Constitutive modeling lies at the core of mechanics, allowing us to map strains onto stresses for a material in a given mechanical setting. Historically, researchers relied on phenomenological modeling where simple mathematical relationships were derived through experimentation and curve fitting. Recently, to automate the constitutive modeling process, data-driven approaches based on neural networks

The resolution and accuracy of numerical partial differential equation solvers are governed by the mesh density and the order of accuracy of the solver. Anisotropic mesh adaptation combined with a posteriori error estimation is known to be a powerful tool to enhance the efficiency of the solvers. However, in engineering applications involving multiple complex configurations, optimization or uncertainty

This paper presents a novel three-phase damage model for the prediction of the post-peak responses of composite materials, such as recycled aggregate concrete (RAC). The proposed damage model is based on composite damage mechanics and is composed of three phases: cement paste, interface transition zone (ITZ), and aggregate. All phases are assumed to be linearly elastic and isotropic materials. The

In cardiovascular mechanics, reaching consensus in simulation results within a physiologically relevant range of parameters is essential for reproducibility purposes. Although currently available benchmarks contain some of the features that cardiac mechanics models typically include, some important modeling aspects are missing. Therefore, we propose a new set of cardiac benchmark problems and solutions

The cascading reliability evaluation of multi-failure modes of complex system/structure usually needs to repeatedly establish mathematical models with the step-by-step modeling strategy, which weakens the correlation between multi-failure modes. To improve the efficiency and precision of cascading reliability evaluation, a hybrid adaptive coordination surrogate modeling-based improved moving regression

This paper presents a comprehensive framework for spatiotemporal flow field analysis based on complex network theory, emphasizing dimensionality reduction, spatiotemporal feature identification, modeling, and sparsification. The framework first redefines transient flow fields using graph theory and applies clustering techniques to discretize the flow field into different vortex structures, achieving

Kriging is a prevalent surrogate model technique in optimization and data-driven analysis, known for its high accuracy and statistical error estimation. However, training Kriging models often requires extensive global optimization of hyperparameters, posing significant challenges when applying these methods to large-scale datasets. Previous research has mainly focused on expediting the training process

This article presents stochastic augmented Lagrangian multiplier methods to solve contact problems with uncertainties, in which stochastic contact constraints are imposed by weak penalties and stochastic Lagrangian multipliers. The stochastic displacements of original stochastic contact problems are first decomposed into two parts, including contact and non-contact stochastic solutions. Each part is

Currently, due to the complexity of multi-scale topology optimization (MSTO), most of them are optimized based on deterministic conditions, ignoring the influence of uncertain factors on multi-scale structural design optimization. This article aims to develop a novel approach to probabilistic reliability-based topology optimization of multi-scale structure (RBTOM) to address the optimization design

Aircraft design requires extensive aerodynamic data to characterize various flight conditions throughout the aircraft’s flight envelope. Typically, the aerodynamic data is acquired through wind tunnel testing or numerical analysis, which are costly and inevitably entails multiple sources of uncertainty. In the present work, we propose a multi-fidelity Bayesian neural network (MFBNN) framework for multi-source

The growing demand for accurate, efficient, and scalable solutions in computational mechanics highlights the need for advanced operator learning algorithms that can efficiently handle large datasets while providing reliable uncertainty quantification. This paper introduces a novel Gaussian Process (GP) based neural operator for solving parametric differential equations. The approach proposed leverages

Few studies have investigated the fatigue of composite laminates under cyclic compression loading. Moreover, the self-heating approach to rapidly predict fatigue life has rarely been applied to this type of material. The objective of this work is to study the fatigue of a quasi-isotropic laminate under compression-compression loadings and to assess the possibility of rapidly determining an endurance

High-strain rate deformation caused by microparticles impacting at high velocities is used to refine the microstructure of metallic materials to the nanocrystalline regime. Under these conditions, metallic targets and particles show a gradient distribution of nanograins, with size increasing away from the impact surface. Some of the mechanisms responsible for the refinement process are still not fully

Scientific machine learning has seen significant progress with the emergence of operator learning. However, existing methods encounter difficulties when applied to problems on unstructured grids and irregular domains. Spatial graph neural networks utilize local convolution in a neighborhood to potentially address these challenges, yet they often suffer from issues such as over-smoothing and over-squashing

We introduce a generative learning framework to model high-dimensional parametric systems using gradient guidance and virtual observations. We consider systems described by Partial Differential Equations (PDEs) discretized with structured or unstructured grids. The framework integrates multi-level information to generate high fidelity time sequences of the system dynamics. We demonstrate the effectiveness

