Heng Hu

Wuhan University | WHU ·  College of Civil Engineering

Buckling instability is one of the factors that limit the ultimate load-carrying capacity of I-section beams, and the coupling of global buckling and local buckling makes it difficult to predict the mechanical behavior of I-section beams. Hierarchical one-dimensional finite elements for the global/local buckling analysis of I-section beams are pres...

Data-driven Computational Mechanics (DDCM) has been proposed as a new computational paradigm in recent years. Most of the DDCM models are discretised in the FEM framework. In this paper, two strategies are employed in the framework of DDCM to improve computational efficiency. Firstly, an advanced structural theory, Carrera Unified Formula, is used...

Composite plates are widely used in many engineering fields such as aerospace and automotive. An accurate and efficient multiscale modeling and simulation strategy is of paramount importance to improve design and manufacture. To this end, we propose an efficient data-driven computing scheme based on the classical plate theory for the multiscale ana...

Membrane instability typically exhibits small wavelength compared to the structural size, which often leads to numerical difficulties in computational efficiency and convergence problem. Recently, the Fourier-based reduced technique that is similar to the famous Ginzburg–Landau equation has shown the potential to overcome these difficulties. Howeve...

In this work, a layerwise beam model based on Carrera’s Unified Formulation (CUF) is developed to solve the geometrically nonlinear problem of sandwich beams with a special emphasis on global–local buckling interaction. In the framework of CUF, the order of a beam theory can be chosen freely to ensure the desired accuracy and computational effort....

The aim of this work is to investigate the coupling of data-driven (DD) computing and model-driven (MD) computing for the analyses of engineering structures. The data-driven computing was initially introduced by Kirchdoerfer and Ortiz (2016), the main idea of which is to directly embedding the experimental material data into mechanical simulations,...

The paper describes the modelling and the subsequent implementation of an integrated system that consists of a composite material microstructure and its Material Twin (MT). The developed MT is based on statistical continuum theory and probability functions. The MT is used to reproduce/reconstruct 3D porous composite material microstructures, to sim...

As a material with an almost negligible bending stiffness, membranes may easily lose their mechanical stability. Generally, the wave lengths of the wrinkles are quite small, leading to the intensive computation in numerical simulations. To deal with the issue, a Fourier based reduced model is recently developed by Huang et al. (2019) showing good p...

In this paper, we propose a multiscale data-driven framework for Fiber Reinforced Polymer (FRP) composites. At the mesoscopic scale, the 3D stress–strain material database is collected by the multilevel computational homogenization (FE²), in which the Representative Volume Elements (RVEs) are generated through the X-ray microtomography (Micro-CT) a...

The multi-stability of composite shells often exhibits complex mechanical behaviors, accompanied by large deformation, strong nonlinearity and multiple equilibrium branches. We present a numerical framework for stability analysis of laminated composite shells, which is capable of efficiently computing nonlinear equilibrium paths and critical points...

Over the last few years, several studies have shown the potential of multi-stability in engineering applications such as shape-adaptive structures and energy harvesting devices. Due to their highly non-linear mechanics, multi-stable structures are inherently more complex to model than conventional engineering structures. Especially when composite m...

This paper aims to study the boundary effects on stretch-induced membrane wrinkling. Towards this end, several typical distributions of tensile loads, that are applied at the short ends of rectangular membranes, are investigated, which produce a system of forces statically equivalent to force and moment. In addition, we explore the relevance of a d...

This paper aims to propose a novel data-driven multiscale finite element method (data-driven FE²) for composite materials and structures. The correlated scales in the classical FE² method are here split to be computed sequentially and separately: the microscopic problems are calculated in advance to construct an offline material genome database, wh...

In Liquid Composite Molding (LCM), compaction of the reinforcement occurs during several stages of the entire process, including before and during resin injection, which leads to significant deformation of the fibrous architecture. This affects not only the manufacturing process, but also the mechanical properties of final parts.This article aims to st...

In Liquid Composite Molding (LCM), compaction of the reinforcement occurs during several stages of the entire process, including before and during resin injection, which leads to significant deformations of fibrous architecture. This article aims to study by X-ray microtomography the mesoscopic deformations of 2D glass woven fabrics under transvers...

This paper couples the Carrera's Unified Formulation (CUF) with the Asymptotic Numerical Method (ANM) for investigating geometrically nonlinear behaviors of beam structures. On the basis of CUF, a family of advanced one-dimensional beam models is firstly established by deriving a fundamental nucleus. The ANM that is an efficient and robust nonlinea...

