arXiv subjects

Stefanie Reese

Publications and source records attributed to Stefanie Reese.

At least 19 recordsLinked to original sources

arXiv2026

Component-wise hyperreduction for nonlinear solid mechanics problems

Hyperreduced nonlinear solid-mechanics components can be generated offline and reused as transferable building blocks across different assemblies, boundary conditions, meshes, material parameters, and constitutive models. We use proper orthogonal decomposition (POD) and energy conserving sampling and weighting (ECSW) on the component level and connect the substructures by mortar mesh tying. The POD modes and the ECSW weights and elements are computed offline from simulations of single components and the finite rigid body motions are treated by 12 additional rigid body modes per substructure. The numerical examples demonstrate errors below 1 \% for large quasi-static assemblies while evaluating less than 10 \% of the elements. The same component bases and ECSW elements are successfully reused for finite-strain viscoelastic dynamics, although they were trained only on elastic Neo-Hookean component simulations. These results indicate that component-wise hyperreduction can provide reusable reduced building blocks for modular nonlinear solid-mechanics simulations.

cs.CE↗

arXiv2026

Reduced integration with scaled boundary parametrization for virtual elements at finite strains

This contribution presents an alternative stabilization technique for the virtual element method (VEM) based on reduced integration combined with a scaled boundary parametrization. To this end, a Taylor series expansion of the constitutive quantities with respect to the sectional center is carried out, enabling analytical integration of the weak form and reducing the need for integration points to only one per section. The accuracy of the proposed formulation is shown by several numerical examples, including a non-linear patch test. Different loading, e.g. compression under large deformations, and material conditions, such as hyperelastic anisotropy and elasto-plasticity, are considered. The biquadratic serendipity finite element formulation (Q2) and the low-order finite element formulation with hourglass stabilization (Q1STc+) are used for comparison. While the patch test was not fulfilled using higher order shape functions, the formulation led to good results and was able to capture the structure's response accurately. Furthermore, the formulation performed better when the physical element resembled the pre-assigned parent elements. The example of the asymmetrically notched specimen under elasto-plastic material behavior showed that the proposed formulation is able to capture inelasticities.

cs.CE↗

arXiv2026

Development of a Model Order Reduced Arbitrary Lagrangian Eulerian (MORALE) formulation for structures subjected to dynamic moving loads

In recent developments, it has been demonstrated that the Arbitrary Lagrangian Eulerian (ALE) formulation can be utilized to improve computational efficiency, when simulating the response of structures subjected to moving loads. It is also well established in literature, that Model Order Reduction (MOR) techniques significantly enhance calculation speed. This contribution details the combination of both these tools into a novel Model Order Reduced Arbitrary Lagrangian Eulerian (MORALE) formulation. Both hyperelastic and viscoelastic material models are considered. Simulations of pavement structures subjected to moving loads are then carried out, which show a significant enhancement in computational speed and efficiency. Such an efficient and fast simulation framework is of vital importance in technologies such as digital twins of roadway infrastructure (like pavements), as it enables engineers to quickly run what-if analyses and make informed decisions about the management of the structure under consideration.

math.NA↗

arXiv2025

Multi-field decomposed hyper-reduced order modeling of damage-plasticity simulations

This paper presents a multi-field decomposed approach for hyper-reduced order modeling to overcome the limitations of traditional model reduction techniques for gradient-extended damage-plasticity simulations. The discrete empirical interpolation method (DEIM) and the energy-conserving sampling and weighting method (ECSW) are extended to account for the multi-field nature of the problem. Both methods yield stable reduced order simulations, while significantly reducing the computational cost compared to full-order simulations. Two numerical examples are presented to demonstrate the performance and limitations of the proposed approaches. The decomposed ECSW method has overall higher accuracy and lower computational cost than the decomposed DEIM method.

cs.CE↗

arXiv2025

A unified multi-perspective quadratic manifold for mitigating the Kolmogorov barrier in multiphysics damage

