A novel Isogeometric topology optimization (ITO) method considering stress constraint and load uncertainties is proposed for the fiber reinforced composite structures. Firstly, with the density and fiber orientations at the control points of Non-Uniform Rational B-Splines (NURBS) defined as design variables while the magnitudes and direction angles of uncertain external loads described as interval

This paper develops a novel Hybrid Particle Element Method (HPEM) to model large deformation problems in solid mechanics, combining the strengths of both mesh-based and particle approaches. In the proposed method, the computational domain is discretized into two independent components: a set of finite elements and a set of particles. The finite elements serve as a temporary tool to compute the spatial

High-temperature oxidation damage in C/SiC composite, alongside mechanical failure, has becoming a focal point of developing high performance motor components. However, most of existing models focus on only one field and thus can hardly to simulate a complete process. To address this, a thermodynamically consistent phase field model tailored specifically for C/SiC composites is proposed. This model

A complete understanding of the wrinkling of compressed films on curved substrates remains illusive due to the limitations of both analytical and current numerical methods. The difficulties arise from the fact that the energetically minimal distribution of deformation localizations is primarily influenced by the inherent nonlinearities and that the deformation patterns on curved surfaces are additionally

The phase field model (PFM) has emerged as a popular computational framework for analyzing and simulating complex fracture problems. Despite PFM's inherent capacity to model relatively complex fracture phenomena such as nucleation, branching, deflection, etc., the computational costs involved in the analysis are quite high. Hence, a multi-level adaptive mesh refinement framework is proposed for a unified

In this paper, a novel time-weighted residual methodology is developed in the two-field form of structural dynamics problems to enable generalized class of optimal zero-order overshooting Linear Multi-Step (LMS) algorithms by design. For the first time, we develop a novel time-weighted residual methodology in the two-field form of the second-order time-dependent systems, leading to the newly proposed

We propose a novel framework of generalised Petrov–Galerkin Dynamical Low Rank (DLR) Approximations in the context of random PDEs. It builds on the standard Dynamical Low Rank Approximations in their Dynamically Orthogonal formulation. It allows to seamlessly build-in many standard and well-studied stabilisation techniques that can be framed as either generalised Galerkin methods, or Petrov–Galerkin

The First-Order Reliability Method (FORM) is renowned for its high computational efficiency, but its accuracy declines when addressing the nNar Limit-State Function (LSF). The Second-Order Reliability Method (SORM) offers greater accuracy; however, its approximation formula can sometimes introduce errors. Additionally, SORM requires extra calculations involving the Hessian matrix, which can reduce

We propose a relatively simple and mesh-independent approach to model crack branching and merging using the Shifted Fracture Method (SFM), within the class of Shifted Boundary Methods. The proposed method achieves mesh independency by accurately accounting for the area of the fracture surface, in contrast to traditional element-deletion/node-release techniques. In the SFM, the true fracture is embedded

We consider the coupled Navier–Stokes/transport equations with nonlinear transmission conditions, which constitute one of the most common models utilized to simulate a reverse osmosis effect in water desalination processes when considering feed and permeate channels coupled through a semi-permeate membrane. The variational formulation consists of a set of equations where the velocities, the concentrations

We propose a randomized data-driven solver for multiscale mechanics problems which improves accuracy by escaping local minima and reducing dependency on metric parameters, while requiring minimal changes relative to non-randomized solvers. We additionally develop an adaptive data-generation scheme to enrich data sets in an effective manner. This enrichment is achieved by utilizing material tangent

High fidelity modeling of multiphysical systems is typically achieved using nonlinear coupled differential equations, often with multiscale model coefficients. These simulations are performed using finite-element methods with implicit time stepping. Within each time step, nonlinearities are numerically linearized using Newton-like iterative solvers, which increases the computational complexity. For

We study the numerical approximation of advection–diffusion equations with highly oscillatory coefficients and possibly dominant advection terms by means of the Multiscale Finite Element Method (MsFEM). The latter method is a now classical, finite element type method that performs a Galerkin approximation on a problem-dependent basis set, itself precomputed in an offline stage. The approach is implemented

The statistics obtained from turbulent flow simulations are generally uncertain due to finite time averaging. Most techniques available in the literature to accurately estimate these uncertainties typically only work in an offline mode, that is, they require access to all available samples of a time series at once. In addition to the impossibility of online monitoring of uncertainties during the course

This paper proposes a new infill criterion for the optimization of expensive black-box design problems. The method complements the classical Efficient Global Optimization algorithm by considering the distribution of improvement instead of merely the expectation. During the optimization process, we maximize a penalized expected improvement acquisition function from a specially collected infill candidate

Understanding uncertainty is critical, especially when data are sparse and variations are large. Bayesian neural networks offer a powerful strategy to build predictable models from sparse data, and inherently quantify both, aleatoric uncertainties of the data and epistemic uncertainties of the model. Yet, classical Bayesian neural networks ignore the fundamental laws of physics, they are non-interpretable

The advantages of data science have inspired the development of data-driven approaches for solving constitutive modeling problems, which have become a new research focus in engineering mechanics. These approaches help fully utilize the information inherent in the data, bypassing the traditional modeling processes.

