arXiv subjects

Philipp Junker

Publications and source records attributed to Philipp Junker.

9 recordsLinked to original sources

arXiv2026

First- and Second-Order Phase Transformation Modeling Based on the Hamilton Principle: A Coupled Thermo-Mechanical Approach for Glass Additive Manufacturing

Additive manufacturing of glass inherently involves complex thermal histories characterized by extreme heating and rapid cooling rates. These extreme conditions directly govern the final microstructure and mechanical integrity of the printed material. This work presents a comprehensive multi-physics material model derived from the extended Hamilton principle, establishing a unified variational framework for coupled thermal, mechanical, and phase transformation processes at finite strains. The formulation integrates a rigorous thermodynamic description of first-order melting and second-order glass transitions with a kinematic split accounting for thermal expansion, phase specific density changes, and viscoelastic deformation. A temperature dependent viscosity model is employed to capture the kinetic freezing of the microstructure inherent to vitrification. The numerical implementation utilizes a monolithic Neighbored Element Method (NEM) for the solution of the heat equation, ensuring computational efficiency and stability. Numerical investigations at the material point level validate the models ability to reproduce Time-Temperature-Transformation (TTT) behavior under varying cooling rates. Furthermore, three dimensional Finite Element simulations in ANSYS of a laser-based deposition process demonstrate the accumulation of residual stresses and macroscopic warpage resulting from the interplay between phase transformation kinetics and viscous relaxation.

cs.CE↗

arXiv2026

A space-time LATIN-PGD strategy for solving Newtonian compressible flows

Simulating flow problems is at the core of many engineering applications but often requires high computational effort, especially when dealing with complex models. This work presents a novel approach for resolving flow problems using the LATIN-PGD solver. In this contribution, we place ourselves within the framework of Newtonian compressible and laminar flows. This specific and relatively simple case enables focusing on flows for which a state equation provides a direct relation between pressure and density. It is then possible to use the LATIN solver to set up a pressure-velocity decoupling algorithm. Moreover, Proper Generalised Decomposition (PGD) is natively included in the solver and yields two independent space-time decompositions for the velocity and the pressure fields. As a first step, the solver is validated on a problem for which an analytical solution is available. It is then applied to slightly more complex problems. The results show good agreement with the literature, and we expect that the solver could be used to compute more complicated material laws in the future.

math.NA↗

arXiv2025

Bayesian Updating of constitutive parameters under hybrid uncertainties with a novel surrogate model applied to biofilms

Accurate modeling of bacterial biofilm growth is essential for understanding their complex dynamics in biomedical, environmental, and industrial settings. These dynamics are shaped by a variety of environmental influences, including the presence of antibiotics, nutrient availability, and inter-species interactions, all of which affect species-specific growth rates. However, capturing this behavior in computational models is challenging due to the presence of hybrid uncertainties, a combination of epistemic uncertainty (stemming from incomplete knowledge about model parameters) and aleatory uncertainty (reflecting inherent biological variability and stochastic environmental conditions). In this work, we present a Bayesian model updating (BMU) framework to calibrate a recently introduced multi-species biofilm growth model. To enable efficient inference in the presence of hybrid uncertainties, we construct a reduced-order model (ROM) derived using the Time-Separated Stochastic Mechanics (TSM) approach. TSM allows for an efficient propagation of aleatory uncertainty, which enables single-loop Bayesian inference, thereby avoiding the computationally expensive nested (double-loop) schemes typically required in hybrid uncertainty quantification. The BMU framework employs a likelihood function constructed from the mean and variance of stochastic model outputs, enabling robust parameter calibration even under sparse and noisy data. We validate our approach through two case studies: a two-species and a four-species biofilm model. Both demonstrate that our method not only accurately recovers the underlying model parameters but also provides predictive responses consistent with the synthetic data.

cs.CE↗

arXiv2025

A continuum multi-species biofilm model with a novel interaction scheme

Biofilms are complex structures which are inhabited by numerous amount of different species of microorganisms. Due to their ubiquity, they influence human life on an everyday basis. It is therefore important to understand the interactions between different biofilm components and reactions to outside conditions. For this purpose, mathematical models and in silico experiments have proven themselves to be fundamental. In combination with in vitro and in vivo experiments, they can give more insights and focus researchers' attention, reducing costs in the process. In this work, a comprehensive multi-species continuum-based biofilm model is presented. This model is capable of replicating a variety of different biofilm interactions with an arbitrary number of species, while still being comprehensive to encourage usage by researchers less familiar with mathematical modeling. In addition to a nutrient source, antibiotic agents and their effect on the biofilm can also be depicted. The model is derived using Hamilton's principle of stationary action, ensuring thermodynamic consistency automatically. The results show good quantitative agreement with biofilm behavior.

cs.CE↗

arXiv2024

Efficient damage simulations under material uncertainties in a weakly-intrusive implementation

