A coupling approach of the isogeometric–meshfree method and the peridynamic method is developed for static and dynamic crack propagation. The coupling approach exhibits advantages in the flexibility of modeling cracks and the exactness of geometry representation. The isogeometric–meshfree method, which adopts the moving least-squares approximations to establish the equivalence between meshfree shape

In this work, we propose an efficient solution of the inverse Stefan problem by multi-fidelity Bayesian optimization. We construct a multi-fidelity Gaussian process surrogate model by combining many low-fidelity estimates of a solidification problem with only a few high-fidelity measurements. To solve the inverse problem, we employ the Gaussian process model in a Bayesian optimization approach based

Phase-field modeling has already proved to be a suitable framework to predict the initiation and propagation of drying cracks in variably saturated porous media. In this paper, we focus on some fundamental modeling aspects which have not yet been given sufficient attention. In the first part, different formulations for the total energy, characterized by different choices for the coupling between the

Isogeometric analysis (IGA) provides a feasible technique to seamlessly integrate computer-aided design (CAD) into the existing finite element analysis. In this article, a Bézier elements-based IGA method is established to address the stress-related topology optimization of structures, which incorporates geometrical representation, structural analysis and topology optimization into a unified process

Projection-based reduced-order models (pROMs) show great promise as a means to accelerate many-query applications such as forward error propagation, solving inverse problems, and design optimization. In order to deploy pROMs in the context of high-consequence decision making, accurate error estimates are required to determine the region(s) of applicability in the parameter space. The following paper

Mechanical cloaks can hide objects and make them unfeelable by reproducing the surrounding displacement field without the objects and cloaks. In the existing works, mechanical cloaks have been considered for hiding a void, while this work develops a generic method to design cloaks for solids with a given stiffness. As materials with properties beyond natural materials are required to achieve this task

This contribution focuses on the development of an adaptive hierarchical FFT-based approach for the efficient solution of microscale boundary value problems. To this end, the classic Moulinec–Suquet scheme is revisited and enhanced by making use of wavelet analysis. Governing fields are represented in a wavelet basis and higher level stress approximations in a nested set of approximation spaces are

Elements of the periodic homogenization framework and deep neural network were seamlessly connected for the first time to construct a new micromechanics theory for thermoconductive composites called physically informed Deep Homogenization Network (DHN). This method utilizes a two-scale expansion of the temperature field of spatially uniform composites in terms of macroscopic and fluctuating contributions

Data-Driven (DD) computing is an emerging field of Computational Mechanics, motivated by recent technological advances in experimental measurements, the development of highly predictive computational models, advances in data storage and data processing, which enable the transition from a material data-scarce to a material data-rich era. The predictive capability of DD simulations is contingent on the

This work presents a rigorous mathematical formulation for topology optimization of a macro structure undergoing ductile failure. The prediction of ductile solid materials which exhibit dominant plastic deformation is an intriguingly challenging task and plays an extremely important role in various engineering applications. Here, we rely on the phase-field approach to fracture which is a widely adopted

We present a data-driven approach to mathematically model physical systems whose governing partial differential equations are unknown, by learning their associated Green’s function. The subject systems are observed by collecting input–output pairs of system responses under excitations drawn from a Gaussian process. Two methods are proposed to learn the Green’s function. In the first method, we use

A simplified technique for the enforcement of boundary conditions along solid profiles is proposed in the framework of the Smoothed Particle Hydrodynamics. The main idea relies on a local definition of the normal and tangent vectors to the solid body, along with a local mirroring of the flow fields. This compound approach allows for a robust and accurate modelling of the fluid–solid interaction close

In this work we develop a discretisation method for the Brinkman problem that is uniformly well-behaved in all regimes (as identified by a local dimensionless number with the meaning of a friction coefficient) and supports general meshes as well as arbitrary approximation orders. The method is obtained combining ideas from the Hybrid High-Order and Discrete de Rham methods, and its robustness rests

In this work, we propose Bayesian parameter estimation of a nonlinear mechanics based model describing the behaviour of mortar subjected to double shear test with externally bonded carbon fibre reinforced polymer (CFRP) plates. With the Bayesian approach, it is possible to identify mechanical material parameters of different phases of the mortar mesostructure, i.e. hardened cement paste, aggregates