This paper presents a convolution tensor decomposition based model reduction method for solving the Allen–Cahn equation. The Allen–Cahn equation is usually used to characterize phase separation or the motion of anti-phase boundaries in materials. Its solution is time-consuming when high-resolution meshes and large time scale integration are involved. To resolve these issues, the convolution tensor

In this paper, we introduce a novel, data-driven approach for solving high-dimensional Bayesian inverse problems based on partial differential equations (PDEs), called Weak Neural Variational Inference (WNVI). The method complements real measurements with virtual observations derived from the physical model. In particular, weighted residuals are employed as probes to the governing PDE in order to formulate

Non-probabilistic convex models are powerful tools for structural model updating with uncertain‑but-bounded parameters. However, existing non-probabilistic model updating (NPMU) methods often struggle with detecting parameter correlation due to limited prior information. Worth still, the unique core steps of NPMU, involving nested inner layer forward uncertainty propagation and outer layer inverse

Time-dependent deformation and damage in viscoelastic materials exhibit distinct characteristics compared to purely brittle or ductile materials, especially under large deformations. These behaviours become even more complex in the presence of pre-cracks. To model this process, we propose an improved non-ordinary state-based peridynamics (NOSB-PD) with implicit adaptive time-stepping (IATS). The proposed

The computational cost associated with structural reliability analysis increases substantially when dealing with multiple response metrics and high-dimensional input spaces. To address this challenge, an innovative global prediction framework is proposed which leverages multi-output Gaussian process (MOGP) modeling. This framework reduces the computational burden for high-dimensional, multi-response

Uncertainty quantification (UQ) and inference involving a large number of parameters are valuable tools for problems associated with heterogeneous and non-stationary behaviors. The difficulty with these problems is exacerbated when these parameters are statistically dependent requiring statistical characterization over joint measures. Probabilistic modeling methodologies stand as effective tools in

Pulmonary capillary perfusion and gas exchange are physiological processes that take place at the alveolar level and that are fundamental to sustaining life. Present-day computational simulations of these phenomena are based on low-dimensional mathematical models solved in idealized alveolar geometries, where the chemical reactions between O2-CO2 and hemoglobin are simplified. While providing general

This paper presents an innovative methodology that seamlessly integrates the peridynamic method with advanced deep learning techniques, specifically utilizing the Gated Recurrent Unit (GRU) neural network. This integration results in the development of a highly accurate and efficient model for predicting fatigue cracking and life. This model can effectively forecast the fatigue crack patterns and fatigue

The aim of the present work is to design, analyze theoretically, and test numerically, a generalized Dryja–Smith–Widlund (GDSW) preconditioner for composite Discontinuous Galerkin discretizations of multicompartment parabolic reaction–diffusion equations, where the solution can exhibit natural discontinuities across the domain. We prove that the resulting preconditioned operator for the solution of

Modeling damage and failure behaviors of hyperelastic composites under large deformations is pivotal for advancing the design of cutting-edge elastomers used in biomedical engineering and soft robotics. However, existing methods struggle with capturing the non-linearities and singularities in the displacement field under such conditions. To address these difficulties, we propose a novel bond-based

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

In engineering applications, surface modifications of materials can greatly influence the lifetime of parts and structures. For instance, laser melt injection (LMI) of ceramic particles into a metallic substrate can greatly improve abrasive resistance. The LMI process is challenging to model due to the rapid temperature changes, which induce high mechanical stresses. Ultimately, this leads to plastification

An efficient SGBEM–FEM framework for predicting transient hydrocarbon production by coupling transient Darcy flow and channel flow is proposed, which extends the steady state analysis framework developed in Hu and Mear (2022). The governing equation of transient Darcy flow in the matrix is formulated by an integral equation method, and that of channel flow in the fracture is cast in a weak form suitable

Stress and material deformation field predictions are among the most important tasks in computational mechanics. These predictions are typically made by solving the governing equations of continuum mechanics using finite element analysis, which can become computationally prohibitive considering complex microstructures and material behaviors. Machine learning (ML) methods offer potentially cost effective

