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Wolfgang A. Wall

Publications and source records attributed to Wolfgang A. Wall.

At least 37 records · Page 2Linked to original sources
arXiv2024

Adaptive integration of history variables in constrained mixture models for organ-scale growth and remodeling

In the last decades, many computational models have been developed to predict soft tissue growth and remodeling (G&R). The constrained mixture theory describes fundamental mechanobiological processes in soft tissue G&R and has been widely adopted in cardiovascular models of G&R. However, even after two decades of work, large organ-scale models are rare, mainly due to high computational costs (model evaluation and memory consumption), especially in long-range simulations. We propose two strategies to adaptively integrate history variables in constrained mixture models to enable large organ-scale simulations of G&R. Both strategies exploit that the influence of deposited tissue on the current mixture decreases over time through degradation. One strategy is independent of external loading, allowing the estimation of the computational resources ahead of the simulation. The other adapts the history snapshots based on the local mechanobiological environment so that the additional integration errors can be controlled and kept negligibly small, even in G&R scenarios with severe perturbations. We analyze the adaptively integrated constrained mixture model on a tissue patch for a parameter study and show the performance under different G&R scenarios. To confirm that adaptive strategies enable large organ-scale examples, we show simulations of different hypertension conditions with a real-world example of a biventricular heart discretized with a finite element mesh. In our example, adaptive integrations sped up simulations by a factor of three and reduced memory requirements to one-sixth. The reduction of the computational costs gets even more pronounced for simulations over longer periods. Adaptive integration of the history variables allows studying more finely resolved models and longer G&R periods while computational costs are drastically reduced and largely constant in time.

q-bio.TO↗
arXiv2024

A novel mesh regularization approach based on finite element distortion potentials: Application to material expansion processes with extreme volume change

The accuracy of finite element solutions is closely tied to the mesh quality. In particular, geometrically nonlinear problems involving large and strongly localized deformations often result in prohibitively large element distortions. In this work, we propose a novel mesh regularization approach allowing to restore a non-distorted high-quality mesh in an adaptive manner without the need for expensive re-meshing procedures. The core idea of this approach lies in the definition of a finite element distortion potential considering contributions from different distortion modes such as skewness and aspect ratio of the elements. The regularized mesh is found by minimization of this potential. Moreover, based on the concept of spatial localization functions, the method allows to specify tailored requirements on mesh resolution and quality for regions with strongly localized mechanical deformation and mesh distortion. In addition, while existing mesh regularization schemes often keep the boundary nodes of the discretization fixed, we propose a mesh-sliding algorithm based on variationally consistent mortar methods allowing for an unrestricted tangential motion of nodes along the problem boundary. Especially for problems involving significant surface deformation (e.g., frictional contact), this approach allows for an improved mesh relaxation as compared to schemes with fixed boundary nodes. To transfer data such as tensor-valued history variables of the material model from the old (distorted) to the new (regularized) mesh, a structure-preserving invariant interpolation scheme for second-order tensors is employed, which has been proposed in our previous work and is designed to preserve important mechanical properties of tensor-valued data such as objectivity and positive definiteness... {continued see pdf}

cs.CE↗
arXiv2024

High-performance matrix-free unfitted finite element operator evaluation

Unfitted finite element methods, like CutFEM, have traditionally been implemented in a matrix-based fashion, where a sparse matrix is assembled and later applied to vectors while solving the resulting linear system. With the goal of increasing performance and enabling algorithms with polynomial spaces of higher degrees, this contribution chooses a more abstract approach by matrix-free evaluation of the operator action on vectors instead. The proposed method loops over cells and locally evaluates the cell, face, and interface integrals, including the contributions from cut cells and the different means of stabilization. The main challenge is the efficient numerical evaluation of terms in the weak form with unstructured quadrature points arising from the unfitted discretization in cells cut by the interface. We present design choices and performance optimizations for tensor-product elements and demonstrate the performance by means of benchmarks and application examples. We demonstrate a speedup of more than one order of magnitude for the operator evaluation of a discontinuous Galerkin discretization with polynomial degree three compared to a sparse matrix-vector product and develop performance models to quantify the performance properties over a wide range of polynomial degrees.

