Journal: Computer Methods in Applied Mechanics and Engineering

Abbreviation

Comput. Methods Appl. Mech. Eng.

Publisher

Elsevier

Journal Volumes

ISSN

0045-7825
1879-2138

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Publications 1 - 10 of 122
  • Investigation of the influence of viscoelasticity on oncotripsy
    Item type: Journal Article
    Heyden, Stefanie; Ortiz, Michael (2017)
    Computer Methods in Applied Mechanics and Engineering
    Oncotripsy has recently been proposed as a means of selectively targeting cancer cells via resonant harmonic excitation (Heyden and Ortiz, 2016). The method makes use of aberrations in material properties of cancerous cells which allow to induce local resonance up to membrane lysis in cancerous cells while leaving healthy cells intact. Here, we explore the influence of viscoelasticity on the oncotripsy effect. Based on Rayleigh damping, we derive viscoelastic target frequencies and simulate the fully nonlinear transient response of healthy and cancerous cells at resonance. Results confirm the viability of oncotripsy with viscoelastic material behavior of cell constituents accounted for.
  • Second-order phase-field formulations for anisotropic brittle fracture
    Item type: Journal Article
    Gerasimov, Tymofiy; De Lorenzis, Laura (2022)
    Computer Methods in Applied Mechanics and Engineering
    We address brittle fracture in anisotropic materials featuring two-fold and four-fold symmetric fracture toughness. For these two classes, we develop two variational phase-field models based on the family of regularizations proposed by Focardi (2001), for which Γ-convergence results hold. Since both models are of second order, as opposed to the previously available fourth-order models for four-fold symmetric fracture toughness, they do not require basis functions of C1-continuity nor mixed variational principles for finite element discretization. For the four-fold symmetric formulation we show that the standard quadratic degradation function is unsuitable and devise a procedure to derive a suitable one. The performance of the new models is assessed via several numerical examples that simulate anisotropic fracture under anti-plane shear loading. For both formulations at fixed displacements (i.e. within an alternate minimization procedure), we also provide some existence and uniqueness results for the phase-field solution.
  • Sparse data assimilation for under-resolved large-eddy simulations
    Item type: Journal Article
    Plogmann, Justin; Brenner, Oliver; Jenny, Patrick (2026)
    Computer Methods in Applied Mechanics and Engineering
    The need for accurate and fast scale-resolving simulations of fluid flows, where turbulent dispersion is a crucial physical feature, is evident. Large-eddy simulations (LES) are computationally more affordable than direct numerical simulations, but their accuracy depends on sub-grid scale models and the quality of the computational mesh. In order to compensate related errors, a data assimilation approach for LES is devised in this work. The presented method is based on variational assimilation of sparse time-averaged velocity reference data. Working with the time-averaged LES momentum equation allows to employ a stationary discrete adjoint method. Therefore, a stationary corrective force in the unsteady LES momentum equation is iteratively updated within the gradient-based optimization framework in conjunction with the adjoint gradient. After data assimilation, corrected anisotropic Reynolds stresses are inferred from the stationary corrective force. Ultimately, this corrective force that acts on the mean velocity is replaced by a term that scales the velocity fluctuations through nudging of the corrected anisotropic Reynolds stresses. Efficacy of the proposed framework is demonstrated for turbulent flow over periodic hills and around a square cylinder. Coarse meshes are leveraged to further enhance the speed of the optimization procedure. Time- and spanwise-averaged velocity reference data from high-fidelity simulations is taken from the literature. Our results demonstrate that adjoint-based assimilation of averaged velocity enables the optimization of the mean flow, vortex shedding frequency (i. e., Strouhal number), and anisotropic Reynolds stresses. This highlights the superiority of scale-resolving simulations such as LES over simulations based on the (unsteady) Reynolds-averaged equations.
  • Recurrent neural network plasticity models: Unveiling their common core through multi-task learning
    Item type: Journal Article
    Heidenreich, Julian N.; Mohr, Dirk (2024)
    Computer Methods in Applied Mechanics and Engineering
    Recurrent neural network models are known to be particularly suitable for data-driven constitutive modeling due to their built-in memory variables. The main challenge preventing their widespread application to engineering materials lies in their excessive need of data for training. Here, we postulate that RNN models of elasto-plastic solids feature a large common core that is shared by all materials of the same class. The common core is complemented by material-specific layers with parameters that vary from material-to-material. After training RNN models for 25 different von Mises materials, we identify the common core of a multi-task model. Furthermore, we demonstrate through ensemble transfer learning that adding a new material to the multi-task model requires datasets that are two to three orders of magnitude smaller than the datasets needed for training an RNN from scratch. In addition, to multi-task learning, we introduce probabilistic ensembles of RNN plasticity models to quantify the epistemic uncertainty. A deep drawing simulation is performed to demonstrate the superior generalization capabilities of RNNs identified via multi-task learning as compared to those obtained through single task training.
  • A scalable, matrix-free multigrid preconditioner for finite element discretizations of heterogeneous Stokes flow
    Item type: Journal Article
    May, Dave A.; Brown, Jed; Le Pourhiet, Laetitia (2015)