In fields where predictions may have vital consequences, uncertainty quantification (UQ) plays a crucial role, as it enables more accurate forecasts and mitigates the potential risks associated with decision-making. However, performing uncertainty quantification in real-world scenarios necessitates multiple evaluations of complex computational models, which can be both costly and time-consuming. To

We present a novel high order semi-implicit hybrid finite volume/virtual element numerical scheme for the solution of compressible flows on Voronoi tessellations. The method relies on the operator splitting of the compressible Navier–Stokes equations into three sub-systems: a convective sub-system solved explicitly using a finite volume (FV) scheme, and the viscous and pressure sub-systems which are

Double–Double (DD) laminates, incorporating a repetition of sub-plies featuring two groups of balanced angles, offer broad design flexibility together with the ease of design and manufacturing. In this work, a novel optimization design method is proposed for DD composite laminates based on multi-material topology optimization. First, the uniform multiple laminates interpolation (UMLI) model is proposed

The Physics-informed neural network method (PINN) has shown promise in resolving unknown physical fields in solid mechanics, owing to its success in solving various partial differential equations. Nonetheless, effectively solving engineering-scale boundary value problems, particularly heterogeneity and path-dependent elastoplasticity, remains challenging for PINN. To address these issues, this study

Direct numerical simulations of mechanical metamaterials are prohibitively expensive due to the separation of scales between the lattice and the macrostructural size. Hence, multiscale continuum analysis plays a pivotal role in the computational modeling of metastructures at macroscopic scales. In the present work, we assess the continuum limit of mechanical metamaterials via homogenized models derived

We construct direct serendipity finite elements on general cuboidal hexahedra, which are H1-conforming and optimally approximate to any order. The new finite elements are direct in that the shape functions are directly defined on the physical element. Moreover, they are serendipity by possessing a minimal number of degrees of freedom satisfying the conformity requirement. Their shape function spaces

Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to their coupled nature. While experimental data on certain state variables may be available, integrating these data with numerical solvers remains a significant challenge. Physics-informed neural networks (PINNs) have shown

In this work, we propose an two-level computational approach to enrich a seven degree-of-freedom kinematically exact rod model for thin-walled members, allowing for a simple elastoplastic-hardening constitutive equation. The novelty lies in upper-level description, where the effects of coupled elastoplastic-local geometrical instabilities are characterized in terms of cross-sectional stress resultants

The aim of this article is to extend Moulinec and Suquet (1998)’s FFT-based method for heterogeneous elasticity to non-periodic Dirichlet/Neumann boundary conditions. The method is based on a decomposition of the displacement into a known term verifying the boundary conditions and a fluctuation term, with no contribution on the boundary, and described by appropriate sine–cosine series. A modified auxiliary

Smoothed particle hydrodynamics (SPH) offers distinct advantages for modeling many engineering problems, yet achieving high-order consistency in its conservative formulation remains to be addressed. While zero- and higher-order consistencies can be obtained using particle-pair differences and kernel gradient correction (KGC) approaches, respectively, for SPH gradient approximations, their applicability

Stability is a basic requirement when studying the behavior of dynamical systems. However, stabilizing dynamical systems via reinforcement learning is challenging because only little data can be collected over short time horizons before instabilities are triggered and data become meaningless. This work introduces a reinforcement learning approach that is formulated over latent manifolds of unstable

When simulating pressure-driven fracture with the Finite Element Method (FEM), significant difficulties can arise upon representing newly formed complex damage surfaces and their concurrent crack face loading. Application of this loading can also be required when additional physics is involved as in the case of hydraulic fracture where fluid physics inside a damage need to be considered. This paper

We introduce a second-order computational homogenization procedure designed to address heterogeneous poromechanical media. Our approach relies on the method of multiscale virtual power, a variational multiscale method that extends the Hill–Mandel principle of macro-homogeneity. Constraints on displacement and pore pressure fields are managed using periodic and second-order minimally constrained fluctuating

Uncertainty quantification (UQ) in scientific machine learning (SciML) becomes increasingly critical as neural networks (NNs) are being widely adopted in addressing complex problems across various scientific disciplines. Representative SciML models are physics-informed neural networks (PINNs) and neural operators (NOs). While UQ in SciML has been increasingly investigated in recent years, very few

Specially tailored skeletal schemes enable cell and face variables linked with a stabilisation and a fine-tuned parameter can provide guaranteed lower eigenvalue bounds for the Laplacian. This paper briefly presents a unified derivation of skeletal higher-order methods from Carstensen, Zhai, and Zhang (2020), Carstensen, Ern, and Puttkammer (2021), and Carstensen, Gräßle, and Tran (2024). It suggests