The eigenmodes of resonating structures, e.g., electromagnetic cavities, are sensitive to deformations of their shape. In order to compute the sensitivities of the eigenpair with respect to a scalar parameter, we state the Laplacian and Maxwellian eigenvalue problems and discretize the models using isogeometric analysis. Since we require the derivatives of the system matrices, we differentiate the

This study presents a unified method to model electrodeposition and galvanic corrosion. The governing equations and boundary conditions are recast in their nonlocal form by using the peridynamic differential operator. Electric potential and mass transport equations are solved simultaneously in ANSYS through implicit algorithms for computational efficiency and complex geometry. Deposition and corrosion

Stiffened thin-walled structures are widely used in various fields as load-carrying components, but the process of design, analysis and optimization still remains challenging. In this paper, a new design-analysis-optimization workflow is proposed based on isogeometric paradigms for stiffened structures, which is on the basis of a simpler and more efficient method, called multi-level NURBS-based free-form

We investigate variational phase-field formulations of anisotropic brittle fracture to model zigzag crack patterns in cubic materials. Our objective is twofold: (i) to analytically derive and numerically test the fundamental behavioral aspects predicted by the two main available fourth-order models, and to guide the calibration of their unknown parameters; (ii) motivated by the pronounced non-uniqueness

Much work has been done in topology optimization of multiscale structures for maximum stiffness or minimum compliance design. Such approaches date back to the original homogenization-based work by Bendsøe and Kikuchi from 1988, which lately has been revived due to advances in manufacturing methods like additive manufacturing. Orthotropic microstructures locally oriented in principal stress directions

This paper is concerned with topology optimization based on a level set method using (doubly) nonlinear diffusion equations. Topology optimization using the level set method is called level set-based topology optimization, which is possible to determine optimal configurations that minimize objective functionals by updating level set functions. In this paper, as an update equation for level set functions

Particle-based methods such as SPH have been proven to be powerful numerical tools for addressing challenges in solving coupled large deformation and failure of porous materials. In these applications, explicit time integration schemes are commonly adopted to integrate the coupled pore-water pressure equation. The Courant–Friedrichs–Lewy condition is required and imposes a strong restriction on the

This work presents a novel theoretical/numerical model for the simulation of self-aerated flows under a Reynolds-Averaged Navier-Stokes (RANS) framework. The new formulation is based on a three-phase mixture approach composed of a continuous air phase, a bubble phase, and a continuous water phase. A mass transfer mechanism that does not depend on an entrainment function and does not require calibration

In the present work we propose and analyze a fully-coupled virtual element method of high order for solving the two dimensional nonstationary Boussinesq system in terms of the stream-function and temperature fields. The discretization for the spatial variables is based on the coupling C1- and C0-conforming virtual element approaches, while a backward Euler scheme is employed for the temporal variable

The design of versatile soft actuators remains a challenging task, as it is a complex trade-off between robotic adaptability and structural complexity. Recently, researchers have used statistical and physical models to simulate the mechanical behavior of soft actuators. These simulations can help identify optimal actuator designs that fulfill specific robotic objectives. However, automated optimization

G-splines are a generalization of B-splines that deals with extraordinary points by imposing G1 constraints across their spoke edges, thus obtaining a continuous tangent plane throughout the surface. Using the isoparametric concept and the Bubnov–Galerkin method to solve partial differential equations with G-splines results in discretizations with global C1 continuity in physical space. Extraordinary

A thermoelastic topology optimization method considering stress and manufacturing constraints is developed for engineering structures under thermo-mechanical coupled field in this paper. A design dependent non-uniform temperature field is considered for the heat conduction and the thermoelastic analysis during the topology optimization. Based on the solid isotropic material with penalization (SIMP)

Simulating structures with history-dependent material models and uncertain material parameters is often computationally expensive. In contrast, the time-separated stochastic mechanics (TSM) has proven to provide an efficient yet accurate method for the computation of stochastic visco-elastic materials. In this work, the TSM is extended for viscoelastic structures with local random material fluctuations

Bayesian optimization (BO) is increasingly employed in critical applications such as materials design and drug discovery. An increasingly popular strategy in BO is to forgo the sole reliance on high-fidelity data and instead use an ensemble of information sources which provide inexpensive low-fidelity data. The overall premise of this strategy is to reduce the total sampling costs by querying inexpensive

This study presents a novel unsupervised convolutional Neural Network (NN) architecture with nonlocal interactions for solving Partial Differential Equations (PDEs). The nonlocal Peridynamic Differential Operator (PDDO) is employed as a convolutional filter for evaluating derivatives the field variable. The NN captures the time-dynamics in smaller latent space through encoder–decoder layers with a