In multiphysics damage problems, material degradation is often modeled using local or global damage variables, whose evolution introduces strong nonlinearities and significant computational costs. Linear projection-based reduced-order models (ROMs) are widely used to accelerate these simulations but often fail to capture complex nonlinear damage evolution effectively. This limitation arises from the slow decay of the Kolmogorov n-width, which leads to a phenomenon known as the Kolmogorov barrier in linear approximation. To overcome this challenge, this study proposes a novel unified multi-perspective (multi-field and multi-state) quadratic manifold-based ROM framework for thermo-mechanically coupled damage-plasticity problems. A key feature lies in a multi-field and multi-state decomposition strategy that is grounded in the material's physical response to guide the selection of mode numbers for each coupled field. Moreover, the framework decouples both material states and physical fields, providing clearer insights into the contributions and interactions of each field within the overall multiphysics simulation. Benchmark tests demonstrate that the proposed approach mitigates the Kolmogorov barrier of linear projection-based ROMs by ensuring a smooth and monotonic decrease in error as the number of modes increases. The proposed multi-perspective quadratic manifold framework offers a robust and flexible approach for efficiently reducing complex damage-involved multiphysics problems and shows strong potential for industrial applications.

math-ph↗

arXiv2025

A Spectral-based Physics-informed Finite Operator Learning for Prediction of Mechanical Behavior of Microstructures

A novel physics-informed operator learning technique based on spectral methods is introduced to model the complex behavior of heterogeneous materials. The Lippmann-Schwinger operator in Fourier space is employed to construct physical constraints with minimal computational overhead, effectively eliminating the need for automatic differentiation. The introduced methodology accelerates the training process by enabling gradient construction on a fixed, finite discretization in Fourier space. Later, the spectral physics-informed finite operator learning (SPiFOL) framework is built based on this discretization and trained to map the arbitrary shape of microstructures to their mechanical responses (strain fields) without relying on labeled data. The training is done by minimizing equilibrium in Fourier space concerning the macroscopic loading condition, which also guarantees the periodicity. SPiFOL, as a physics-informed operator learning method, enables rapid predictions through forward inference after training. To ensure accuracy, we incorporate physical constraints and diversify the training data. However, performance may still degrade for out-of-distribution microstructures. SPiFOL is further enhanced by integrating a Fourier Neural Operator (FNO). Compared to the standard data-driven FNO, SPiFOL shows higher accuracy in predicting stress fields and provides nearly resolution-independent results. Additionally, its zero-shot super-resolution capabilities are explored in heterogeneous domains. Finally, SPiFOL is extended to handle 3D problems and further adapted to finite elasticity, demonstrating the robustness of the framework in handling nonlinear mechanical behavior. The framework shows great potential for efficient and scalable prediction of mechanical responses in complex material systems while also reducing the training time required for training physics-informed neural operators.

cond-mat.mtrl-sci↗

arXiv2025

Reduced-order structure-property linkages for stochastic metamaterials

The capabilities of additive manufacturing have facilitated the design and production of mechanical metamaterials with diverse unit cell geometries. Establishing linkages between the vast design space of unit cells and their effective mechanical properties is critical for the efficient design and performance evaluation of such metamaterials. However, physics-based simulations of metamaterial unit cells across the entire design space are computationally expensive, necessitating a materials informatics framework to efficiently capture complex structure-property relationships. In this work, principal component analysis of 2-point correlation functions is performed to extract the salient features from a large dataset of randomly generated 2D metamaterials. Physics-based simulations are performed using a fast Fourier transform (FFT)-based homogenization approach to efficiently compute the homogenized effective elastic stiffness across the extensive unit cell designs. Subsequently, Gaussian process regression is used to generate reduced-order surrogates, mapping unit cell designs to their homogenized effective elastic constant. It is demonstrated that the adopted workflow enables a high-value low-dimensional representation of the voluminous stochastic metamaterial dataset, facilitating the construction of robust structure-property maps. Finally, an uncertainty-based active learning framework is utilized to train a surrogate model with a significantly smaller number of data points compared to the original full dataset. It is shown that a dataset as small as $0.61\%$ of the entire dataset is sufficient to generate accurate and robust structure-property maps.

cs.CE↗

arXiv2025

A Comprehensive Framework for Predictive Computational Modeling of Growth and Remodeling in Tissue-Engineered Cardiovascular Implants

