.
The data set contains the calculated complex Poisson's ratio of three measured PMMA samples
A Modular Framework for Non-Linear Optimization of Linear Viscoelastic Model Parameters using a Second-Order Fractional Approach
No full text This repository presents a reproducible workflow for fitting the Linear Second-order Fractional (LSF) model to mastercurves of thermoplastic polymers.
The dataset is associated with the publication Fauser et al. (2025) and complements the dataset Data Sets for a Fractional Moisture-Dependent Viscoelasticity Model for Thermoplastic Polymers.
The LSF model effectively captures the broad relaxation spectra typical of polymers, but its interdependent parameters require robust non-linear optimization. To ensure clarity and maintainability, the fitting workflow is organized into three modular components: Viscoelastic Models Class (models.py) Configuration File (configuration_file.py) Model Fitting Notebook (main.ipynb)
1. Viscoelastic Models Class (models.py) This module serves as the core library of constitutive models. Each model is implemented as a self-contained, object-oriented class. Purpose Encapsulate mathematical definitions of viscoelastic models, enabling modular extensions and reuse. Key Component: The LSF Model The Second-Order Fractional (LSF) model is defined by its complex modulus:
E*(ω) = (Ξ₀ + (iω)^α₁ Ξ₁ + (iω)^α₂ Ξ₂) / (Λ₀ + (iω)^α₁ Λ₁ + (iω)^α₂ Λ₂)
Parameters:
Ξ₀, Ξ₁, Ξ₂ → strain-related coefficients
Λ₀, Λ₁, Λ₂ → stress-related coefficients
α₁, α₂ → fractional exponents
Parent Class: ViscoelasticityModel
Defines methods for computing the real/imaginary parts of the complex modulus, as well as the storage modulus, loss modulus, and loss factor:
class ViscoelasticityModel(torch.nn.Module):
"""
Parent class for viscoelasticity models
"""
def __init__(self):
super().__init__()
def complexModulus(self, w):
raise Exception
def forward(self, w):
comp = self.complexModulus(w)
return comp.imag / comp.real
def storageModulus(self,w):
comp = self.complexModulus(w)
return comp.real
def lossModulus(self,w):
comp = self.complexModulus(w)
return comp.imag
Subclass: SecondOrderFractionalDerivativeModel Implements the LSF model, with parameters represented as torch.nn.Parameter for optimization. A scaling factor normalizes experimental and model data for stability.
class SecondOrderFractionalDerivativeModel(ViscoelasticityModel):
"""
Class for a second order derivative model
(G0 + d/dt^alpha G1 + d/dt^beta G2) stress
= (E0 + d/dt^alpha E1 + d/dt^beta E2) strain
"""
def __init__(self,E0,E1,E2,G0,G1,G2,alpha,beta):
super().__init__()
self.E0 = torch.nn.Parameter(E0 * torch.ones(1, dtype=torch.float64))
self.E1 = torch.nn.Parameter(E1 * torch.ones(1, dtype=torch.float64))
self.E2 = torch.nn.Parameter(E2 * torch.ones(1, dtype=torch.float64))
# normalize G0 to 1, G0 is not fitted
self.G0 = 1 * torch.ones(1, dtype=torch.float64)
self.G1 = torch.nn.Parameter(G1 * torch.ones(1, dtype=torch.float64))
self.G2 = torch.nn.Parameter(G2 * torch.ones(1, dtype=torch.float64))
self.alpha1 = torch.nn.Parameter(alpha * torch.ones(1, dtype=torch.float64))
self.alpha2 = torch.nn.Parameter(beta * torch.ones(1, dtype=torch.float64))
def complexModulus(self, w):
w = w[:,None]
iw = torch.view_as_complex(torch.cat((torch.zeros(w.size()),w),1))
iw_alpha1 = iw ** self.alpha1
iw_alpha2 = iw ** self.alpha2
comp = ((self.E0 + self.E1 * iw_alpha1 + self.E2 * iw_alpha2)
/ (self.G0 + self.G1 * self.E1 * iw_alpha1 + self.G2 * self.E2 * iw_alpha2))
return comp
2. Configuration File (configuration_file.py)
This module centralizes all hyperparameters for non-linear optimization. Separating configuration ensures reproducibility, readability, and simplified parameter tuning.
