Material point method simulation of hydro-mechanical behaviour in twophase porous geomaterials: A state-of-the-art review

The material point method(MPM)has been gaining increasing popularity as an appropriate approach to the solution of coupled hydro-mechanical problems involving large deformation.In this paper,we survey the current state-of-the-art in the MPM simulation of hydro-mechanical behaviour in two-phase porous geomaterials.The review covers the recent advances and developments in the MPM and their extensions to capture the coupled hydro-mechanical problems involving large deformations.The focus of this review is aiming at providing a clear picture of what has or has not been developed or implemented for simulating two-phase coupled large deformation problems,which will provide some direct reference for both practitioners and researchers.

The energy release rate for hygrothermal coupling elastic materials

In the fracture problems of hydrophilic elastic materials under coupling effects of heat conduction, moisture diffusion and mechanical deformation, the conventional J-integral is no longer path independent. The value of J is unequal to the energy release rate in hygrothermal coupling cases. In the present paper, we derived a general form of the energy release rate for hygrothermal fracture problems of the hydrophilic elastic materials on the basis of energy balance equation in cracked areas. By introducing the constitutive relations and the essential equations of irreversible thermodynamics, a specific expression of the energy release rate was obtained, and the expression can be reformmulated as path independent integrals, which is equivalent to the energy release rate of the fracture body. The path independence of the integrals is then verified numerically.

Efficient Inverse Analysis for Solving a Coupled Conduction,Convection and Radiation Problem Involving Non⁃gray Participating Media

The presence of non-gray radiative properties in a reheating furnace’s medium that absorbs,emits,and involves non-gray creates more complex radiative heat transfer problems.Furthermore,it adds difficulty to solving the coupled conduction,convection,and radiation problem,leading to suboptimal efficiency that fails to meet real-time control demands.To overcome this difficulty,comparable gray radiative properties of non-gray media are proposed and estimated by solving an inverse problem.However,the required iteration numbers by using a least-squares method are too many and resulted in a very low inverse efficiency.It is necessary to present an efficient method for the equivalence.The Levenberg-Marquardt algorithm is utilized to solve the inverse problem of coupled heat transfer,and the gray-equivalent radiative characteristics are successfully recovered.It is our intention that the issue of low inverse efficiency,which has been observed when the least-squares method is employed,will be resolved.To enhance the performance of the Levenberg-Marquardt algorithm,a modification is implemented for determining the damping factor.Detailed investigations are also conducted to evaluate its accuracy,stability of convergence,efficiency,and robustness of the algorithm.Subsequently,a comparison is made between the results achieved using each method.

Multiscale Nonlinear Thermo-Mechanical Coupling Analysis of Composite Structures with Quasi-Periodic Properties

This paper reports a multiscale analysis method to predict the thermomechanical coupling performance of composite structures with quasi-periodic properties.In these material structures,the configurations are periodic,and the material coefficients are quasi-periodic,i.e.,they depend not only on the microscale information but also on the macro location.Also,a mutual interaction between displacement and temperature fields is considered in the problem,which is our particular interest in this study.The multiscale asymptotic expansions of the temperature and displacement fields are constructed and associated error estimation in nearly pointwise sense is presented.Then,a finite element-difference algorithm based on the multiscale analysis method is brought forward in detail.Finally,some numerical examples are given.And the numerical results show that the multiscale method presented in this paper is effective and reliable to study the nonlinear thermo-mechanical coupling problem of composite structures with quasiperiodic properties.

An Efficient Three-Dimensional Coupled Normal Mode Model and Its Application to Internal Solitary Wave Problems

We present an efficient three-dimensional coupled-mode model based on the Fourier synthesis technique. In principle, this model is a one-way model, and hence provides satisfactory accuracy for problems where the forward scattering dominates. At the same time, this model provides an efficiency gain of an order of magnitude or more over two-way coupled-mode models. This model can be applied to three-dimensional range-dependent problems with a slowly varying bathymetry or internal waves. A numerical example of the latter is demonstrated in this work. Comparisons of both accuracy and efficiency between the present model and a benchmark model are also provided.

Transfer Matrix Approach for Two-State Scattering Problem with Arbitrary Coupling

The present work deals with the calculation of transition probability between two diabatic potentials coupled by any arbitrary coupling. The method presented in this work is applicable to any type of coupling while for numerical calculations we have assumed the arbitrary coupling as Gaussian coupling. This arbitrary coupling is expressed as a collection of Dirac delta functions and by the use of the transfer matrix technique the transition probability from one diabatic potential to another diabatic potential is calculated. We examine our approach by considering the case of two constant potentials coupled by Gaussian coupling as an arbitrary coupling.