How to compute a Taylor series with respect to a coordinate system, when this series is known with respect to alternative coordinates? This paper gives an answer to this question, as well as applications to Partial Differential Equations. An alternative technique is also proposed by applying the change of variables directly on the PDE. Such procedu...

The transverse permeability of fibrous reinforcement is one of the critical parameters that govern fabrication efficiency and production quality in several liquid composite molding process variants devised to achieve transverse impregnation of fibrous reinforcements. It is difficult to precisely measure and predict the transverse permeability, beca...

The aim of this work is to investigate the effects of kinematics approximation on post-buckling analysis of sandwich structures. To this end, a novel one-dimensional (1D) layer-wise model is proposed, where the core is approximated by Mac Laurin's polynomial functions, and the skins are modelled by Euler-Bernoulli beam theory. The resulting nonline...

In this paper, a new paradigm for Carrera’s Unified Formulation (CUF) based on multiscale structural modelling is accomplished by bridging micromechanics and the advanced CUF one-dimensional/beam structural theories by means of the Multilevel Finite Element (also known as FE2) framework. Under the framework of the FE2 method, the analysis is divide...

This paper aims to propose an efficient and accurate framework for the post-buckling analysis of sandwich structures with elastic-plastic material behaviors. Correspondingly, efforts are made in two aspects, i.e., the model and the nonlinear solver. A new one-dimensional sandwich model is firstly established, in which the skins are described by Eul...

Engineering textiles are used as fibrous reinforcements in high performance polymer composites. The mechanical properties of composite materials depend on their dual-scale porous structure: long and elongated microscopic open spaces (micropores) appear between the filaments of fiber tows, and up to two orders of magnitude larger mesoscopic spaces (...

The paper discusses Trefftz discretization techniques with a focus on their coupling with shape functions computed by the method of Taylor series. The paper highlights are, on one hand the control of ill-conditioning and the solving of large scale problems, on the other hand the applications to non-linear Partial Differential Equations. Indeed, des...

The paper discusses Trefftz discretization techniques with a focus on their coupling with shape functions computed by the method of Taylor series. The paper highlights are, one one hand the control of ill-conditioning and the solving of large scale problems, on the other hand the applications to non-linear Partial Differential Equations. Indeed, de...

A bridging technique based on Lagrange multipliers, namely the Arlequin method, is widely used for coupling multi-scale models. However, the definition of the following key parameters is still unclear: the energy partition functions, the characteristic length of the coupling operator and the size of the coupling zone. This work aims to investigate...

This chapter addresses a multi-scale analysis of beam structures using the Carrera Unified Formulation (CUF). Under the framework of the \(\text {FE}^{2}\) method, the analysis is divided into a macroscopic/structural problem and a microscopic/material problem. At the macroscopic level, several higher-order refined beam elements can be easily imple...

The formulation of a family of advanced one-dimensional finite elements for the geometrically nonlinear static analysis of beam-like structures is presented in this paper. The kinematic field is axiomatically assumed along the thickness direction via a Unified Formulation (UF). The approximation order of the displacement field along the thickness i...

This work aims at developing a multiscale model by combining the Fourier-related double scale analysis and the bridging domain method to study membrane instabilities. Towards this end, a Fourier reduced membrane model is firstly established based on the Föppl-Von Karman plate equations, where the initial unknowns are expanded into Fourier series an...

In this paper, the superelasticity effects of architected shape memory alloys (SMAs) are focused on by using a multiscale approach. Firstly, a parametric analysis at the cellular level with a series of representative volume elements (RVEs) is carried out to predict the relations between the void fraction, the total stiffness, the hysteresis effect...

As a soft material with an almost negligible bending stiffness, a membrane may easily lose its mechanical stability. To capture its entire instability process, intensive computation is required, especially in the case of short wave length. The objective of this paper is to construct an efficient model to simulate and study the instability phenomena...

A recently proposed meshless method is discussed in this article. It relies on Taylor series, the shape functions being high degree polynomials deduced from the Partial Differential Equation (PDE). In this framework, an efficient technique to couple several polynomial approximations has been presented in (Tampango, Potier‐Ferry, Koutsawa, Tiem, Int...