Developing clinically viable tissue-engineered cardiovascular implants remains a formidable challenge. Achieving reliable and durable outcomes requires a deeper understanding of the fundamental mechanisms driving tissue evolution during in vitro maturation. Although considerable progress has been made in modeling soft tissue growth and remodeling, studies focused on the early stages of tissue engineering remain limited. Here, we present a general, thermodynamically consistent model to predict tissue evolution and mechanical response throughout maturation. The formulation utilizes a stress-driven homeostatic surface to capture volumetric growth, coupled with an energy-based approach to describe collagen densification via the strain energy of the fibers. We further employ a co-rotated intermediate configuration to ensure the model's consistency and generality. The framework is demonstrated with two numerical examples: a uniaxially constrained tissue strip validated against experimental data, and a biaxially constrained specimen subjected to a perturbation load. These results highlight the potential of the proposed model to advance the design and optimization of tissue-engineered implants with clinically relevant performance.

cs.CE↗

arXiv2025

An enhanced single Gaussian point continuum finite element formulation using automatic differentiation

This contribution presents an improved low-order 3D finite element formulation with hourglass stabilization using automatic differentiation (AD). Here, the former Q1STc formulation is enhanced by an approximation-free computation of the inverse Jacobian. To this end, AD tools automate the computation and allow a direct evaluation of the inverse Jacobian, bypassing the need for a Taylor series expansion. Thus, the enhanced version, Q1STc+, is introduced. Numerical examples are conducted to compare the performance of both element formulations for finite strain applications, with particular focus on distorted meshes. Moreover, the performance of the new element formulation for an elasto-plastic material is investigated. To validate the obtained results, a volumetric locking-free element based on scaled boundary parametrization is used. Both the implementation of the element routine Q1STc+ and the corresponding material subroutine are made accessible to the public at https://doi.org/10.5281/zenodo.14259791

cs.CE↗

arXiv2024

Component based model order reduction with mortar tied contact for nonlinear quasi-static mechanical problems

In this work, we present a model order reduction technique for nonlinear structures assembled from components.The reduced order model is constructed by reducing the substructures with proper orthogonal decomposition and connecting them by a mortar-tied contact formulation. The snapshots for the substructure projection matrices are computed on the substructure level by the proper orthogonal decomposition (POD) method. The snapshots are computed using a random sampling procedure based on a parametrization of boundary conditions. To reduce the computational effort of the snapshot computation full-order simulations of the substructures are only computed when the error of the reduced solution is above a threshold. In numerical examples, we show the accuracy and efficiency of the method for nonlinear problems involving material and geometric nonlinearity as well as non-matching meshes. We are able to predict solutions of systems that we did not compute in our snapshots.

cs.CE↗

arXiv2024

A two-scale computational homogenization approach for elastoplastic truss-based lattice structures

The revolutionary advancements in metal additive manufacturing have enabled the production of alloy-based lattice structures with complex geometrical features and high resolutions. This has encouraged the development of nonlinear material models, including plasticity, damage, etc., for such materials. However, the prohibitive computational cost arising from the high number of degrees of freedom for engineering structures composed of lattice structures highlights the necessity of homogenization techniques, such as the two-scale computational homogenization method. In the present work, a two-scale homogenization approach with on-the-fly exchange of information is adopted to study the elastoplastic behavior of truss-based lattice structures. The macroscopic homogenized structure is represented by a two-dimensional continuum, while the underlying microscale lattices are modeled as a network of one-dimensional truss elements. This helps to significantly reduce the associated computational cost by reducing the microscopic degrees of freedom. The microscale trusses are assumed to exhibit an elastoplastic material behavior characterized by a combination of nonlinear exponential isotropic hardening and linear kinematic hardening. Through multiple numerical examples, the performance of the adopted homogenization approach is examined by comparing forces and displacements with direct numerical simulations of discrete structures for three types of stretching-dominated lattice topologies, including triangular, X-braced and X-Plus-braced unit cells. Furthermore, the principle of scale separation, which emphasizes the need for an adequate separation between the macroscopic and microscopic characteristic lengths, is investigated.