In this work, an efficient thermo-mechanically coupled two-scale finite element (FE)-fast Fourier transform (FFT)-based simulation approach for elasto-viscoplastic polycrystalline materials is proposed. Assuming a separation of scales, the macroscopic and microscopic boundary value problems are solved individually and linked by a scale transition. While the macroscopic boundary value problems are solved

We present Basis-to-Basis (B2B) operator learning, a novel approach for learning operators on Hilbert spaces of functions based on the foundational ideas of function encoders. We decompose the task of learning operators into two parts: learning sets of basis functions for both the input and output spaces and learning a potentially nonlinear mapping between the coefficients of the basis functions. B2B

In this work, we introduce two innovative types of discontinuity-removing physics-informed neural networks (DR-PINNs) aimed at solving variable coefficient elliptic interface problems on curved surfaces, i.e., decoupling DR-PINN and coupling DR-PINN. Initially, by leveraging the level set function associated with the surface, we reframe the surface differential operators as conventional differential

Advancements in manufacturing technologies have enabled material system design optimization across multiple length scales. However, microstructural anomalies (defects) that are present at different scales have not been considered comprehensively enough for systems to be robust to manufacturing variations and uncertainties. Addressing these anomalies through uncertainty quantification and propagation

The critical challenge in enhancing the fretting fatigue performance of A100 ultra-high strength steel (A100 steel) involved reconciling the conflicting attributes of strength and toughness. In our study, the ultrasonic surface rolling process (USRP) was harnessed to induce gradient nanostructures and a compressive residual stress field on the surface of A100 steel, with the goal of strengthening its

This paper discusses the problem of macroscopic modeling a knitted technical fabric with the aim to determine a constitutive law for adequately modeling the material response under real-life load. As phenomenological, hyperelastic material laws reveal different parameters due to different test modalities used to identify such parameters, an optimization scheme is proposed to determine an objective

A weak interface model with a predefined traction-separation relationship (denoted as the cohesive zone law), when embedded in a bulk solid, is oftentimes adopted to simulate the crack advancement and thus determine the crack resistance under either monotonic or cyclic loading conditions. To-date, various types of loading-unloading irreversibility and hysteresis are only presumed in the cohesive zone

Pores in granular materials may occupy significant material volume. Pore-scale dynamics, therefore, strongly influence the macroscopic response of these materials when they are subjected to rapid compaction. In Part I of this series, Ghosh et al. (2024) employed in-situ X-ray imaging coupled with mesoscale finite element modeling to reconstruct the 3D time-resolved kinematics and kinetics of aluminum

Accurately modelling the interactions between continuous and discontinuous materials is essential for advancing engineering solutions across a wide range of fields. Owing to fundamental differences in the governing equations of discontinuous and continuous numerical models, distinct solution schemes have been developed, presenting challenges for their coupling. This paper proposes a unified scheme

The mean strain effect on AISI 304 stainless steel was examined through strain-controlled low-cycle fatigue tests under uniaxial and non-proportional random loading. Under uniaxial loading, cyclic stress responses showed initial hardening followed by continuous softening, typical of austenitic stainless steel. In contrast, non-proportional loading resulted in consistent hardening. Mean strain primarily

This paper experimentally investigates the fatigue behavior and failure mechanism of a quasi-three-dimensional woven composite (Q3DWC) under combined high and low cycle fatigue loading (CCF) for the first time. In this study, to develop a composite with high tensile strength and sufficient delamination resistance, a Q3DWC structure is firstly designed. Then, a novel biaxial experimental platform, including

The machine learning (ML) methods have been applied to numerical solutions to partial differential equations (PDEs) in recent years and achieved great success in PDEs with smooth solutions and in high dimensional PDEs. However, it is still challenging to develop high-precision ML solvers for PDEs with non-smooth solutions. The linear elastic fracture mechanics equation is a typical non-smooth problem

The macroscopic stress formulation for periodic systems in Kohn–Sham density functional theory is critically examined. The identification of the stress through the partial variation of the energy with respect to cell deformation is cast in a strictly large deformation context. The nature of the non-uniqueness in the stress expression which emanates from this variation is extensively discussed. The

Multi-fidelity surrogate models combining dimensionality reduction and an intermediate surrogate in the reduced space allow a cost-effective emulation of simulators with functional outputs. The surrogate is an input–output mapping learned from a limited number of simulator evaluations. This computational efficiency makes surrogates commonly used for many-query tasks. Diverse methods for building them

In this work, a NiTi shape memory alloy (SMA) with excellent elastocaloric performance (with an ultrahigh coefficient of performance, i.e., COPmat of ∼46.5 and an adiabatic temperature change of ∼10.5 K) and good cyclic stability is prepared. A thermo-mechanically coupled and crystal-plasticity-based phase field model including both the descriptions of Ni4Ti3 precipitation and martensitic transformation