The focus of this paper is on application of peridynamics (PD) to propagation of elastic waves in unbounded domains. We construct absorbing boundary conditions (ABCs) derived from a semi-analytical solution of the PD governing equation at the exterior region. This solution is made up of a finite series of plane waves, as fundamental solutions (modes), which satisfy the PD dispersion relations. The

In previous work, Zhang et al. (2021) developed an integrated smoothed particle hydrodynamics (SPH) method to simulate the principle aspects of cardiac function, including electrophysiology, passive and active mechanical response of the myocardium. As the inclusion of the Purkinje network in electrocardiology is recognized as fundamental to accurately describing the electrical activation in the right

We develop a novel a posteriori error estimator for the L2 error committed by the finite element discretization of the solution of the fractional Laplacian. Our a posteriori error estimator takes advantage of the semi-discretization scheme using rational approximations which allow to reformulate the fractional problem into a family of non-fractional parametric problems. The estimator involves applying

Although “classical” multi-scale methods can capture the behaviour of cellular, including lattice, materials, when considering lattices or metamaterial local instabilities, corresponding to a change of the micro-structure morphology, classical computational homogenisation methods fail. On the one hand, first order computational homogenisation, which considers a classical continuum at the macro-scale

Abstract not available

This work proposes two advances on kinematically exact rod models for thin-walled open section members: (i) an explicit analytical expression for the cross-section warping function, including both primary and secondary warping for arbitrary section geometries, and (ii) a nonlinear elastic constitutive equation with all higher-order strain terms included, suitable for truly finite strains. By not neglecting

Driven by the need to accelerate numerical simulations, the use of machine learning techniques is rapidly growing in the field of computational solid mechanics. Their application is especially advantageous in concurrent multiscale finite element analysis (FE2) due to the exceedingly high computational costs often associated with it and the high number of similar micromechanical analyses involved. To

Solid nano-structures exhibiting fast ion transport (cations moving in anionic crystal structures) are becoming increasingly relevant in industrial applications. However, it is challenging to model their mechanics due to the presence of electromagnetic couplings. In this paper, a mathematical, physical, and computational framework is introduced, for a cation particle moving through an anion sub-lattice

Mechanical structures are often simultaneously subjected to thermal and mechanical loading, both of which can lead to buckling failure. Developing efficient structural forms with better capacity for stability is important to keep structures safe. This study aims to optimize structural buckling capacity by using a density-based topology optimization scheme. Instead of treating the mechanical and thermal

Reliability-based design optimization (RBDO) is critical in improving the design objective and guaranteeing the safety level of mechanical and engineering structures. However, a large number of multi-source uncertainties exist in the real-world, and their applications pose significant challenges owing to the lack of unity and generality of the RBDO theory and high performance computational methods

An isogeometric boundary element method (IGABEM) is developed for the analysis of two-dimensional linear and isotropic elastic bodies governed by the couple stress theory. This theory is the simplest generalized continuum theory that can effectively model size effects in solids. The couple stress fundamental solutions are explicitly derived and used to construct the boundary integral equations. A new

We present a novel computational framework to simulate the electromechanical response of self-sensing carbon nanotube (CNT)-based composites experiencing fracture. The computational framework combines electrical-deformation-fracture finite element modelling with a mixed micromechanics formulation. The latter is used to estimate the constitutive properties of CNT-based composites, including the elastic

Shell finite element is computationally efficient and thereby favored in large-scale structural analysis. With the application of advanced materials, understanding the relation between micro-heterogeneities and structural behavior is important. To this end, we propose a multiscale method in the current contribution for modeling thin-walled fiber reinforced composite laminates with Mindlin–Reissner

A new algorithm based on the convolution finite element method (CFEM) is proposed for the nonlinear wave propagation in elastic media. The formulation is developed in the context of the total Lagrangian framework, encompassing contributions due to both geometrical and material nonlinearities. As a basis, a counterpart of equations of motion – namely, the alternative field equations – is first established

The development of highly accurate constitutive models for materials that undergo path-dependent processes continues to be a complex challenge in computational solid mechanics. Challenges arise both in considering the appropriate model assumptions and from the viewpoint of data availability, verification, and validation. Recently, data-driven modeling approaches have been proposed that aim to establish

