Non‐linear finite element analysis of mechanical electrochemical phenomena in hydrated soft tissues based on triphasic theory

The well‐accepted triphasic theory for modelling the mechano‐electrochemical phenomena of charged hydrated soft tissue has been limited to infinitesimal deformation problems due to the difficulty of defining a common reference configuration for the whole tissue. In this paper, an imaginary reference configuration for soft tissue under large deformation is established based on the reference configuration of a solid matrix and a Piola transformation of the relative velocities of the fluid and ionic phases. A non‐linear finite element analysis formulation is proposed by applying a weighted residual method to the reformulated governing equations of triphasic theory reformulated in the imaginary reference configuration, with the displacement of the solid, fluid flows, ionic molar flows, hydrostatic pressure, and electrical potential as the unknown variables. After verifying the proposed finite‐element formulation by comparing the results of a linear‐confined compression problem with those obtained by the finite difference method, the numerical analysis of a three‐dimensional free‐swelling problem of articular cartilage with large deformation, and a strong non‐linearity in the material properties is carried out to reproduce the curling behaviour of articular cartilage strips in vitro when submerged in solution baths of various concentrations. The results obtained by finite element analysis are in agreement with those measured experimentally. Copyright © 2005 John Wiley & Sons, Ltd.     

A two‐scale approach for fluid flow in fractured porous media

A two‐scale numerical model is developed for fluid flow in fractured, deforming porous media. At the microscale the flow in the cavity of a fracture is modelled as a viscous fluid. From the micromechanics of the flow in the cavity, coupling equations are derived for the momentum and the mass couplings to the equations for a fluid‐saturated porous medium, which are assumed to hold on the macroscopic scale. The finite element equations are derived for this two‐scale approach and integrated over time. By exploiting the partition‐of‐unity property of the finite element shape functions, the position and direction of the fractures is independent from the underlying discretization. The resulting discrete equations are non‐linear due to the non‐linearity of the coupling terms. A consistent linearization is given for use within a Newton–Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach, and show that faults in a deforming porous medium can have a significant effect on the local as well as on the overall flow and deformation patterns. Copyright © 2006 John Wiley & Sons, Ltd.     

The enriched space–time finite element method (EST) for simultaneous solution of fluid–structure interaction

The paper introduces a weighted residual‐based approach for the numerical investigation of the interaction of fluid flow and thin flexible structures. The presented method enables one to treat strongly coupled systems involving large structural motion and deformation of multiple‐flow‐immersed solid objects. The fluid flow is described by the incompressible Navier–Stokes equations. The current configuration of the thin structure of linear elastic material with non‐linear kinematics is mapped to the flow using the zero iso‐contour of an updated level set function. The formulation of fluid, structure and coupling conditions uniformly uses velocities as unknowns. The integration of the weak form is performed on a space–time finite element discretization of the domain. Interfacial constraints of the multi‐field problem are ensured by distributed Lagrange multipliers. The proposed formulation and discretization techniques lead to a monolithic algebraic system, well suited for strongly coupled fluid–structure systems. Embedding a thin structure into a flow results in non‐smooth fields for the fluid. Based on the concept of the extended finite element method, the space–time approximations of fluid pressure and velocity are properly enriched to capture weakly and strongly discontinuous solutions. This leads to the present enriched space–time (EST) method. Numerical examples of fluid–structure interaction show the eligibility of the developed numerical approach in order to describe the behavior of such coupled systems. The test cases demonstrate the application of the proposed technique to problems where mesh moving strategies often fail. Copyright © 2007 John Wiley & Sons, Ltd.     

A simultaneous solution procedure for strong interactions of generalized Newtonian fluids and viscoelastic solids at large strains

The paper presents a methodology for numerical analyses of coupled systems exhibiting strong interactions of viscoelastic solids and generalized Newtonian fluids. In the monolithic approach, velocity variables are used for both solid and fluid, and the entire set of model equations is discretized with stabilized space–time finite elements. A viscoelastic material model for finite deformations, which is based on the concept of internal variables, describes the stress‐deformation behaviour of the solid. In the generalized Newtonian approach for the fluid, the viscosity depends on the shear strain rate, leading to common non‐Newtonian fluid models like the power‐law. The consideration of non‐linear constitutive equations for solid and fluid documents the capability of the monolithic space–time finite element formulation to deal with complex material models. The methodology is applied to fluid‐conveying cantilevered pipes in order to determine the influence of material non‐linearities on stability characteristics of coupled systems. Copyright © 2005 John Wiley & Sons, Ltd.     