Multi-material topology optimization has become a promising method in structural design due to its excellent structural performance. However, existing research assumes that the multi-material structures are joined by welding, adhesive, or other methods that do not support reassembly and disassembly and are unsuitable for manufacturing, limiting the practical application of topology optimization. An

This paper proposes a dual experimental/computational data-driven analysis framework for apparent strength estimation of composite structures consisting of randomly arranged unidirectional fiber-reinforced plastics. In the proposed framework, multiscale stochastic analysis is performed with random field modeling of local apparent quantities such as apparent elastic modulus or strength. Significant

In this paper we present an efficient numerical algorithm to solve stationary problems of hydrodynamic lubrication with cavitation in bearings using the method of characteristics in a finite element framework. The problem is based on the Elrod–Adams mathematical model for the lubricant fluid behavior. To achieve realistic pressure solutions, cavitation must be considered. This leads to a non-linear

Surrogate model development is a critical step for uncertainty quantification or other sample-intensive tasks for complex computational models. In this work we develop a multi-output surrogate form using a class of neural networks (NNs) that employ shortcut connections, namely Residual NNs (ResNets). ResNets are known to regularize the surrogate learning problem and improve the efficiency and accuracy

In this paper, two Eulerian and Lagrangian variational formulations of non-linear kinematic hardening are derived in the context of finite thermoplasticity. These are based on the thermo-mechanical variational framework introduced by Heuzé and Stainier (2022), and follow the concept of pseudo-stresses introduced by Mosler and Bruhns (2009). These formulations are derived from a thermodynamical framework

In the present work the evolution of viscous drops oscillating under the action of surface tension is tackled. Thanks to its structure, the SPH scheme allows for an analysis of the energy balance that is rarely addressed to in the general Computational Fluid Dynamics literature for this kind of flows. A procedure for checking the consistency between the energy of the surface-tension force and the free-surface

Partial differential equations whose solution is dominated by a combination of hyperbolic and dispersive waves are common in multiphase flows. We show that for these problems, the application of classical stabilized finite elements based on Streamline-Upwind/Petrov–Galerkin (SUPG) without accounting for the dispersive features of the solution leads to a downwind discretization and an unstable numerical

We propose a new second-order accurate lattice Boltzmann formulation for linear elastodynamics that is stable for arbitrary combinations of material parameters under a CFL-like condition. The construction of the numerical scheme uses an equivalent first-order hyperbolic system of equations as an intermediate step, for which a vectorial lattice Boltzmann formulation is introduced. The only difference

The generalized finite element method (GFEM) without extra degrees of freedom (dof) is extended to solve incompressible Navier-Stokes (N-S) equations. Unlike the existing extra-dof-free GFEM, we propose a new approach to construct the nodal enrichments based on the weighted least-squares. As a result, the essential boundary conditions can be imposed more accurately. The Characteristic-Based Split (CBS)

The complex structure of bituminous mixtures ranging from nanoscale binder components to macroscale pavement performance requires a comprehensive approach to material characterization and performance prediction. This paper provides a critical analysis of advanced techniques in paving materials modeling. It focuses on four main approaches: finite element method (FEM), discrete element method (DEM),

A variational phase field model for dynamic ductile fracture is presented. The model is designed for elasto-viscoplastic materials subjected to rapid deformations in which the effects of heat generation and material softening are dominant. The variational framework allows for the consistent inclusion of plastic dissipation in the heat equation as well as thermal softening. It employs a coalescence

Simulating spatiotemporal turbulence with high fidelity remains a cornerstone challenge in computational fluid dynamics (CFD) due to its intricate multiscale nature and prohibitive computational demands. Traditional approaches typically employ closure models, which attempt to represent small-scale features in an unresolved manner. However, these methods often sacrifice accuracy and lose high-frequency/wavenumber

Bayesian (probabilistic) model updating is a fundamental concept in computational science, allowing for the incorporation of prior beliefs with observed data to reduce prediction uncertainty of a computer simulator. However, the efficient evaluation of posterior probability density functions (PDFs) of model parameters poses challenges, particularly for computationally expansive simulators. This work

Snow exhibits unique mechanical behaviour due to its evolving properties influenced by temperature, stress conditions, and viscous effects. This paper introduces a nonlinear constitutive model for snow, featuring new formulations for the yield function and strain rate potential, and incorporating viscosity, sintering, and degradation effects. The model is numerically integrated into the Abaqus/Standard