Example
def get_diaplex_50_optimization_params():
dict = {}
dict["lr"] = 1e-3
dict["n_iter"] = 40000
dict["data_range"] = [5e-6,1e4]
dict["w_threshold"] = 0.0032
dict["w_left"] = 1
dict["w_right"] = 2
dict["criterion"] = torch.nn.MSELoss(reduction="sum")
return dict
Key Parameters lr → learning rate for Adam optimizer n_iter → number of optimization iterations data_range → frequency range for fitting w_threshold → frequency of peak loss factor w_left, w_right → weighting around w_threshold criterion → loss function (L2 norm)
3. Model Fitting (main.ipynb)
The Jupyter notebook orchestrates the full workflow for fitting fractional viscoelastic models to experimental mechanical data.
It performs data loading, preprocessing, model definition, and optimization of material parameters using Adam optimizer.
Workflow Overview
Load configuration and utilities
Imports helper functions and parameters from configuration_file.py:
get_diaplex_filenames() — returns paths to experimental CSV data.
get_diaplex_50_optimization_params() — provides hyperparameters (learning rate, iteration count, weighting, etc.).
Initializes the fractional viscoelastic model SecondOrderFractionalDerivativeModel for each dataset.
Load and preprocess experimental data
Reads CSV files, extracts and sorts:
Extensional Reduced Frequency
Extensional Storage Modulus (E′)
Extensional Loss Modulus (E″)
Data are converted to PyTorch tensors for GPU-based optimization.
Define training configuration
For each dataset:
Finds the frequency corresponding to the loss peak (tan δ = E″/E′).
Loads optimization settings: criterion, lr, n_iter, w_left, w_right, and data_range.
Computes data_scaling to weight frequency ranges differently around the loss peak.
Optimization Loop
for t in tqdm(range(n_iter)):
pred = models[key](angfreq[key][indices[key]])
meas = ((lossmod[key])/(stormod[key]))[indices[key]]
loss = criterion(meas/meas * data_scaling, pred/meas * data_scaling)
optimizer.zero_grad()
loss.backward()
optimizer.step()
The optimization minimizes the difference between measured and predicted loss factor (tan δ).
Weighting (w_left, w_right) emphasizes frequencies below or above the loss peak for improved robustness.
Convergence depends strongly on initial guesses, data range, and learning rate.
Visualization and Output
After convergence, the notebook produces log–log plots comparing model predictions and measurements:
Loss factor (tan δ)
Storage modulus (E′)
Figures are saved as *_fig_loss_factor.pdf and *_fig_storage_modulus.pdf, ready for publication.
Key Notes
Convergence sensitivity: Good initial parameter guesses and suitable step sizes are essential.
Weighting strategy: Improves robustness near the loss peak, particularly for noisy data.
Modular design: New datasets or model variants can be added easily through configuration files.
4. Fitted Parameters
In addition to the Python scripts for non-linear optimization, this repository also provides the fitted parameters of each master curve. These parameters, published in the related dataset
(Data Sets for a Fractional Moisture-Dependent Viscoelasticity Model for Thermoplastic Polymers), are available for both the LSF model and the Generalized Maxwell model.
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Direct and Indirect Measurement of Complex Poisson's Ratio - Direct Measurement in Compression
No full textThis data set contains directly determined complex Poisson's ratio from axial and transversal strain measurements. Here, the axial and transverse strains were measured locally with strain gauges (K-CXY3-0060-3-350-O, HBK, Darmstadt, Germany) on cylindric polymethyl methacrylate (PMMA, EH-Design, Wörrstadt, Germany) samples with a diameter of d = 30 mm.