An enhanced pipe elbow element—application in plastic limit analysis of pipe structures

In this paper, we present a new pipe elbow element based on a previous simplified model proposed by Bathe and Almeida [1, 2] and modified by Militello and Huespe [3]. It is really a beam‐type element but it describes the ovalization, warping, radial expansion and non‐symmetric deformation of cross‐section of curved pipe with Fourier series. Therefore, it could model precisely enough a real pipe elbow structure but remains simple. The extensive loading cases are effectively implemented by the proposed numerical techniques and displacement model. The developed element is used in this paper in plastic limit analysis of pipe elbow structures. This is realized by means of a direct mathematical programming technique. Various elastic and plastic limit state analyses of straight pipes and elbow structures are presented, which illustrates the efficiency of the element and the numerical method. Copyright © 1999 John Wiley & Sons, Ltd.     

A stabilized finite element formulation for monolithic thermo‐hydro‐mechanical simulations at finite strain

An adaptively stabilized monolithic finite element model is proposed to simulate the fully coupled thermo‐hydro‐mechanical behavior of porous media undergoing large deformation. We first formulate a finite‐deformation thermo‐hydro‐mechanics field theory for non‐isothermal porous media. Projection‐based stabilization procedure is derived to eliminate spurious pore pressure and temperature modes due to the lack of the two‐fold inf‐sup condition of the equal‐order finite element. To avoid volumetric locking due to the incompressibility of solid skeleton, we introduce a modified assumed deformation gradient in the formulation for non‐isothermal porous solids. Finally, numerical examples are given to demonstrate the versatility and efficiency of this thermo‐hydro‐mechanical model. Copyright © 2015 John Wiley & Sons, Ltd.     

Coupled mechanics and finite element for non‐linear laminated piezoelectric shallow shells undergoing large displacements and rotations

A theoretical framework is presented for analysing the coupled non‐linear response of shallow doubly curved adaptive laminated piezoelectric shells undergoing large displacements and rotations. The formulated mechanics incorporate coupling between in‐plane and flexural stiffness terms due to geometric curvature, coupling between mechanical and electric fields, and encompass geometric non‐linearity effects due to large displacements and rotations. The governing equations are formulated explicitly in orthogonal curvilinear co‐ordinates and are combined with the kinematic assumptions of a mixed‐field shear‐layerwise shell laminate theory. Based on the above formulation, a finite element methodology together with an incremental‐iterative technique, based on Newton–Raphson method is formulated. An eight‐node coupled non‐linear shell element is also developed. Various evaluation cases on laminated curved beams and cylindrical panels illustrate the capability of the shell finite element to predict the complex non‐linear behaviour of active shell structures including buckling, which is not captured by linear shell models. The numerical results also show the inherent capability of piezoelectric shell structures to actively induce large displacements through piezoelectric actuators, by jumping between multiple equilibrium states. Copyright © 2005 John Wiley & Sons, Ltd.     

New development in extended finite element modeling of large elasto‐plastic deformations

This paper presents new achievements in the extended finite element modeling of large elasto‐plastic deformation in solid problems. The computational technique is presented based on the extended finite element method (X‐FEM) coupled with the Lagrangian formulation in order to model arbitrary interfaces in large deformations. In X‐FEM, the material interfaces are represented independently of element boundaries, and the process is accomplished by partitioning the domain with some triangular sub‐elements whose Gauss points are used for integration of the domain of elements. The large elasto‐plastic deformation formulation is employed within the X‐FEM framework to simulate the non‐linear behavior of materials. The interface between two bodies is modeled by using the X‐FEM technique and applying the Heaviside‐ and level‐set‐based enrichment functions. Finally, several numerical examples are analyzed, including arbitrary material interfaces, to demonstrate the efficiency of the X‐FEM technique in large plasticity deformations. Copyright © 2008 John Wiley & Sons, Ltd.     

A combined fluid–structure interaction and multi–field scalar transport model for simulating mass transport in biomechanics

Mass transport processes are known to play an important role in many fields of biomechanics such as respiratory, cardiovascular, and biofilm mechanics. In this paper, we present a novel computational model considering the effect of local solid deformation and fluid flow on mass transport. As the transport processes are assumed to influence neither structure deformation nor fluid flow, a sequential one‐way coupling of a fluid–structure interaction (FSI) and a multi‐field scalar transport model is realized. In each time step, first the non‐linear monolithic FSI problem is solved to determine current local deformations and velocities. Using this information, the mass transport equations can then be formulated on the deformed fluid and solid domains. At the interface, concentrations are related depending on the interfacial permeability. First numerical examples demonstrate that the proposed approach is suitable for simulating convective and diffusive scalar transport on coupled, deformable fluid and solid domains. Copyright © 2014 John Wiley & Sons, Ltd.     