This work aims at deriving special types of one-dimensional Finite Elements (1D FE) for efficiently modeling heterogeneous prismatic structures, in the small strains regime, by means of reduced-order modeling (ROM) and domain decomposition techniques. The employed partitioning framework introduces “fictitious” interfaces between contiguous subdomains, leading to a formulation with both subdomain and

This paper pushes further the intrinsic capabilities of the GFEMgl global-local approach introduced initially in Duarte et al. (2007). We develop a distributed computing approach using MPI (Message Passing Interface) both for the global and local problems. Regarding local problems, a specific scheduling strategy is introduced. Then, to measure correctly the convergence of the iterative process, we

The imminent impact of immersive technologies in society urges for active research in real-time and interactive physics simulation for virtual worlds to be realistic. In this context, realistic means to be compliant to the laws of physics. In this paper we present a method for computing the dynamic response of (possibly non-linear and dissipative) deformable objects induced by real-time user interactions

In this work, the problem of finite generalized and viscoelastic deformation of thin membranes with different geometries, made of incompressible hyperelastic materials, is formulated. The multiplicative decomposition of the deformation gradient tensor into elastic and viscous parts, and making use of dissipation inequality, nonlinear evolution equations for the internal variables of the models are

A recently developed measure-theoretic framework solves a stochastic inverse problem (SIP) for models where uncertainties in model output data are predominantly due to aleatoric (i.e., irreducible) uncertainties in model inputs (i.e., parameters). The subsequent inferential target is a distribution on parameters. Another type of inverse problem is to quantify uncertainties in estimates of “true” parameter

The total Lagrangian smoothed particle hydrodynamics (TL-SPH) for elastic solid dynamics suffers from hourglass modes which can grow and lead to the failure of simulation for problems with large deformation. To address this long-standing issue, we present an essentially non-hourglass formulation based on volumetric-deviatoric stress decomposition. Inspired by the fact that the artifact of nonphysical

Physics-informed neural networks have attracted considerable attention for solving scientific and engineering problems because of their low data dependence and physical outputs. The most popular way to embed the laws of physics into neural networks is to apply partial differential equations. However, many complex mechanical problems, such as displacements near the phase interface in heterogeneous plates

Multi-fidelity Monte Carlo methods leverage low-fidelity and surrogate models for variance reduction to make tractable uncertainty quantification even when numerically simulating the physical systems of interest with high-fidelity models is computationally expensive. This work proposes a context-aware multi-fidelity Monte Carlo method that optimally balances the costs of training low-fidelity models

Additive manufacturing of metal parts involves phase transformations and high temperature gradients which lead to uneven thermal expansion and contraction, and, consequently, distortion of the fabricated components. The distortion has a great influence on the structural performance and dimensional accuracy, e.g., for assembly. It is therefore of critical importance to model, predict and, ultimately

Fractures have attracted the attention of computational scientists for several decades. The modeling and simulation of fractures have been a major motivation for developing enriched finite element methods (FEMs), such as the numerical manifold method (NMM). However, ill-conditioning has always haunted NMM and other enriched FEMs when they are utilized for linear elastic fracture problems. Generally

The fourth-order phase-field modeling of ductile fracture in elastic–plastic materials is performed via an adaptive isogeometric-meshfree approach. In the developed phase-field model, the total energy functional consists of the elastic contribution and the dissipated contribution because of fracture and plasticity. The coupling of the plasticity to fracture is implemented by a degradation function

We provide an optimization framework that is capable of identifying the material parameters and contact traction field from two measured deformed geometries of a soft body in contact. The novelty of the framework is the idea of parametrizing the missing contact traction field and incorporating it into the inverse+forward hyper-elasticity formulation. We provide the continuum- and finite element formulation

Understanding and projecting seasonal variations in sea ice is necessary to improve global climate predictions. However, accurately capturing changes in sea ice and its interactions with ocean and atmosphere variability remains a challenge for models, notably due to its complex behavior at the floe scale. In this work, we introduce a method to capture the floe-like behavior of sea ice, named the ‘Level

This paper presents the first asynchronous version of the Global/Local non-invasive coupling, capable of dealing efficiently with multiple, possibly adjacent, patches. We give a new interpretation of the coupling in terms of primal domain decomposition method, and we prove the convergence of the relaxed asynchronous iteration. The asynchronous paradigm lifts many bottlenecks of the Global/Local coupling