Because of the huge specific surface area at the micro/nano scale, inter-surface adhesion and surface effects play a critical role in the behavior of solid-to-solid contact. The inter-surface adhesion originates from the intermolecular traction between two surfaces, while the surface effects, including residual surface stress and surface elasticity, result from the physical discrepancy between the

Miura-Ori, a celebrated origami pattern that facilitates functionality in matter, has found multiple applications in the field of mechanical metamaterials. Modifications of Miura-Ori pattern can produce curved configurations during folding, thereby enhancing its potential functionalities. Thus, a key challenge in designing generalized Miura-Ori structures is to tailor their folding patterns to achieve

In engineering applications, the Metropolis-Hastings (M-H) algorithm with high rejection rates is employed to evaluate implicit response functions, making reliability analysis for small failure probabilities with multiple input random variables difficult and inefficient. To address the challenge and estimate highly nonlinear limit state functions in a more efficient and accurate way, a novel reliability

This work introduces an efficient methodology for: (i) predicting dynamic responses across a broad frequency band for large-scale, highly complex structures, and (ii) forecasting their high-frequency response using associated low-frequency information. Structures of interest are characterized by a large number of degrees of freedom (DOFs) and numerous local vibration modes that couple, within the frequency

Many parts made of thin steel sheet are subjected to two types of loads: tension and bending. In this study, we define and suggestnovel fatigue failure criteria based on the outcomes of testing specimens with various notch lengths under these two loading modes at constant and different stress ratios. Large cyclic plastic strains occurred near the notch, which were taken into account in the evaluation

This paper focuses on the characterisation of fatigue crack initiation mechanisms under fully reversed torsional loads for the porosity-containing cast AlSi7Mg0.3 aluminium alloy by synchrotron X-ray tomographic imaging and Diffraction Contrast Tomography (DCT). The aim is to analyse the relation between crack initiation and the microstructure, in the fatigue regime close to the fatigue limit of the

For structural applications subjected to rapid and cyclic loading, impact toughness and fatigue strength are critical properties that determine material suitability. CrCoNi medium entropy alloys (MEAs) have garnered attention due to their exceptional mechanical properties. Therefore, it is essential to assess the structural integrity of this alloy under harsh environments. This study investigates the

We present a novel probabilistic approach for generating multi-fidelity data while accounting for errors inherent in both low- and high-fidelity data. In this approach a graph Laplacian constructed from the low-fidelity data is used to define a multivariate Gaussian prior density for the coordinates of the true data points. In addition, few high-fidelity data points are used to construct a conjugate

We study in detail the pressure stabilizing effects of the non-iterated fixed-stress splitting in poromechanical problems which are nearly undrained and incompressible. When applied in conjunction with a spatial discretization which does not satisfy the discrete inf–sup condition, namely a mixed piecewise linear–piecewise constant spatial discretization, the explicit fixed-stress scheme can have a

The mesh flexibility offered by the virtual element method has made it increasingly popular in the context of adaptive remeshing. There exists a healthy literature concerning error estimation and adaptive refinement techniques for virtual elements while the topic of adaptive coarsening (i.e. de-refinement) is in its infancy. The notion of a quasi-optimal mesh is based on the principle of quasi-even

In this work, polyacrylamide (PAAm) hydrogels with different water contents (WCs) were prepared, and stress-controlled cyclic experiments were carried out. The effect of water content on the mechanical behavior of PAAm hydrogels was observed through stress–strain curves, apparent modulus, and dissipation energy across various loading cycles. It is concluded that with the increase in the WC, the peak

The double network hydrogels (DN gels) process high fracture toughness due to their considerable energy dissipation during fracture. To effectively interpret the energy dissipation, it is imperative to conduct a study on the quantitative characterization of the dissipated energy density distribution and the damage zone around the crack tip. In this study, we propose a series of tearing tests on pre-stretched

Data-based uncertainty quantification plays a significant role in the design of various patterns of new materials and structures. However, significant challenges remain due to missing data, inherent uncertainties, and incomplete material properties arising from the manufacturing process. In this paper, we quantitatively investigate the uncertainty in the probability of the mechanical response of bio-inspired

The rapid advancement in technology and engineering leads to increasingly complex structural working conditions. Especially, in the field of aeronautics and astronautics, structures are frequently subjected to high temperatures together with external forces, posing great threat to structural health. Consequently, the identification of both mechanical and thermal loads is crucial for structural health

This paper presents a probabilistic approach to represent and quantify model-form uncertainties in the reduced-order modeling of complex systems using operator inference techniques. Such uncertainties can arise in the selection of an appropriate state–space representation, in the projection step that underlies many reduced-order modeling methods, or as a byproduct of considerations made during training