    Computer Methods in Applied Mechanics and Engineering
    In this paper we describe a computational methodology that is specifically designed for studying three-dimensional geodynamic processes governed by heterogeneous visco-plastic Stokes flow. The method employs a hybrid spatial discretization consisting of a Q2-P1disc mixed finite element formulation for the Stokes problem, coupled to a material-point formulation which is used for representing material state and history-dependent variables. The applicability and practicality of this methodology is realized through the development of an efficient, scalable and robust variable viscosity Stokes preconditioner. In this work, these objectives are achieved through exploiting matrix-free operators and a geometric multigrid preconditioner employing hybrid coarse level operators, Chebyshev smoothers and hybrid Krylov coarse level solvers. The robustness and parallel efficiency of this strategy is demonstrated using an idealized geodynamic model. Lastly, we apply the new methodology to study geodynamic models of continental rifting and break-up in order to understand the diverse range of passive continental margins we observe on Earth today.
  • Learning physics-consistent material behavior from dynamic displacements
    Item type: Journal Article
    Han, Zhichao; Pundir, Mohit; Fink, Olga; et al. (2025)
    Computer Methods in Applied Mechanics and Engineering
    Accurately modeling the mechanical behavior of materials is crucial for numerous engineering applications. The quality of these models depends directly on the accuracy of the constitutive law that defines the stress–strain relation. However, discovering these constitutive material laws remains a significant challenge, in particular when only material deformation data is available. To address this challenge, unsupervised machine learning methods have been proposed to learn the constitutive law from deformation data. Nonetheless, existing approaches have several limitations: they either fail to ensure that the learned constitutive relations are consistent with physical principles, or they rely on boundary force data for training which are unavailable in many in-situ scenarios. Here, we introduce a machine learning approach to learn physics-consistent constitutive relations solely from material deformation without boundary force information. This is achieved by considering a dynamic formulation rather than static equilibrium data and applying an input convex neural network (ICNN). We validate the effectiveness of the proposed method on a diverse range of hyperelastic material laws. We demonstrate that it is robust to a significant level of noise and that it converges to the ground truth with increasing data resolution. We also show that the model can be effectively trained using a displacement field from a subdomain of the test specimen and that the learned constitutive relation from one material sample is transferable to other samples with different geometries. The developed methodology provides an effective tool for discovering constitutive relations. It is, due to its design based on dynamics, particularly suited for applications to strain-rate-dependent materials and situations where constitutive laws need to be inferred from in-situ measurements without access to global force data.
  • A stable discontinuous Galerkin method for linear elastodynamics in 3D geometrically complex elastic solids using physics based numerical fluxes
    Item type: Journal Article
    Duru, Kenneth; Rannabauer, Leonhard; Gabriel, Alice-Agnes; et al. (2022)
    Computer Methods in Applied Mechanics and Engineering
    Time-stable, high order accurate and explicit numerical methods are effective for hyperbolic wave propagation problems. As a result of the complexities of real geometries, internal interfaces and nonlinear boundary and interface conditions, discontinuities and sharp wave fronts may become fundamental features of the solution. Therefore, geometrically flexible and adaptive numerical algorithms are crucial for high fidelity and efficient simulations of wave phenomena in many applications. Adaptive curvilinear meshes hold promise to minimise the effort to represent complicated geometries or heterogeneous material data avoiding the bottleneck of feature-preserving meshing. To enable the design of stable DG methods on three space dimensional (3D) curvilinear elements we construct a structure preserving skew-symmetric coordinate transformation motivated by the underlying physics. Using a physics-based numerical penalty-flux, we develop a 3D provably energy-stable discontinuous Galerkin finite element approximation of the elastic wave equation in geometrically complex and heterogeneous media. By construction, our numerical flux is upwind and yields a discrete energy estimate analogous to the continuous energy estimate. The ability to treat conforming and non-conforming curvilinear elements allows for flexible adaptive mesh refinement strategies. The numerical scheme has been implemented in ExaHyPE, a simulation engine for parallel dynamically adaptive simulations of wave problems on adaptive Cartesian meshes. We present 3D numerical experiments of wave propagation in heterogeneous isotropic and anisotropic elastic solids demonstrating stability and high order accuracy. We demonstrate the potential of our approach for computational seismology in a regional wave propagation scenario in a geologically constrained 3D model including the geometrically complex free-surface topography of Mount Zugspitze, Germany.
  • A Bayesian framework for constitutive model identification via use of full field measurements, with application to heterogeneous materials
    Item type: Journal Article
    Jafari, Abbas; Vlachas, Konstantinos; Chatzi, Eleni; et al. (2025)
    Computer Methods in Applied Mechanics and Engineering