Three-Dimensional Isogeometric Analysis of Flexoelectricity with MATLAB Implementation

Flexoelectricity is a general electromechanical phenomenon where the electric polarization exhibits a linear dependency to the gradient of mechanical strain and vice versa.The truncated pyramid compression test is among the most common setups to estimate the flexoelectric effect.We present a three-dimensional isogeometric formulation of flexoelectricity with its MATLAB implementation for a truncated pyramid setup.Besides educational purposes,this paper presents a precise computational model to illustrate how the localization of strain gradients around pyramidal boundary shapes contributes in generation of electrical energy.The MATLAB code is supposed to help learners in the Isogeometric Analysis and Finite Elements Methods community to learn how to solve a fully coupled problem,which requires higher order approximations,numerically.The complete MATLAB code which is available as source code distributed under a BSD-style license,is provided in the part of Supplementary Materials of the paper.

Coupled Electromagnetic-Thermal-Fluidic Analysis of Permanent Magnet Synchronous Machines with a Modified Model

The researches on the heat generation and dissipa-tion of the permanent magnet synchronous machines(PMSMs)are integrated problems involving multidisciplinary studies of electromagnetism,thermomechanics,and computational fluid dynamics.The governing equations of the multi-physical prob-lems are coupled and hard to be solved and illustrated.The high accuracy mathematical model in the algebraically integral con-servative forms of the coupled fields is established and computed in this paper.And the equation coupling with the fluid flow and the temperature variation is modified to improve the positive definiteness and the symmetry of the global stiffness matrix.The computational burden is thus reduced by the model modification.A 20kW 4500rpm permanent magnet synchronous machine(PMSM)is taken as the prototype,and the calculation results are validated by experimental ones.

Numerical techniques for coupling hydrodynamic problems in ship and ocean engineering

Most hydrodynamic problems in ship and ocean engineering are complex and highly coupled.Under the trend of intelligent and digital design for ships and ocean engineering structures,comprehensive performance evaluation and optimization are of vital importance during design.In this process,various coupling effects need to be accurately predicted.With the significant progress of computational fluid dynamics(CFD),many advanced numerical models were proposed to simulate the complex coupling hydrodynamic problems in ship and ocean engineering field.In this paper,five key coupling hydrodynamic problems are introduced,which are hull-propeller-rudder coupling,wave-floating structure coupling,aerodynamic-hydrodynamic coupling,fluid structure coupling and fluid-noise coupling,respectively.The paper focuses on the numerical simulation techniques corresponding to each coupling problem,including the theories and the applications.Future directions and conclusions are provided finally.

Formulations of a hydromechanical interface element

A hydromechanical interface element is proposed for the consideration of the hydraulic-mechanical coupling effect along the interface.The fully coupled governing equations and the relevant finite element formulations are derived in detail for the interface element.All the involved matrices are of the same form as those of a solid element,which makes the incorporation of the model into a finite element program straightforward.Three examples are then numerically simulated using the interface element.Reasonable results confirm the correctness of the proposed model and motivate its application in hydromechanical contact problems in the future.

Stabilized Crouzeix-Raviart element for the coupled Stokes and Darcy problem

This paper introduces a new stabilized finite element method for the coupled Stokes and Darcy problem based on the nonconforming Crouzeix-Raviart element. Optimal error estimates for the fluid velocity and pressure are derived. A numerical example is presented to verify the theoretical predictions.

FINITE ELEMENT SOLUTION TO COUPLED THERMO－ELASTICCONTACT STRESS AND IMPACTRESPONSE OF MESHING GEARS

A mixed finite element solution of contact stresses in meshing gears is investigated with the consideration of coupled thermo-elastic deformation and impact behavior. A simulation procedure of finite element solution of meshing gears is developed. The versatility of the procedure for both numerical accuracy and computational efficiency is verified by numerical analysis of meshing gear teeth.

A GENERAL SOLUTION AND THE APPLICATION OF SPACE AXISYMMETRIC PROBLEM IN PIEZOELECTRIC MATERIAL

According to the structure feature of the governing equations of spaceaxisymmetric problem in transversely, isotropic piezoelectric material. using the methodof introducing potential .function one by. one, in this paper we obtain the so-calledgeneral solution of displacement and eleclric potential function denoied by uniquepoiential.function which satisfies specific partiality equations. As an applying exampleof the general solution, we solve problem of semi-infinile boodt. made of piezoelectricmaterial, on the surface of the semi-infinite body a concentrative .force is applied, andget the analytic .formulations of stress and electric displacement comiponenis. Thegeneral solution provided by this paper can be used as a tool to analyse the mechanical-electrical coupling behavior of piezoelecrtic material which conlains defects such ascavity inclusion. penny-shape crack. and so on. The result of the solved problem canbe used directly to analyse contact problems which take place between twopiezoelectric bodies or piezoelectric body. and elastic body .