In this paper, we propose several improvements to existing fictitious domain/distributed Lagrange multiplier (FD/DLM) type immersed fluid–structure interaction (FSI) methods targeted for FSI analysis of heart valve dynamics. We utilize the variational multiscale (VMS) method to improve accuracy and robustness on under-resolved grids expected with immersed FSI techniques, as well as for the wide range

Physics-Informed Neural Networks (PINN) are a machine learning tool that can be used to solve direct and inverse problems related to models described by Partial Differential Equations by including in the cost function to minimise during training the residual of the differential operator. This paper proposes an adaptive inverse PINN applied to different transport models, from diffusion to advection–diffusion–reaction

In recent years, the architected structures have attracted extensive attention due to their lightweight feature and excellent mechanical properties. The development of additive manufacturing technologies has expedited the development of the computational design of architected structures. However, the parametric design and simulation of architected structures are full of challenges because of their

In this paper, we introduce a fully-monolithic, implicit finite element method designed for investigating fluid–structure interaction problems within a fully Eulerian framework. Our approach employs a coupled Navier–Stokes Cahn–Hilliard phase-field model, recently developed by Mokbel et al. (2018). This model adeptly addresses significant challenges such as large solid deformations, topology changes

This work introduces a new solution-transfer process for slab-based space–time finite element methods. The new transfer process is based on Hsieh–Clough–Tocher (HCT) splines and satisfies the following requirements: (i) it maintains high-order accuracy up to 4th order, (ii) it preserves a discrete maximum principle, (iii) it asymptotically enforces mass conservation, and (iv) it constructs a smooth

An incremental high-cycle fatigue damage model is combined with topology optimization to design structures subject to non-proportional loads. The optimization aims to minimize the mass under compliance and fatigue constraints. The fatigue model is based on the concept of an evolving endurance surface and a system of ordinary differential equations that model the local fatigue damage evolution. A recent

Many blood vessels exist in brain tissue. Their internal blood pressure plays a crucial role in physiological disorders, such as brain edema, stroke, or traumatic brain injury (concussion). Homogenized continuum mechanics-based brain tissue models can provide an attractive approach to rapidly simulate blood-pressure related physiological disorders, and traumatic brain injury. These homogenized models

This paper presents a concurrent optimization method for structural topology and fabrication sequence, aiming at designing for multi-axis additive manufacturing. The proposed method involves two fields: the density field representing the structure, and the time field representing the manufacturing sequence. In addition, angle variables are introduced to represent the designable build directions. The

Enriched finite element methods (e-FEMs) have become a popular choice for modeling problems containing material discontinuities (e.g., multi-phase materials and fracture). The main advantage as compared to the standard finite element method (FEM) remains the versatility in the choice of discretizations, since e-FEMs resolve discontinuities by completely decoupling them from the finite element mesh

In-situ SEM fatigue testing is performed to investigate crack propagation through the heat affected zone as well as in the base material and deposited material in a wire and arc additive manufacturing (WAAM) low-carbon steel part. The slip band formation and development prior to crack initiation and the crack growth rate are monitored in-situ and compared using fatigue testing specimens sampled from

To comprehensively investigate the influence of water content on the mechanical and crack propagation characteristics of coal rock assemblage (CRA) with a rough interface, uniaxial compression tests were conducted on specimens with varying water content. Nuclear magnetic resonance (NMR) and acoustic emission (AE) techniques were employed to monitor the water content and AE signals throughout the experiment

The use of carbon and kevlar fiber-reinforced composite materials continues to grow in high-tech applications such as aerospace engineering. One of the most desired properties in composite structures is a strong interfacial bond between the matrix and the fiber. Nano-material reinforcement is one of the most preferred methods for strengthening the fiber-matrix interfacial bond. In the present research

Many historical earthen buildings are damaged due to fire exposure in the past. It is important to understand the strength degradation of rammed earth after elevated temperature for guiding the strategy of building protection or rehabilitation. A total of 24 unconfined compression tests are conducted on lime-stabilized rammed earth specimens after elevated temperature up to 700°C. A quasi-linear reduction

This paper presents a novel equilibrium-based approach to the linear homogenization of shear-deformable beams and plates with periodic heterogeneity. The proposed approach leverages the fact that, under equilibrium, the stress resultants and sectional strains in beams and plates vary at most linearly with respect to the axial or in-plane coordinates. Consequently, the displacement fields within a representative

This study aims to systematically investigate the effects of hole diameter and sheet thickness on the quasi-static and fatigue behaviors of PH-SPR joints of high-strength steel and aluminum alloy. Quasi-static shear and fatigue tests, full-field strain measurements, numerical simulations, and microscopic observations are conducted to analyze the mechanical properties, failure behavior, failure mechanism