Efficient non‐linear solid–fluid interaction analysis by an iterative BEM/FEM coupling

An iterative coupling of finite element and boundary element methods for the time domain modelling of coupled fluid–solid systems is presented. While finite elements are used to model the solid, the adjacent fluid is represented by boundary elements. In order to perform the coupling of the two numerical methods, a successive renewal of the variables on the interface between the two subdomains is performed through an iterative procedure until the final convergence is achieved. In the case of local non‐linearities within the finite element subdomain, it is straightforward to perform the iterative coupling together with the iterations needed to solve the non‐linear system. In particular a more efficient and a more stable performance of the new coupling procedure is achieved by a special formulation that allows to use different time steps in each subdomain. Copyright © 2005 John Wiley & Sons, Ltd.     

竖向地震荷载下输液管道弯曲振动的有限元分析

将与固定构筑物连接处的管道视为弹性梁，并考虑管道基础的不均匀沉降竖向地震荷载的作用及管内液体流动引起的耦联振动，建立数学模型，进行动力响应分析，针对某些介质和结构参数，给出了一些数值结果，得出了流速对管道动力响应管道动力响应影响及管端不均匀沉降对其动力响应影响的若干初步结论。     

Finite Element Analysis of Modeling Residual Stress Distribution in All-position Duplex Stainless Steel Welded Pipe

On the basis of the thermal-elastic-plastic theory, a three-dimensional finite element numerical simulation is performed on the girth welded residual stresses of the duplex stainless steel pipe with ANSYS nonlinear finite element program for the first time. Three-dimensional FEM using mobile heat source for analysis transient temperature field and welding stress field in circumferential joint of pipes is founded. Distributions of axial and hoop residual stresses of the joint are investigated. The axial and the hoop residual stresses at the weld and weld vicinity on inner surface of pipes are tensile, and they are gradually transferred into compressive with the increase of the departure from the weld. The axial residual stresses at the weld and weld vicinity on outer surface of pipes is compressive while the hoop one is tensile. The distributions of residual stresses compared positive-circle with negative-circle show distinct symmetry. These results provide theoretical knowledge for the optimization of p     

Analysis of Pipes Containing Plain and Gouged Dents

Abstract: The paper discusses numerical results obtained for pipes subjected to transverse denting by a rigid indenter. Dents produced by different shapes of indenters are assessed for the amount of cross‐sectional distortion of the pipe and for propagation of this distortion along the length of the pipe. The contact area between the rigid indenter and the deformable pipe, as well as between the pipe and the rigid support is calculated for different loading configurations and for different shapes of indenters. Pipe supports considered include elastic springs, a rigid saddle and a rigid plate. In numerical work, axial cracks and gouges of different sizes have been introduced to the pipe's outer surface. Damaged pipes are then subjected to denting and results, including denting forces, distortion of the cross‐sectional area and limit loads are compared with the corresponding results obtained for non‐dented and non‐gouged geometries as well as with non‐dented but gouged cases. Finally, selected numerical results are compared to experimental data in order to demonstrate the adequacy of the adopted modelling and analysis approach.     

Hybrid finite element/volume method for shallow water equations

A hybrid numerical scheme based on finite element and finite volume methods is developed to solve shallow water equations. In the recent past, we introduced a series of hybrid methods to solve incompressible low and high Reynolds number flows for single and two‐fluid flow problems. The present work extends the application of hybrid method to shallow water equations. In our hybrid shallow water flow solver, we write the governing equations in non‐conservation form and solve the non‐linear wave equation using finite element method with linear interpolation functions in space. On the other hand, the momentum equation is solved with highly accurate cell‐center finite volume method. Our hybrid numerical scheme is truly a segregated method with primitive variables stored and solved at both node and element centers. To enhance the stability of the hybrid method around discontinuities, we introduce a new shock capturing which will act only around sharp interfaces without sacrificing the accuracy elsewhere. Matrix‐free GMRES iterative solvers are used to solve both the wave and momentum equations in finite element and finite volume schemes. Several test problems are presented to demonstrate the robustness and applicability of the numerical method. Copyright © 2010 John Wiley & Sons, Ltd.     