math.NA↗
arXiv2024

Exploration of improved, roller-based spreading strategies for cohesive powders in additive manufacturing via coupled DEM-FEM simulations

Spreading of fine (D50 <=20um) powders into thin layers typically requires a mechanism such as a roller to overcome the cohesive forces between particles. Roller-based spreading requires careful optimization and can result in low density and/or inconsistent layers depending on the characteristics of the powder feedstock. Here, we explore improved, roller-based spreading strategies for highly cohesive powders using an integrated discrete element-finite element (DEM-FEM) framework. Powder characteristics are emulated using a self-similarity approach based on experimental calibration for a Ti-6Al-4V 0-20um powder. We find that optimal roller-based spreading relies on a combination of surface friction of the roller and roller kinematics that impart sufficient kinetic energy to break cohesive bonds between powder particles. However, excess rotation can impart excessive kinetic energy, causing ejection of particles and a non-uniform layer. Interestingly, the identified optimal surface velocities for counter-rotation as well as rotational oscillation are very similar, suggesting this quantity as the critical kinematic parameter. When these conditions are chosen appropriately, layers with packing fractions beyond 50% are predicted for layer thicknesses as small as ~2 times D90 of the exemplary powder, and the layer quality is robust with respect to substrate adhesion over a 10-fold range. The latter is an important consideration given the spatially varying substrate conditions in AM due to the combination of fused/bound and bare powder regions. As compared to counter-rotation, the proposed rotational oscillation is particularly attractive because it can overcome practical issues with mechanical runout of roller mechanisms. In particular, the application to rubber-coated rollers, which promises to reduce the risk of tool damage and particle streaking, is recommended for future investigation.

cs.CE↗
arXiv2024

A highly efficient computational approach for part-scale microstructure predictions in Ti-6Al-4V additive manufacturing

Fast and efficient simulations of metal additive manufacturing (AM) processes are highly relevant to exploring the full potential of this promising manufacturing technique. The microstructure composition plays an important role in characterizing the part quality and deriving mechanical properties. When complete parts are simulated, one often needs to resort to strong simplifications such as layer-wise heating due to the large number of simulated time steps compared to the small time step sizes. This article proposes a scan-resolved approach to the coupled thermo-microstructural problem. Building on a highly efficient thermal model, we discuss the implementation of a phenomenological microstructure model for the evolution of the three main constituents of Ti-6Al-4V: stable $α_s$-phase, martensite $α_m$-phase and $β$-phase. The implementation is tailored to modern hardware features using vectorization and fast approximations of transcendental functions. A performance model and numerical examples verify the high degree of optimization. We demonstrate the applicability and predictive power of the approach and the influence of scan strategy and geometry. Depending on the specific example, results can be obtained with moderate computational resources in a few hours to days. The numerical examples include a prediction of the microstructure on the full NIST AM Benchmark cantilever specimen.

cs.CE↗
arXiv2024

A conservative and efficient model for grain boundaries of solid electrolytes in a continuum model for solid-state batteries

A formulation is presented to efficiently model ionic conduction inside, i.e. across and along, grain boundaries. Efficiency and accuracy is achieved by reducing it to a two-dimensional manifold while guaranteeing the conservation of mass and charge at the intersection of multiple grain boundaries. The formulation treats the electric field and the electric current as independent solution variables. We elaborate on the numerical challenges this formulation implies and compare the computed solution with results from an analytical solution by quantifying the convergence towards the exact solution. Towards the end of this work, the model is firstly applied to setups with extreme values of crucial parameters of grain boundaries to study the influence of the ionic conduction in the grain boundary on the overall battery cell voltage and, secondly, to a realistic microstructure to show the capabilities of the formulation.

physics.chem-ph↗
arXiv2023

Solving Bayesian Inverse Problems With Expensive Likelihoods Using Constrained Gaussian Processes and Active Learning