In this paper, we propose an efficient and accurate approach to investigate the post-buckling behavior of sandwich structures. In this framework, a novel one-dimensional layer-wise model using Euler-Bernoulli beam theory in the skins and higher-order kinematics in the core is proposed. The resulting nonlinear governing equations are then solved by...

The Taylor Meshless Method (TMM) is a true meshless integration-free numerical method for solving elliptic Partial Differential Equations (PDEs). The basic idea of this method is to use high-order polynomial shape functions that are approximated solutions to the PDE and are computed by the technique of Taylor series. Currently, this new method has...

A true integration-free meshless method based on Taylor series named Taylor meshless method (TMM) has been proposed to solve two-dimensional partial differential equations (PDEs). In this framework, the shape functions are approximated solutions of the PDE, and the discretization concerns only the boundary. In this paper, the applicability of TMM t...

A multi-scale analysis of fibre reinforced composite beams was proposed by this presentation. At structural level, several higher-order refined beam theories can be easily implemented on the basis of Carrera's unified formulation (CUF) by deriving a fundamental nucleus that does not depend upon the approximation order nor the number of nodes per el...

A true meshless integration-free method based on Taylor series named Taylor Meshless Method (TMM) has been proposed recently to solve Partial Differential Equations (PDEs), where the shape functions are high degree polynomials and the discretization concerns only the boundary. With high computational efficiency and exponential convergence, the TMM...

Composite structure operating under severe temperature conditions and/or wet environments are very common is several engineering fields such as aeronautics, space and transportation. Hygro-thermal solicitation of beam-like structures results in a three- dimensional response that classical one-dimensional models are not always capable of describe ef...

In this paper, an efficient Fourier-series finite element solution framework is proposed to simulate the wrinkling phenomena in two-dimensional film/substrate system. In the method, the displacement field is transformed into the slowly variable Fourier coefficient, i.e., the macroscopic displacement field, which permits to capture the wrinkling evo...

This paper presents a Fourier-related double scale analysis to study the instability phenomena of sandwich plates. By expanding the displacement field into Fourier series, the sandwich plate model proposed by Yu et al. (2015), using the classical plate theory in the skins and high-order kinematics in the core, is transformed into a new Fourier-base...

This paper presents a family of beam higher-orders finite elements based on a hierarchical one-dimensional unified formulation for a free vibration analysis of three-dimensional sandwich structures. The element stiffness and mass matrices are derived in a nucleal form that corresponds to a generic term in the displacement field approximation over t...

In this paper, a new Fourier-related double scale approach is presented to study the wrinkling of thin films on compliant substrates. By using the method of Fourier series with slowly variable coefficients, the 1D microscopic model proposed by Yang et al. (2015) is transformed into a 1D macroscopic film/substrate model whose mesh size is independen...

In this work, the thermoelastic response of functionally graded beams is studied. To this end, a family of advanced one-dimensional finite elements is derived by means of a unified formulation that is not dependent on the order of approximation of the displacements upon the beam cross-section. The temperature field is obtained via a Navier-type sol...

The paper is concerned by multi-scale methods to describe instability pattern formation, especially the method of Fourier series with variable coefficients. In this respect, various numerical tools are available. For instance in the case of membrane models, shell finite element codes can predict the details of the wrinkles, but with difficulties du...

Solid and higher-order plate finite elements are coupled for the analysis of composite structures by means of the Arlequin method. Plate and solid elements are derived by a Unified Formulation (UF) and they do not depend on the number of nodes. Higher-order and zig-zag plate elements are easily formulated regardless the approximation order along th...

The mechanical strength of graphene is much larger than any other materials, but is orientation-dependent and can be significantly weakened by vacancy defects existing in the lattices. In this work, we investigated the orientational anisotropic effect on the fracture strength of vacancy-defective graphene using molecular dynamics simulations. The r...

Bridging techniques between microscopic and macroscopic models are discussed in the case of wrinkling analysis. The considered macroscopic models are related to envelope equations of Ginzburg−Landau type, but generally, they are not valid up to the boundary. To this end, a multi-scale approach is considered: the reduced model is implemented in the...

Membrane modeling in the presence of wrinkling is revisited from a multi-scale point of view. In the engineering literature, wrinkling is generally accounted at a macroscopic level by nonlinear constitutive laws without compressive stiffness, but these models ignore the properties of wrinkles, such as their wavelength, their size and spatial distri...