含非贯穿直裂纹管道的振动特性分析

摘 要：根据线性断裂力学理论和应变能释放原理,推导了管道在轴力、剪力和弯矩等荷载作用下由非贯穿直裂纹引入的附加局部柔度,利用适应性Simpson数值积分编写了局部柔度计算程序,克服了当前方法仅针对特定的荷载模式或非空心截面的缺陷,通过与Naniwadekar等人试验结果进行对比验证本文局部柔度系数的合理性。建立了裂纹管结构的有限元模型,对悬臂裂纹管和简支裂纹管的自由振动特性进行了分析。研究结果表明：裂纹位置、裂纹深度对裂纹管类结构的自振频率影响明显。     

Micropolar hyper‐elastoplasticity: constitutive model,consistent linearization,and simulation of 3D scale effects

A computational model for micropolar hyperelastic‐based finite elastoplasticity that incorporates isotropic hardening is developed. The basic concepts of the non‐linear micropolar kinematic framework are reviewed, and a thermodynamically consistent constitutive model that features Neo‐Hooke‐type elasticity and generalized von Mises plasticity is described. The integration of the constitutive initial value problem is carried out by means of an elastic‐predictor/plastic‐corrector algorithm, which retains plastic incompressibility. The solution procedure is developed carefully and described in detail. The consistent material tangent is derived. The micropolar constitutive model is implemented in an implicit finite element framework. The numerical example of a notched cylindrical bar subjected to large axial displacements and large twist angles is presented. The results of the finite element simulations demonstrate (i) that the methodology is capable of capturing the size effect in three‐dimensional elastoplastic solids in the finite strain regime, (ii) that the formulation possesses a regularizing effect in the presence of strain localization, and (iii) that asymptotically quadratic convergence rates of the Newton–Raphson procedure are achieved. Throughout this paper, effort is made to present the developments as a direct extension of standard finite deformation computational plasticity. Copyright © 2012 John Wiley & Sons, Ltd.     

一种基于应变插值大变形梁单元的刚-柔耦合动力学分析

柔性多体系统动力学中的“动力刚化”现象起因于变形间的耦合。一次近似模型成功地解决了小变形情况下的刚柔耦合建模问题,但在大变形情况下则需要考虑更多的耦合效应。本文选取表征梁弯曲应变的曲率和轴向应变作为单元参数进行离散;在大变形大转动基础上得到了单元两端节点运动学参数的递推关系,构造出了能够自动计及“动力刚化项”且适用于大变形刚柔耦合动力学分析的平面梁单元。最后采用本文所提应变插值单元求解了包含大变形和刚柔耦合动力学柔性梁的数值算例,验证了文中算法的正确性和有效性。     

信道阻尼边界对井下钻杆声传输的影响

为改善低频声波沿钻杆管肇的传输性能，分析了影响声遥测的阻尼机制。考虑钻杆内外沿轴向流动的钻井液的阻尼影响，引入流体的粘性阻尼力，建立了一维纵波波动方程。基于圆柱源辐射理论，研究纵波的径向耦合损耗，并将地层等效为Kelvin粘弹性介质，应用有限单元法求解时域波动方程，讨论了钻井液粘性阻尼和粘弹性地层边界对行波传播特性的影响。理论分析表明，径向辐射和由此产生的波型耦合是声阻尼损耗的主要形式，地层粘弹性系数的变化列低频特性影响很大，但并不改变信道通阻带交替的梳状滤波器频谱。     

作大范围运动的矩形板动力分析

作高速大范围运动的弹性体,由于运动和变形的耦合将产生动力刚化现象,传统的动力学理论难以计及这种影响.本文在有限元方法中首次引入了单元耦合形函数(阵),以此将单元弹性位移表示成为单元结点位移的二阶小量形式.利用几何非线性的应变-位移关系式,在小变形假设条件下确定了单元耦合形函数.在此基础上,根据Kane方程.运用模态坐标压缩,并采用适当的线性化处理,得到了包含动力刚度项的线性动力学方程.针对矩形板编制了动力刚化有限元分析程序.仿真算例证明了理论和算法的正确性.     

Numerical modelling of non‐linear electroelasticity

The numerical modelling of non‐linear electroelasticity is presented in this work. Based on well‐established basic equations of non‐linear electroelasticity a variational formulation is built and the finite element method is employed to solve the non‐linear electro‐mechanical coupling problem. Numerical examples are presented to show the accuracy of the implemented formulation. Copyright © 2006 John Wiley & Sons, Ltd.