Solving inverse problems using Bayesian methods can become prohibitively expensive when likelihood evaluations involve complex and large scale numerical models. A common approach to circumvent this issue is to approximate the forward model or the likelihood function with a surrogate model. But also there, due to limited computational resources, only a few training points are available in many practically relevant cases. Thus, it can be advantageous to model the additional uncertainties of the surrogate in order to incorporate the epistemic uncertainty due to limited data. In this paper, we develop a novel approach to approximate the log likelihood by a constrained Gaussian process based on prior knowledge about its boundedness. This improves the accuracy of the surrogate approximation without increasing the number of training samples. Additionally, we introduce a formulation to integrate the epistemic uncertainty due to limited training points into the posterior density approximation. This is combined with a state of the art active learning strategy for selecting training points, which allows to approximate posterior densities in higher dimensions very efficiently. We demonstrate the fast convergence of our approach for a benchmark problem and infer a random field that is discretized by 30 parameters using only about 1000 model evaluations. In a practically relevant example, the parameters of a reduced lung model are calibrated based on flow observations over time and voltage measurements from a coupled electrical impedance tomography simulation.

cs.CE↗
arXiv2023

An efficient computational model of the in-flow capturing of magnetic nanoparticles by a cylindrical magnet for cancer nanomedicine

Magnetic nanoparticles have emerged as a promising approach to improving cancer treatment. However, many novel nanoparticle designs fail in clinical trials due to a lack of understanding of how to overcome the in vivo transport barriers. To address this shortcoming, we develop a novel computational model aimed at the study of magnetic nanoparticles in vitro and in vivo. In this paper, we present an important building block for this overall goal, namely an efficient computational model of the in-flow capture of magnetic nanoparticles by a cylindrical permanent magnet in an idealised test setup. We use a continuum approach based on the Smoluchowski advection-diffusion equation, combined with a simple approach to consider the capture at an impenetrable boundary, and derive an analytical expression for the magnetic force of a cylindrical magnet of finite length on the nanoparticles. This provides a simple and numerically efficient way to study different magnet configurations and their influence on the nanoparticle distribution in three dimensions. Such an in silico model can increase insight into the underlying physics, help to design novel prototypes and serve as a precursor to more complex systems in vivo and in silico.

physics.comp-ph↗
arXiv2023

A highly efficient computational framework for fast scan-resolved simulations of metal additive manufacturing processes on the scale of real parts

This article proposes a novel high-performance computing approach for the prediction of the temperature field in powder bed fusion (PBF) additive manufacturing processes. In contrast to many existing approaches to part-scale simulations, the underlying computational model consistently resolves physical scan tracks without additional heat source scaling, agglomeration strategies or any other heuristic modeling assumptions. A growing, adaptively refined mesh accurately captures all details of the laser beam motion. Critically, the fine spatial resolution required for resolved scan tracks in combination with the high scan velocities underlying these processes mandates the use of comparatively small time steps to resolve the underlying physics. Explicit time integration schemes are well-suited for this setting, while unconditionally stable implicit time integration schemes are employed for the interlayer cool down phase governed by significantly larger time scales. These two schemes are combined and implemented in an efficient fast operator evaluation framework providing significant performance gains and optimization opportunities. The capabilities of the novel framework are demonstrated through realistic AM examples on the centimeter scale including the first scan-resolved simulation of the entire NIST AM Benchmark cantilever specimen, with a computation time of less than one day. Apart from physical insights gained through these simulation examples, also numerical aspects are thoroughly studied on basis of weak and strong parallel scaling tests. As potential applications, the proposed thermal PBF simulation framework can serve as a basis for microstructure and thermo-mechanical predictions on the part-scale, but also to assess the influence of scan pattern and part geometry on melt pool shape and temperature, which are important indicators for well-known process instabilities.

cs.CE↗
arXiv2023

Pressure- and time-dependent alveolar recruitment/derecruitment in a spatially resolved patient-specific computational model for injured human lungs