This work presents several higher-order atomistic-refined models for the static and free vibration analysis of nano-plates. Stemming from a two-dimensional approach and thanks to a compact notation for the a priori kinematic field approximation over the plate through-the-thickness direction, a general model derivation is used where the approximatio...

A new macroscopic approach to the modelling of membrane wrinkling is presented. Most of the studies of the literature about membrane behaviour are macroscopic and phenomenological, the influence ofwrinkles being accounted for by nonlinear constitutive laws without compressive stiffness. The present method is multi-scale and it permits to predict th...

A Fourier-related nonlocal reduction-based coupling, using the bridging domain methodology, is investigated to analyze the influence of boundary conditions on wrinkling patterns. The nonlocal reduction-based coupling approach is based on the well-known Arlequin framework. The analysis of the effect of boundary conditions on instability patterns is...

This work presents several higher-order atomistic-refined models for the static, free vibration and stability analysis of three-dimensional nano-beams. Stemming from a one-dimensional approach and thanks to a compact notation for the a priori kinematic field approximation over the beam cross-section, the model derivation is made general regardless...

A new efficient and simple algorithm based on two-point probability functions was developed to construct isotropic and anisotropic heterogeneous microstructures with desired effective physical property. To take into account the complex heterogeneities geometry, the developed microstructure design tool uses the strong-contrast formulations of the st...

Two multi-scale techniques will be applied in this paper to analyze buckling and wrinkling phenomena in sandwich structures. The first one is a Fourier-related analysis, where the unknowns are slowly variable Fourier coefficients of the basic fields. As shown in [19], it permits to describe the coupling between global and local buckling without des...

This paper develops a nonlocal reduced coupling approach via Arlequin method to analyse the effect of boundary conditions on instability patterns. The present paper first analyses a nonlocal reduced coupling approach with the concept of Fourier transform from microscopic behaviour to Fourier coefficients. This reduction methodology is applied in th...

In this paper, we study the temperature's effect on a plate under global tensile stress. For this aim, the Fourier double scale method is used in order to develop a macroscopic model that is a generalized continuum. This model couples local and global instabilities in wrinkling phenomena. The advantage of this technique is to remain valid away from...

Various macroscopic models to describe instability pattern formation are discussed in this paper. They are similar to the Ginzburg-Landau envelope equation, but they can remain valid away from the bifurcation and are based on the technique of Fourier series with slowly varying coefficients. We focus on two questions: the need to take phase changes...

In this work, plate elements based on different kinematic assumptions and variational principles are combined through the Arlequin method. Computational costs are reduced assuming refined models only in those zones with a quasi-three-dimensional stress field, whereas computationally cheap, low-order elements are used in the remaining parts of the p...

In this paper, we present a new Fourier-related double scale analysis to study instability phenomena of sandwich structures. By using the technique of slowly variable Fourier coefficients, a zig-zag theory based microscopical sandwich model is transformed into a macroscopical one that offers three numerical advantages. Firstly, only the envelopes o...

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Recently, a new approach by the Technique of Slowly Variable Fourier Coefficient is developped to study the instabilities with nearly periodic pattern. The aim of this paper is to study its computational efficiency and limitations via an instability investigation of beams on nonlinear Winkler foundation.

Ce travail a pour objectif la comparaison numérique de trois modèles macroscopiques pour l'analyse des instabilités cellulaires. Ces phénomènes peuvent être traités par une analyse de bifurcation de type LandauGinzburg. Dans l’exemple élémentaire du flambage d’une poutre reposant sur une fondation non linéaire élastique, on établit une variante d...

In this work, we present a macroscopic technique, based on the concept of Fourier series with slowly varying coefficients that permits to analyze the appearance of instability patterns. In this method, the Fourier coefficients are the unknowns of the macroscopic problem. The aim is the numerical evaluation of macroscopic models. The results of the...

In this work, beam elements based on different kinematic assumptions are combined through the Arlequin method. Computational costs are reduced assuming refined models only in those zones with a quasi-three-dimensional stress field. Variable kinematics beam elements are formulated on the basis of a unified formulation (UF). This formulation is exten...

The paper is devoted to macroscopic descriptions of cellular instability problems, such as wrinkling of membranes, buckling of long plates or of cylindrical shells, Rayleigh-Bénard convection in large boxes, buckling of carbon nanotubes or thin elastic film bound to compliant substrate, fibre micro-buckling of composites that permits to predict the...