cs.CE↗

arXiv2024

FFT-based surrogate modeling of auxetic metamaterials with real-time prediction of effective elastic properties and swift inverse design

Auxetic structures, known for their negative Poisson's ratio, exhibit effective elastic properties heavily influenced by their underlying structural geometry and base material properties. While periodic homogenization of auxetic unit cells can be used to investigate these properties, it is computationally expensive and limits design space exploration and inverse analysis. In this paper, surrogate models are developed for the real-time prediction of the effective elastic properties of auxetic unit cells with orthogonal voids of different shapes. The unit cells feature orthogonal voids in four distinct shapes, including rectangular, diamond, oval, and peanut-shaped voids, each characterized by specific void diameters. The generated surrogate models accept geometric parameters and the elastic properties of the base material as inputs to predict the effective elastic constants in real-time. This rapid evaluation enables a practical inverse analysis framework for obtaining the optimal design parameters that yield the desired effective response. The fast Fourier transform (FFT)-based homogenization approach is adopted to efficiently generate data for developing the surrogate models, bypassing concerns about periodic mesh generation and boundary conditions typically associated with the finite element method (FEM). The performance of the generated surrogate models is rigorously examined through a train/test split methodology, a parametric study, and an inverse problem. Finally, a graphical user interface (GUI) is developed, offering real-time prediction of the effective tangent stiffness and performing inverse analysis to determine optimal geometric parameters.

cs.CE↗

arXiv2024

An anisotropic, brittle damage model for finite strains with a generic damage tensor regularization

This paper establishes a universal framework for the nonlocal modeling of anisotropic damage at finite strains. By the combination of two recent works, the new framework allows for the flexible incorporation of different established hyperelastic finite strain material formulations into anisotropic damage whilst ensuring mesh-independent results by employing a generic set of micromorphic gradient-extensions. First, the anisotropic damage model, generally satisfying the damage growth criterion, is investigated for the specific choice of a Neo-Hookean material on a single element. Next, the model is applied with different gradient-extensions in structural simulations of an asymmetrically notched specimen to identify an efficient choice in the form of a volumetric-deviatoric regularization. Thereafter, the universal framework, which is without loss of generality here specified for a Neo-Hookean material with a volumetric-deviatoric gradient-extension, successfully serves for the complex simulation of a pressure loaded rotor blade. After acceptance of the manuscript, we make the codes of the material subroutines accessible to the public at https://doi.org/10.5281/zenodo.11171630.

cs.CE↗

arXiv2024

A finite element-based physics-informed operator learning framework for spatiotemporal partial differential equations on arbitrary domains

We propose a novel finite element-based physics-informed operator learning framework that allows for predicting spatiotemporal dynamics governed by partial differential equations (PDEs). The proposed framework employs a loss function inspired by the finite element method (FEM) with the implicit Euler time integration scheme. A transient thermal conduction problem is considered to benchmark the performance. The proposed operator learning framework takes a temperature field at the current time step as input and predicts a temperature field at the next time step. The Galerkin discretized weak formulation of the heat equation is employed to incorporate physics into the loss function, which is coined finite operator learning (FOL). Upon training, the networks successfully predict the temperature evolution over time for any initial temperature field at high accuracy compared to the FEM solution. The framework is also confirmed to be applicable to a heterogeneous thermal conductivity and arbitrary geometry. The advantages of FOL can be summarized as follows: First, the training is performed in an unsupervised manner, avoiding the need for a large data set prepared from costly simulations or experiments. Instead, random temperature patterns generated by the Gaussian random process and the Fourier series, combined with constant temperature fields, are used as training data to cover possible temperature cases. Second, shape functions and backward difference approximation are exploited for the domain discretization, resulting in a purely algebraic equation. This enhances training efficiency, as one avoids time-consuming automatic differentiation when optimizing weights and biases while accepting possible discretization errors. Finally, thanks to the interpolation power of FEM, any arbitrary geometry can be handled with FOL, which is crucial to addressing various engineering application scenarios.

cs.LG↗

arXiv2024

A multi-field decomposed model order reduction approach for thermo-mechanically coupled gradient-extended damage simulations