We present a novel computational model for the dynamics of alveolar recruitment/derecruitment (RD), which reproduces the underlying characteristics typically observed in injured lungs. The basic idea is a pressure- and time-dependent variation of the stress-free reference volume in reduced dimensional viscoelastic elements representing the acinar tissue. We choose a variable reference volume triggered by critical opening and closing pressures in a time-dependent manner from a straightforward mechanical point of view. In the case of (partially and progressively) collapsing alveolar structures, the volume available for expansion during breathing reduces and vice versa, eventually enabling consideration of alveolar collapse and reopening in our model. We further introduce a method for patient-specific determination of the underlying critical parameters of the new alveolar RD dynamics when integrated into the tissue elements, referred to as terminal units, of a spatially resolved physics-based lung model that simulates the human respiratory system in an anatomically correct manner. Relevant patient-specific parameters of the terminal units are herein determined based on medical image data and the macromechanical behavior of the lung during artificial ventilation. We test the whole modeling approach for a real-life scenario by applying it to the clinical data of a mechanically ventilated patient. The generated lung model is capable of reproducing clinical measurements such as tidal volume and pleural pressure during various ventilation maneuvers. We conclude that this new model is an important step toward personalized treatment of ARDS patients by considering potentially harmful mechanisms - such as cyclic RD and overdistension - and might help in the development of relevant protective ventilation strategies to reduce ventilator-induced lung injury (VILI).

physics.med-ph↗
arXiv2023

In silico high-resolution whole lung model to predict the locally delivered dose of inhaled drugs

The big crux with drug delivery to human lungs is that the delivered dose at the local site of action is unpredictable and very difficult to measure, even a posteriori. It is highly subject-specific as it depends on lung morphology, disease, breathing, and aerosol characteristics. Given these challenges, computational approaches have shown potential, but have so far failed due to fundamental methodical limitations. We present and validate a novel in silico model that enables the subject-specific prediction of local aerosol deposition throughout the entire lung. Its unprecedented spatiotemporal resolution allows to track each aerosol particle anytime during the breathing cycle, anywhere in the complete system of conducting airways and the alveolar region. Predictions are shown to be in excellent agreement with in vivo SPECT/CT data for a healthy human cohort. We further showcase the model's capabilities to represent strong heterogeneities in diseased lungs by studying an IPF patient. Finally, high computational efficiency and automated model generation and calibration ensure readiness to be applied at scale. We envision our method not only to improve inhalation therapies by informing and accelerating all stages of (pre-)clinical drug and device development, but also as a more-than-equivalent alternative to nuclear imaging of the lungs.

physics.med-ph↗
arXiv2023

An efficient approach to include transport effects in thin coating layers in electrochemo-mechanical models for all-solid-state batteries

A novel approach is presented to efficiently include transport effects in thin active material coating layers of all-solid-state batteries using a dimensionally reduced formulation embedded into a three-dimensionally resolved coupled electrochemo-mechanical continuum model. In the literature, the effect of coating layers is so far captured by additional zero-dimensional resistances to circumvent the need for an extremely fine mesh resolution. However, a zero-dimensional resistance cannot capture transport phenomena along the coating layer, which can become significant, as we will show in this work. Thus, we propose a model which resolves the thin coating layer in a two-dimensional manifold based on model assumptions in the direction of the thickness. This two-dimensional formulation is monolithically coupled with a three-dimensional model representing the other components of a battery cell. The approach is validated by showing conservation properties and convergence and by comparing the results with those computed with a fully resolved model. Results for realistic microstructures of a battery cell, including coating layers as well as design recommendations for a preferred coating layer, are presented. Based on those results, we show that existing modeling approaches feature remarkable errors when transport along the coating layer is significant, whereas the novel approach resolves this.

physics.chem-ph↗
arXiv2023

An approach to study recruitment/derecruitment dynamics in a patient-specific computational model of an injured human lung