Dynamic mechanical analysis (DMA) was performed with the piezoelectric actuator (8P-035.20P, Physik Instrumente, Karlsruhe, Germany) driven by the high power amplifier (E-482, Physik Instrumente, Karlsruhe, Germany). Small strain amplitudes
excitation in the frequency range from 0.1 Hz to 1000 Hz are performed. To ensure the oscillation around a strain amplitude, a static preload is applied by a universal testing machine (RM50, Schenk, Germany).
Transversal and axial strain is then measured on the PMMA sample with strain gauges in compression mode. The material response in the time domain is transformed to the frequency domain using the Fast Fourier Transform. This gives the axial and transverse amplitude as well as the axial and transverse phase shift. With the variable from the frequency domain, the complex Poisson's ratio is calculated in post-processing.
The data set contains the calculated complex Poisson's ratio of three measured PMMA samples
Direct and Indirect Measurement of Complex Poisson's Ratio - Indirect Measurement in Torsion and Tension
No full textThis data set contains indirectly calculated complex Poisson's ratio by determining the complex Young's E* and complex shear modulus G* from torsion and tension measurements. The measurements were performed on cylindric polymethyl methacrylate (PMMA, EH-Design, Wörrstadt, Germany) samples with a diameter of d = 3 mm. Frequency measurements were performed with a rheometer (MCR 702, linear motor, Anton-Paar, Graz, Austria) in a angular frequency range of 0.628 rad/s to 188 rad/s with an axial strain of epsilon = 0.01 % and shear strain of gamma = 0.01 % at constant temperatures in the range of 15 to 105 °C. The Elastic Viscoelastic Correspondence Principle (EVCP) is applied to calculate the complex Poisson's ratio
Planning in Brazil, India and Germany
No full textPlanning is a fundamental cognitive ability that helps in organizing and structuring events unfolding in a person\u27s daily life. Two studies are presented that analyze planning behavior in different cultures: Brazil, India, and Germany. The first is a cross-cultural psychological study in which students develop plans for uncertain problem scenarios. The second study follows a cultural psychological tradition. Workers from different domains are interviewed about their life problems and plans. The strengths and the weaknesses of both approaches become obvious in the description and discussion of these two studies. The cross-cultural study sheds light on cross-cultural similarities and differences in planning in Brazil, India, and Germany. The cultural psychological approach yields data regarding a theoretical model on the specific cultural influences on planning
Decision Making in Individualistic and Collectivistic Cultures
No full textHow do cultural values influence individuals\u27 decision making? One would expect answers to this question either from cognitive psychology or from cross-cultural psychology. Cognitive theories on decision making, however, rarely consider the factor of culture, and research in cross-cultural psychology deals only to a small extent with decision making. Therefore the study of culture and decision making is a relatively new and unexplored field. In this paper normative and descriptive approaches to decision making are discussed and three cross-cultural studies on decision making in individualistic and collectivist cultures using different methodologies are described. The results are integrated into a model that can be helpful to derive specific hypotheses for further studies in this field
Dominik Tatarka - wędrowiec
No full textDominik Tatarka is one of the Slovak travel books’s author; he wrotes reports Clovek na cestach. The travelling was important factor of his life: he find an inspiration for his writting and he formulated his life’s philosophy during his journeys. The travelling is one of the important key for reading all his compositions and for understanding his otlook on life: the author presents himself no as the postmodern nomad, but as the pilgrim, who wanders for aim „to unit splits world” and to find a man
Comprehensive analysis of polypropylene recyclates : characterization, representative sampling and quantification approaches of polyolefin cross contaminations of polypropylene recyclates
No full textAuthor DI Dominik Kaineder BSc.Dissertation Johannes Kepler Universität Linz 2025Arbeit nach Ablauf der Sperre auf den öffentlichen PCs in den Bibliotheken der JKU+Medizin abrufba
Comprehensive analysis of polypropylene recyclates : characterization, representative sampling and quantification approaches of polyolefin cross contaminations of polypropylene recyclates
No full textAuthor DI Dominik Kaineder BSc.Dissertation Johannes Kepler Universität Linz 2025Arbeit nach Ablauf der Sperre auf den öffentlichen PCs in den Bibliotheken der JKU+Medizin abrufba
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