Numerical simulations are crucial for comprehending how engineering structures behave under extreme conditions, particularly when dealing with thermo-mechanically coupled issues compounded by damage-induced material softening. However, such simulations often entail substantial computational expenses. To mitigate this, the focus has shifted towards employing model order reduction (MOR) techniques, which hold promise for accelerating computations. Yet, applying MOR to highly nonlinear, multi-physical problems influenced by material softening remains a relatively new area of research, with numerous unanswered questions. Addressing this gap, this study proposes and investigates a novel multi-field decomposed MOR technique, rooted in a snapshot-based Proper Orthogonal Decomposition-Galerkin (POD-G) projection approach. Utilizing a recently developed thermo-mechanically coupled gradient-extended damage-plasticity model as a case study, this work demonstrates that splitting snapshot vectors into distinct physical fields (displacements, damage, temperature) and projecting them onto separate lower-dimensional subspaces can yield more precise and stable outcomes compared to conventional methods. Through a series of numerical benchmark tests, our multi-field decomposed MOR technique demonstrates its capacity to significantly reduce computational expenses in simulations involving severe damage, while maintaining a high level of accuracy.

math.AP↗

arXiv2024

A finite operator learning technique for mapping the elastic properties of microstructures to their mechanical deformations

To obtain fast solutions for governing physical equations in solid mechanics, we introduce a method that integrates the core ideas of the finite element method with physics-informed neural networks and concept of neural operators. This approach generalizes and enhances each method, learning the parametric solution for mechanical problems without relying on data from other resources (e.g. other numerical solvers). We propose directly utilizing the available discretized weak form in finite element packages to construct the loss functions algebraically, thereby demonstrating the ability to find solutions even in the presence of sharp discontinuities. Our focus is on micromechanics as an example, where knowledge of deformation and stress fields for a given heterogeneous microstructure is crucial for further design applications. The primary parameter under investigation is the Young's modulus distribution within the heterogeneous solid system. Our investigations reveal that physics-based training yields higher accuracy compared to purely data-driven approaches for unseen microstructures. Additionally, we offer two methods to directly improve the process of obtaining high-resolution solutions, avoiding the need to use basic interpolation techniques. First is based on an autoencoder approach to enhance the efficiency for calculation on high resolution grid point. Next, Fourier-based parametrization is utilized to address complex 2D and 3D problems in micromechanics. The latter idea aims to represent complex microstructures efficiently using Fourier coefficients. Comparisons with other well-known operator learning algorithms, further emphasize the advantages of the newly proposed method.

cs.LG↗

arXiv2024

In silico reproduction of the pathophysiology of in-stent restenosis

The occurrence of in-stent restenosis following percutaneous coronary intervention highlights the need for the creation of computational tools that can extract pathophysiological insights and optimize interventional procedures on a patient-specific basis. In light of this, a comprehensive framework encompassing multiple physical phenomena is introduced in this work. This framework effectively captures the intricate interplay of chemical, mechanical, and biological factors. In addition, computational approaches for the extraction of hemodynamic indicators that modulate the severity of the restenotic process are devised. Thus, this marks a significant stride towards facilitating computer-assisted clinical methodologies.

physics.bio-ph↗

arXiv2024

In-silico Analysis of Hemodynamic Indicators in Idealized Stented Coronary Arteries for Varying Stent Indentation

In this work, we investigate the effects of stent indentation on hemodynamic indicators in stented coronary arteries. Our aim is to assess in-silico risk factors for in-stent restenosis (ISR) and thrombosis after stent implantation. The proposed model is applied to an idealized artery with Xience V stent for four indentation percentages and three mesh refinements. We analyze the patterns of hemodynamic indicators arising from different stent indentations and propose an empirical frequency analysis of time-averaged WSS (TAWSS), oscillatory shear index (OSI), and relative residence time (RRT). We observe that higher indentations display higher frequency of critically low TAWSS and non-physiological OSI and RRT. Furthermore, an appropriate mesh refinement is needed for accurate representation of hemodynamics in the stent vicinity. The results provide physics-based evidence for the correlation between high indentation and ISR.

physics.med-ph↗