    In this paper, we present a Bayesian framework for the identification of the parameters of nonlinear constitutive material laws using full-field displacement measurements. The concept of force-based Finite Element Model Updating (FEMU-F) is employed, which relies on the availability of measurable quantities such as displacements and external forces. The proposed approach particularly unfolds the advantage of FEMU-F, as opposed to the conventional FEMU, by directly incorporating information from full-field measured displacements into the model. This feature is well-suited for heterogeneous materials with softening, where the localization zone depends on the random microstructure. Besides, to account for uncertainties in the measured displacements, we treat displacements as additional unknown variables to be identified, alongside the constitutive parameters. A variational Bayesian scheme is then employed to identify these unknowns via approximate posteriors under the assumption of multivariate normal distributions. An optimization problem is then formulated and solved iteratively, aiming to minimize the discrepancy between true and approximate posteriors. The benefit of the proposed approach lies in the stochastic nature of the formulation, which allows to tackle uncertainties related to model parameters and measurement noise. We verify the efficacy of our proposed framework on two simulated examples using gradient damage model with a path-dependent nonlinear constitutive law. Based on a nonlocal equivalent strain norm, this constitutive model can simulate a localized damage zone representing softening and cracking. The first example illustrates an application of the FEMU-F approach to cracked structures including sensitivity studies related to measurement noise and parameters of the prior distributions. In this example, the variational Bayesian solver demonstrates a sizable advantage in terms of computational efficiency compared to a traditional least-square optimizer. The second example demonstrates a sub-domain analysis to tackle challenges associated with limited domain knowledge such as uncertain boundary conditions.
  • Moment-based, univariate n-point quadrature rules in application to the full network model of rubber elasticity
    Item type: Journal Article
    Britt, Ben R.; Ehret, Alexander Edmund (2024)
    Computer Methods in Applied Mechanics and Engineering
    In this contribution we provide numerical methods to implement full network models with particular application to affine isotropic networks as they are frequently applied in theories of rubber elasticity. Unlike the common approaches, the average of the single chains’ responses is not obtained by spherical integration but by solving a univariate integral expressed in terms of the squared stretch of a fibre's or chain's end-to-end vector. In addition to the free energy function of these individual elements the methods are informed by the statistical moments of the distribution of stretch in the network, which throughout the work is assumed to be determined by affine kinematics. We exemplify the proposed procedure for two quadrature methods, which distinguish in terms of the positions of the n integration points and the corresponding weights. While the first method uses constant equal weights of 1/n and hence only requires the computation of n integration points, the second, Gauss-type method also requires the determination of the corresponding weights and builds on a recent development, previously implemented for up to 3 points (Britt & Ehret, Comput. Methods Appl. Mech. Engrg. 415, 2023). However, the structure of the solution strategy applies to a wider range of univariate quadrature rules. Both methods exemplified here can be made exact for polynomial chain free energy functions of arbitrary order, and are illustrated in application to the affine full network model of rubber elasticity with non-Gaussian chains. The results indicate high accuracy of the new methods and therefore identify them as useful and efficient alternatives to the existing approaches for computing the full network response.
  • History-Matching of imbibition flow in fractured porous media Using Physics-Informed Neural Networks (PINNs)
    Item type: Journal Article
    Abbasi, Jassem; Moseley, Ben; Kurotori, Takeshi; et al. (2025)
    Computer Methods in Applied Mechanics and Engineering
    In this work, we propose a workflow based on physics-informed neural networks (PINNs) to model multiphase fluid flow in fractured porous media. After validating the workflow in forward and inverse modeling of a synthetic problem of flow in fractured porous media, we applied it to a real experimental dataset in which brine is injected at a constant pressure drop into a CO2 saturated naturally fractured shale core plug. The exact spatial positions of natural fractures and the dynamic in-situ distribution of fluids were imaged using a CT-scan setup. To model the targeted system, we followed a domain decomposition approach for matrix and fractures and a multi-network architecture for the separate calculation of water saturation and pressure. The flow equations in the matrix, fractures and interplay between them were solved during training. Prior to fully-coupled simulations, we suggested pre-training the model. This aided in a more efficient and successful training of the coupled system. Both for the synthetic and experimental inverse problems, we determined flow parameters within the matrix and the fractures. Multiple random initializations of network and system parameters were performed to assess the uncertainty and uniqueness of the resulting calculations. The results confirmed the precision of the inverse calculated parameters in retrieving the main flow characteristics of the system. The consideration of matrix-fracture interactions is commonly overlooked in existing workflows. Accounting for them led to several orders of magnitude variations in the calculated flow properties compared to not accounting for them. The proposed PINNs-based workflow offer a reliable and computationally efficient solution for inverse modeling of multiphase flow in fractured porous media, achieved through history-matching noisy and multi-fidelity experimental measurements.
Publications 1 - 10 of 122