We present a new approach for physics-based computational modeling of diseased human lungs. Our main object is the development of a model that takes the novel step of incorporating the dynamics of airway recruitment/de-recruitment into an anatomically accurate, spatially resolved model of respiratory system mechanics, and the relation of these dynamics to airway dimensions and the biophysical properties of the lining fluid. The importance of our approach is that it potentially allows for more accurate predictions of where mechanical stress foci arise in the lungs, since it is at these locations that injury is thought to arise and propagate from. We match the model to data from a patient with Acute Respiratory Distress Syndrome (ARDS) to demonstrate the potential of the model for revealing the underlying derangements in ARDS in a patient-specific manner. To achieve this, the specific geometry of the lung and its heterogeneous pattern of injury are extracted from medical CT images. The mechanical behavior of the model is tailored to the patient's respiratory mechanics using measured ventilation data. In retrospective simulations of various clinically performed, pressure-driven ventilation profiles, the model adequately reproduces clinical quantities measured in the patient such as tidal volume and change in pleural pressure. The model also exhibits physiologically reasonable lung recruitment dynamics and has the spatial resolution to allow the study of local mechanical quantities such as alveolar strains. This modeling approach advances our ability to perform patient-specific studies in silico, opening the way to personalized therapies that will optimize patient outcomes.

cs.CE↗
arXiv2023

A homogenized constrained mixture model of cardiac growth and remodeling: Analyzing mechanobiological stability and reversal

Cardiac growth and remodeling (G&R) patterns change ventricular size, shape, and function both globally and locally. Biomechanical, neurohormonal, and genetic stimuli drive these patterns through changes in myocyte dimension and fibrosis. We propose a novel microstructure-motivated model that predicts organ-scale G&R in the heart based on the homogenized constrained mixture theory. Previous models, based on the kinematic growth theory, reproduced consequences of G&R in bulk myocardial tissue by prescribing the direction and extent of growth but neglected underlying cellular mechanisms. In our model, the direction and extent of G&R emerge naturally from intra- and extra cellular turnover processes in myocardial tissue constituents and their preferred homeostatic stretch state. We additionally propose a method to obtain a mechanobiologically equilibrated reference configuration. We test our model on an idealized 3D left ventricular geometry and demonstrate that our model aims to maintain tensional homeostasis in hypertension conditions. In a stability map, we identify regions of stable and unstable G&R from an identical parameter set with varying systolic pressures and growth factors. Furthermore, we show the extent of G&R reversal after returning the systolic pressure to baseline following stage 1 and 2 hypertension. A realistic model of organ-scale cardiac G&R has the potential to identify patients at risk of heart failure, enable personalized cardiac therapies, and facilitate the optimal design of medical devices.

q-bio.TO↗
arXiv2023

Towards Additively Manufactured Metamaterials with Powder Inclusions for Controllable Dissipation: The Critical Influence of Packing Density

Particle dampers represent a simple yet effective means to reduce unwanted oscillations when attached to structural components. Powder bed fusion additive manufacturing of metals allows to integrate particle inclusions of arbitrary shape, size and spatial distribution directly into bulk material, giving rise to novel metamaterials with controllable dissipation without the need for additional external damping devices. At present, however, it is not well understood how the degree of dissipation is influenced by the properties of the enclosed powder packing. In the present work, a two-way coupled discrete element - finite element model is proposed allowing for the first time to consistently describe the interaction between oscillating deformable structures and enclosed powder packings. As fundamental test case, the free oscillations of a hollow cantilever beam filled with various powder packings differing in packing density, particle size, and surface properties are considered to systematically study these factors of influence. Critically, it is found that the damping characteristics strongly depend on the packing density of the enclosed powder and that an optimal packing density exists at which the dissipation is maximized. Moreover, it is found that the influence of (absolute) particle size on dissipation is rather small. First-order analytical models for different deformation modes of such powder cavities are derived to shed light on this observation.

cs.CE↗
arXiv2023

A Finite Element Formulation to Three-Dimensionally Resolve Space-Charge Layers in Solid Electrolytes

