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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 125
  • A conforming frictional beam contact model
    Item type: Journal Article
    Karapiperis, Konstantinos; Widmer, Adrian; Pescialli, Elias; et al. (2024)
    Computer Methods in Applied Mechanics and Engineering
    We develop a model for predicting the mechanical behavior of a system of slender one-dimensional bodies (fibers or beams) interacting via frictional contact. Relying on an integral penalty-based formulation, it can robustly capture the behavior in the case of conforming contact occurring over regions of finite size. Two formulations of the model are presented and validated against fully resolved continuum finite element simulations. Overall, the proposed framework is an effective tool in exploring the mechanical behavior of fabrics, textiles as well as three-dimensional frictional architected solids, as demonstrated by the simulation of the effective response of a periodic intertwined metamaterial.
  • 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.
  • Multiphysics modeling of hydrogels with a maximum-entropy-based meshless framework
    Item type: Journal Article
    Castillo-Acuna, Rodrigo; Kochmann, Dennis M. (2025)
    Computer Methods in Applied Mechanics and Engineering
    Hydrogels are soft, stimuli-responsive materials with attractive applications from soft robotics to biomedical engineering. Their multiphysics nature combined with their ability to undergo large deformation and mechanical instability makes their computational modeling challenging. As a potential remedy, we here introduce a meshless multiphysics framework based on enhanced local maximum-entropy (max-ent) interpolants. This formulation, tailored for hydrogel simulations, leverages the flexibility of the meshless max-ent scheme (without the need to remesh up to large deformation and significant distortion), the robustness of the enhanced local max-ent interpolants, and the physio-mechanically coupled monophasic continuum theory of hydrogels (combining a transient Fickian-type diffusion model with quasistatic finite-strain mechanics). The effectiveness of our approach is verified through a series of benchmark tests, including the free swelling of different hydrogel sample geometries in 3D and the deformation of complex 2D and 3D hollow hydrogel structures. Our results demonstrate that the proposed framework maintains stability up to large deformation and large distortions of the initial geometry, thus making it a promising tool for hydrogel simulations, particularly in applications involving complex geometries made possible by recent advances in hydrogel manufacturing, such as 3D printing.
  • Predicting crack nucleation and propagation in brittle materials using Deep Operator Networks with diverse trunk architectures
    Item type: Journal Article
    Kiyani, Elham; Manav, Manav; Kadivar, Nikhil; et al. (2025)
    Computer Methods in Applied Mechanics and Engineering
    Phase-field modeling reformulates fracture problems as energy minimization problems and enables a comprehensive characterization of the fracture process, including crack nucleation, propagation, merging and branching, without relying on ad-hoc assumptions. However, the numerical solution of phase-field fracture problems is characterized by a high computational cost. To address this challenge, in this paper, we employ a deep neural operator (DeepONet) consisting of a branch network and a trunk network to solve brittle fracture problems. We explore three distinct approaches that vary in their trunk network configurations. In the first approach, we demonstrate the effectiveness of a two-step DeepONet, which results in a simplification of the learning task. In the second approach, we employ a physics-informed DeepONet, whereby the mathematical expression of the energy is integrated into the trunk network's loss to enforce physical consistency. The integration of physics also results in a substantially smaller data size needed for training. In the third approach, we replace the neural network in the trunk with a Kolmogorov–Arnold Network and train it without the physics loss. Using these methods, we model crack nucleation in a one-dimensional homogeneous bar under prescribed end displacements, as well as crack propagation and branching in single edge-notched specimens with varying notch lengths subjected to tensile and shear loading. We show that the networks predict the solution fields accurately and the error in the predicted fields is localized near the crack.
  • Simplifying FFT-based methods for solid mechanics with automatic differentiation
    Item type: Journal Article
    Pundir, Mohit; Kammer, David S. (2025)
    Computer Methods in Applied Mechanics and Engineering
    Fast-Fourier Transform (FFT) methods have been widely used in solid mechanics to address complex homogenization problems. However, current FFT-based methods face challenges that limit their applicability to intricate material models or complex mechanical problems. These challenges include the manual implementation of constitutive laws and the use of computationally expensive and complex algorithms to couple microscale mechanisms to macroscale material behavior. Here, we incorporate automatic differentiation (AD) within the FFT framework to mitigate these challenges. We demonstrate that AD-enhanced FFT-based methods can derive stress and tangent stiffness directly from energy density functionals, facilitating the extension of FFT-based methods to more intricate material models. Additionally, automatic differentiation simplifies the calculation of homogenized tangent stiffness for microstructures with complex architectures and constitutive properties. This enhancement renders current FFT-based methods more modular, enabling them to tackle homogenization in complex multiscale systems, especially those involving multiphysics processes. Furthermore, we illustrate the use of the AD-enhanced FFT method for problems that extend beyond homogenization, such as uncertainty quantification and topology optimization where automatic differentiation simplifies the computation of sensitivities. Our work will simplify the numerical implementation of FFT-based methods for complex solid mechanics problems.
  • 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.
  • H(curl)-based approximation of the Stokes problem with weakly enforced no-slip boundary conditions
    Item type: Journal Article
    Boon , Wietse M.; Tonnon , Wouter; Zampa , Enrico (2026)
    Computer Methods in Applied Mechanics and Engineering
    In this work, we show how to impose no-slip boundary conditions for an H(curl,Ω)-based formulation for incompressible Stokes flow, which is used in structure-preserving discretizations of Navier-Stokes and magnetohydrodynamics equations. At first glance, it seems straightforward to apply no-slip boundary conditions: the tangential part is an essential boundary condition on H(curl,Ω) and the normal component can be naturally enforced through integration-by-parts of the divergence term. However, we show that this can lead to an ill-posed discretization and propose a Nitsche-based finite element method instead. We analyze the discrete system, establishing stability and deriving a priori error estimates. Numerical experiments validate our analysis and demonstrate optimal convergence rates for the velocity field.
  • 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.
  • A non-consistent start-up procedure for contact problems with large load-steps
    Item type: Journal Article
    Zavarise, Giorgio; De Lorenzis, Laura; Taylor, Robert L. (2012)
    Computer Methods in Applied Mechanics and Engineering
  • 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.
Publications 1 - 10 of 125