Uncertainty quantification is not yet widely adapted in the design process of engineering components despite its importance for achieving sustainable and resource-efficient structures. This is mainly due to two reasons: 1) Tracing the effect of uncertainty in engineering simulations is a computationally challenging task. This is especially true for inelastic simulations as the whole loading history influences the results. 2) Implementations of efficient schemes in standard finite element software are lacking. In this paper, we are tackling both problems. We are proposing a \rev{weakly}-intrusive implementation of the time-separated stochastic mechanics in the finite element software Abaqus. The time-separated stochastic mechanics is an efficient and accurate method for the uncertainty quantification of structures with inelastic material behavior. The method effectivly separates the stochastic but time-independent from the deterministic but time-dependent behavior. The resulting scheme consists only two deterministic finite element simulations for homogeneous material fluctuations in order to approximate the stochastic behavior. This brings down the computational cost compared to standard Monte Carlo simulations by at least two orders of magnitude while ensuring accurate solutions. In this paper, the implementation details in Abaqus and numerical comparisons are presented for the example of damage simulations.

cs.CE↗

arXiv2023

A new paradigm for the efficient inclusion of stochasticity in engineering simulations

As a physical fact, randomness is an inherent and ineliminable aspect in all physical measurements and engineering production. As a consequence, material parameters, serving as input data, are only known in a stochastic sense and thus, also output parameters, e.g., stresses, fluctuate. For the estimation of those fluctuations it is imperative to incoporate randomness into engineering simulations. Unfortunately, incorporating uncertain parameters into the modeling and simulation of inelastic materials is often computationally expensive, as many individual simulations may have to be performed. The promise of the proposed method is simple: using extended material models to include stochasticity reduces the number of needed simulations to one. This single computation is cheap, i.e., it has a comparable numerical effort as a single standard simulation. The extended material models are easily derived from standard deterministic material models and account for the effect of uncertainty by an extended set of deterministic material parameters. The time-dependent and stochastic material behavior are separated, such that only the deterministic time-dependent behavior of the extended material model needs to be simulated. The effect of stochasticity is then included during post-processing. The feasibility of this approach is demonstrated for three different and highly non-linear material models: viscous damage, viscous phase transformations and elasto-viscoplasticity. A comparison to the Monte Carlo method showcases that the method is indeed able to provide reliable estimates of the expectation and variance of internal variables and stress at a minimal fraction of the computation cost.

cs.CE↗

arXiv2021

An extended Hamilton principle as unifying theory for coupled problems and dissipative microstructure evolution

An established strategy for material modeling is provided by energy-based principles such that evolution equations in terms of ordinary differential equations can be derived. However, there exist a variety of material models that also need to take into account non-local effects to capture microstructure evolution. In this case, the evolution of microstructure is described by a partial differential equation. In this contribution, we present how Hamilton's principle provides a physically sound strategy for the derivation of transient field equations for all state variables. Therefore, we begin with a demonstration how Hamilton's principle generalizes the principle of stationary action for rigid bodies. Furthermore, we show that the basic idea behind Hamilton's principle is not restricted to isothermal mechanical processes. In contrast, we propose an extended Hamilton principle which is applicable to coupled problems and dissipative microstructure evolution. As example, we demonstrate how the field equations for all state variables for thermo-mechanically coupled problems, i.e. displacements, temperature, and internal variables, result from the stationarity of the extended Hamilton functional. The relation to other principles, as principle of virtual work and Onsager's principle, are given. Finally, exemplary material models demonstrate how to use the extended Hamilton principle for thermo-mechanically coupled rate-dependent, rate-independent, and gradient-enhanced materials.

cond-mat.mtrl-sci↗

arXiv2021

Thermodynamic topology optimization for hardening materials

Topology optimization is an important basis for the design of components. Here, the optimal structure is found within a design space subject to boundary conditions. Thereby, the specific material law has a strong impact on the final design. An important kind of material behavior is hardening: then a, for instance, linear-elastic structure is not optimal if plastic deformation will be induced by the loads. Since hardening behavior has a remarkable impact on the resultant stress field, it needs to be accounted for during topology optimization. In this contribution, we present an extension of the thermodynamic topology optimization that accounts for this non-linear material behavior due to the evolution of plastic strains. For this purpose, we develop a novel surrogate model that allows to compute the plastic strain tensor corresponding to the current structure design for arbitrary hardening behavior. We show the agreement of the model with the classic plasticity model for monotonic loading. Furthermore, we demonstrate the interaction of the topology optimization for hardening material behavior results in structural changes.

cs.CE↗

arXiv2021

Efficient and robust numerical treatment of a gradient-enhanced damage model at large deformations

The modeling of damage processes in materials constitutes an ill-posed mathematical problem which manifests in mesh-dependent finite element results. The loss of ellipticity of the discrete system of equations is counteracted by regularization schemes of which the gradient enhancement of the strain energy density is often used. In this contribution, we present an extension of the efficient numerical treatment, which has been proposed in [1], to materials that are subjected to large deformations. Along with the model derivation, we present a technique for element erosion in the case of severely damaged materials. Efficiency and robustness of our approach is demonstrated by two numerical examples.

cs.CE↗