All-solid-state batteries are seen as promising candidates to replace conventional batteries with liquid electrolytes in many applications. However, they are not yet feasible for many relevant applications. One particular question of interest is the identification of physical effects inside all-solid-state batteries and their quantitative influence on the performance of the entire battery cell. Simulation models can contribute to answering the aforementioned question by systematical studies, e.g. enabling or disabling certain physical effects. Especially the influence of space-charge layers (SCLs) is heavily discussed in the scientific community. So far, the different length scales of SCLs and the microstructure of a battery cell made a spatial discretization of realistic microstructures with resolved SCLs infeasible. However, thermodynamically consistent continuum models which are applied to simplified geometries are already established in the literature. In this work, we propose a model that enables the prediction of the spatial development of SCLs within geometrically resolved microstructures by exploiting that effects in SCLs are predominantly one-dimensional. With the proposed approach it is possible to quantify the geometric influence of realistic microstructures on the formation process of SCLs. SCLs in realistic microstructures remarkably differ from SCLs computed with simplified one-dimensional models which are already established in the literature.

physics.chem-ph↗
arXiv2022

Structure-Preserving Invariant Interpolation Schemes for Invertible Second-Order Tensors

Tensor interpolation is an essential step for tensor data analysis in various fields of application and scientific disciplines. In the present work, novel interpolation schemes for general, i.e., symmetric or non-symmetric, invertible square tensors are proposed. Critically, the proposed schemes rely on a combined polar and spectral decomposition of the tensor data $\boldsymbol{T}\!\!=\!\!\boldsymbol{R}\boldsymbol{Q}^T \!\! \boldsymbolΛ \boldsymbol{Q}$, followed by an individual interpolation of the two rotation tensors $\boldsymbol{R}$ and $\boldsymbol{Q}$ and the positive definite diagonal eigenvalue tensor $\boldsymbolΛ$ resulting from this decomposition. Two different schemes are considered for a consistent rotation interpolation within the special orthogonal group $\mathbb{SO}(3)$, either based on relative rotation vectors or quaternions. For eigenvalue interpolation, three different schemes, either based on the logarithmic weighted average, moving least squares or logarithmic moving least squares, are considered. It is demonstrated that the proposed interpolation procedure preserves the structure of a tensor, i.e., $\boldsymbol{R}$ and $\boldsymbol{Q}$ remain orthogonal tensors and $\boldsymbolΛ$ remains a positive definite diagonal tensor during interpolation, as well as scaling and rotational invariance (objectivity). Based on selected numerical examples considering the interpolation of either symmetric or non-symmetric tensors, the proposed schemes are compared to existing approaches such as Euclidean, Log-Euclidean, Cholesky and Log-Cholesky interpolation. In contrast to these existing methods, the proposed interpolation schemes result in smooth and monotonic evolutions of tensor invariants such as determinant, trace, fractional anisotropy (FA), and Hilbert's anisotropy (HA)...{continued see pdf}

cs.CE↗
arXiv2022

Quantitative analysis of thin metal powder layers via transmission X-ray imaging and discrete element simulation: Roller-based spreading approaches

A variety of tools can be used for spreading metal, ceramic, and polymer feedstocks in powder bed additive manufacturing methods. Rollers are often employed when spreading powders with limited flowability, as arises in powders comprising fine particle sizes or high surface energy materials. Here, we study roller-based powder spreading for powder bed AM using the unique combination of a purpose-built powder spreading testbed with a proven method for X-ray mapping of powder layer depth. We focus on the density and uniformity of nominally 100 micrometer thick layers of roller-spread Ti-6Al-4V and Al-10Si-Mg powders. Our results indicate that when rotation is too rapid, roller-applied shear force impedes the creation of dense and uniform layers from powders of high innate flowability, or where inertial forces driven by particle density dominate cohesive forces. Roller counter-rotation augments the uniformity of cohesive powder layers, primarily though reducing the influence of particle clusters in the flowing powder, which are otherwise shown to cause deep, trench-like streaks. Companion discrete element method (DEM) simulations further contextualize the experiments through isolation of the effects of cohesion on layer attributes. Results suggest that roller motion parameters could apply a strategic level of additional shear force to the flowing powder, thereby mitigating the clumping behavior characteristic of highly cohesive feedstocks while maintaining high layer uniformity.

physics.app-ph↗