Determination of Shear Center of Arbitrary Cross-Section

In structural analysis, it is often necessary to determine the geometrical properties of cross section. The location of the shear center is greater importance for an arbitrary cross section. In this study, the problems of coupled shearing and torsional were analyzed by using the finite element method. Namely, the simultaneous equations with respect to the warping, shear deflection, angle of torsion and Lagrange’s multipliers are derived by finite element approximation. Solving them numerically, the matrix of the shearing rigidity and torsional rigidity is obtained. This matrix indicates the coupled shearing and torsional deflection. The shear center can be obtained determining the coordinate axes so as to eliminate the non-diagonal terms. Several numerical examples are performed and show that the present method gives excellent results for an arbitrary cross section.

A DUAL COUPLED METHOD FOR BOUNDARY VALUE PROBLEMS OF PDE WITH COEFFICIENTS OF SMALL PERIOD

In this paper the homogenization method is improved to develop one kind of dual coupled approximate method, which reflects both the macro-scope properties of whole structure and its loadings, and micro-scope configuration properties of composite materials. The boundary value problem of woven membrane is considered, the dual asymptotic expression of the exact solution is given, and its approximation and error estimation are discussed. Finally the numerical example shows the effectiveness of this dual coupled method.

A 3D multi-field element for simulating the electromechanical coupling behavior of dielectric elastomers

We propose a multi-field implicit finite element method for analyzing the electromechanical behavior of dielectric elastomers. This method is based on a four-field variational principle, which includes displacement and electric potential for the electromechanical coupling analysis, and additional independent fields to address the incompressible constraint of the hyperelastic material. Linearization of the variational form and finite element discretization are adopted for the numerical implementation. A general FEM program framework is devel- oped using C＋＋ based on the open-source finite element library deal.II to implement this proposed algorithm. Numerical examples demonstrate the accuracy, convergence properties, mesh-independence properties, and scalability of this method. We also use the method for eigenvalue analysis of a dielectric elastomer actuator subject to electromechanical loadings. Our finite element implementation is available as an online supplementary material.

A Modeling Framework for Coupling Plasticity with Species Diffusion

This paper presents a modeling framework—mathematical model and computational framework—to study the response of a plastic material due to the presenceand transport of a chemical species in the host material. Such a modeling frameworkis important to a wide variety of problems ranging from Li-ion batteries, moisturediffusion in cementitious materials, hydrogen diffusion in metals, to consolidation ofsoils under severe loading-unloading regimes. The mathematical model incorporatesexperimental observations reported in the literature on how (elastic and plastic) material properties change because of the presence and transport of a chemical species.Also, the model accounts for one-way (transport affects the deformation but not viceversa) and two-way couplings between deformation and transport subproblems. Theresulting coupled equations are not amenable to analytical solutions;so, we present arobust computational framework for obtaining numerical solutions. Given that popular numerical formulations do not produce nonnegative solutions, the computationalframework uses an optimized-based nonnegative formulation that respects physicalconstraints (e.g., nonnegative concentrations). For completeness, we also show theeffect and propagation of the negative concentrations, often produced by contemporary transport solvers, into the overall predictions of deformation and concentrationfields. Notably, anisotropy of the diffusion process exacerbates these unphysical violations. Using representative numerical examples, we discuss how the concentrationfield affects plastic deformations of a degrading solid. Based on these numerical examples, we also discuss how plastic zones spread because of material degradation.To illustrate how the proposed computational framework performs, we report variousperformance metrics such as optimization iterations and time-to-solution.

THE COUPLING METHOD OF FINITE ELEMENTS AND BOUNDARY ELEMENTS FOR RADIATION PROBLEM

The paper presents the variational formulation and well posedness of the coupling method offinite elements and boundary elements for radiation problem. The convergence and optimal errorestimate for the approximate solution and numerical experiment are provided.

Aerodynamic design,analysis,and validation techniques for the Tianwen-1 entry module

The clear differences between the atmosphere of Mars and the Earth coupled with the lack of a domestic research basis were significant challenges for the aerodynamic prediction and verification of Tianwen-1.In addition,the Mars entry,descent,and landing(EDL)mission led to specific requirements for the accuracy of the aerodynamic deceleration performance,stability,aerothermal heating,and various complex aerodynamic coupling problems of the entry module.This study analyzes the key and difficult aerodynamic and aerothermodynamic problems related to the Mars EDL process.Then,the study process and results of the design and optimization of the entry module configuration are presented along with the calculations and experiments used to obtain the aerodynamic and aerothermodynamic characteristics in the Martian atmosphere.In addition,the simulation and verification of the low-frequency free oscillation characteristics under a large separation flow are described,and some special aerodynamic coupling problems such as the aeroelastic buffeting response of the trim tab are discussed.Finally,the atmospheric parameters and aerodynamic characteristics obtained from the flight data of the Tianwen-1 entry module are compared with the design data.The data obtained from the aerodynamic design,analysis,and verification of the Tianwen-1 entry module all meet the engineering requirements.In particular,the flight data results for the atmospheric parameters,trim angles of attack,and trim axial forces are within the envelopes of the prediction deviation zones.