A cohesive element approach for viscoelastic interface properties

This paper introduces a time dependent extension of the nonlinear traction separation law for an interface element. The constitutive equations of the load history dependent behaviour of the material are depicted and derived according to a generalized Maxwell‐model. This finite linear, viscoelastic approach allows the consideration of long term loading and time dependent material behaviour in thin layers. The implementation of the presented element formulation and the material approach are verified by numerical examples. The paper gives an outlook on further work and research topics. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

粘弹性方程全离散化有限体积元格式及数值模拟

本文利用有限体积元方法研究二维粘弹性方程, 给出一种时间二阶精度的全离散化有限体积元格式, 并给出这种全离散化有限体积元解的误差估计, 最后用数值例子验证数值结果与理论结果是相吻合的. 通过与有限元方法和有限差分方法相比较, 进一步说明了全离散化有限体积元格式是求解二维粘弹性方程数值解的最有效方法之一.     

粘弹性方程一种新的分裂正定混合元法

本文用分裂正定混合有限元方法研究二阶粘弹性方程. 首先构造一种新的分裂正定混合变分形式和基于这种分裂正定混合变分形式关于时间的半离散格式, 然后绕开关于空间变量的半离散化格式, 直接从时间半离散出发构造出全离散化的分裂正定混合有限元格式, 并给出这种分裂正定混合有限元解的误差估计. 这种研究思路使得理论论证变得更简单,这是处理二阶粘弹性方程的一种新的尝试.     

Finite element method for viscoelastic fluids flows: approximation of the Maxwell model

We discuss about the finite element approximation of viscoelastic fluid flow. We consider a fluid obeying the Oldroyd model and particularly we study the purely viscoelastic case, the so-called Maxwell model, important in practice for the applications. We examine two kinds of methods used for the approximation of the Maxwell model: method using a splitting technique and finite element method satisfying inf-sup conditions relating tensor and velocity. We present numerical results for these methods and we discuss about their stability. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Integration of geometric modeling and advanced finite element preprocessing

The structure to a geometry-based finite element preprocessing system is presented. The key features of the system are the use of geometric operators to support all geometric calculations required for analysis model generation, and the use of a hierarchic boundary-based data structure for the major data sets within the system. The approach presented can support the finite element modeling (FEM) procedures used today as well as the fully automated procedures under development.     

Numerical analysis of evolution problems in nonlinear small strains elastoviscoplasticity

Summary The present paper deals with the mathematical and numerical analysis of evolution problems in nonlinear small strains viscoelasticity of Burger's type. After a brief review of the mechanical model, the viscoelastic problem to be solved is written as an abstract evolution problem. The associated operator is proved to be maximal monotone, thus implying existence and uniqueness of solutions. This problem is then solved numerically by a backward Euler discretization in time, a finite element approximation in space and by using a preconditioned conjugate gradient algorithm for solving the resulting nonlinear algebraic systems. Numerical results are finally presented to illustrate the solution procedure.     

An anisotropic viscoelastic model for collagenous soft tissues at large strains – Computational aspects

This paper focusses on computational aspects related to a recently proposed anisotropic viscoelastic model for soft biological tissues at large strains [1]. A key aspect of this model is the generalisation of micromechanically motivated one-dimensional constitutive equations to three dimensions by numerical integration over the unit sphere. A strong effect of this procedure on the accuracy and in particular on the material symmetry of the model is observed. Finally a finite element example of an artery subject to normotensive blood pressure is presented. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new mixed finite element method for the Stokes problem

We propose a new mixed formulation of the Stokes problem where the extra stress tensor is considered. Based on such a formulation, a mixed finite element is constructed and analyzed. This new finite element has properties analogous to the finite volume methods, namely, the local conservation of the momentum and the mass. Optimal error estimates are derived. For the numerical implementation of this finite element, a hybrid form is presented. This work is a first step towards the treatment of viscoelastic fluid flows by mixed finite element methods.     

The static shape control for intelligent structures

A finite element formulation is presented for modeling the plate structure containing distributed piezoelectric sensors and actuators (S/As). A new plate bending element for analysis of the plate with distributed piezoelectric S/As is developed. This element saves much memory and computation time. Using the bending plate element, a general method of static shape control for the intelligent structure is put forth. Two examples are given to illustrate the application of the method presented in this paper. The purpose of the first example is to check the accuracy of the finite element method presented in this paper. The second example is to study the problem of the static shape control for the intelligent structure. It is concluded that the shape of the intelligent structure can reach the desired shape through passive control or active control.     

Stability and convergence analysis of stabilized finite element method for the Kelvin-Voigt viscoelastic fluid flow model

Numerical Algorithms - In this paper, we consider the Galerkin finite element method (FEM) for the Kelvin-Voigt viscoelastic fluid flow model with the lowest equal-order pairs. In order to overcome...     

Numerical approximation of the Oldroyd‐B model by the weighted least‐squares/discontinuous Galerkin method

We consider a numerical method for the Oldroyd‐B model of viscoelastic fluid flows by a combination of the weighted least‐squares (WLS) method and the discontinuous Galerkin (DG) finite element method. The constitutive equation is decoupled from the momentum and continuity equations, and the approximate solution is computed iteratively by solving the Stokes problem and a linearized constitutive equation using WLS and DG, respectively. An a priori error estimate for the WLS/DG method is derived and numerical results supporting the estimate are presented. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013     

Optimal constrained layer damping with partial coverage

This paper deals with the optimal damping of beams constrained by viscoelastic layers when only one or several portions of the beam are covered. An efficient finite element model for dynamic analysis of such beams is used. The design variables are the dimensions and prescribed locations of the viscoelastic layers and the objective is the maximum viscoelastic damping factor. The method for non-linear programming in structural optimization is the so-called method of moving asymptotes.     

Damping sources interactions in impact of viscoelastic composite plates with damping treated SMA wires,using a hyperbolic plate theory

In the present paper, a comprehensive study is made on effects of the viscoelastic and the phase-transformation-based dissipations and their interactions on impact responses of viscoelastic composite plates with damping treated (structural hierarchy) shape memory alloy (SMA) wires, for the first time. In contrast to almost all of the available researches, a high-order hyperbolic plate theory that includes not only odd but also even functions of the transverse coordinate, is proposed and employed here. While a hierarchical viscoelastic constitutive law is employed for both the orthotropic and SMA materials, Brinson's constitutive law is refined to include the loading fluctuations and structural hierarchy of the SMA wire, simultaneously. The traditional Hertz and Yang-Sun contact laws are modified accordingly. The resulting highly nonlinear piecewise-defined integro-differential finite element governing equations are solved by an iterative algorithm within each time step. The presented discussions show that in contrast to the common belief, the zero-shear traction condition on the top and bottom surfaces of the viscoelastic orthotropic plate cannot be satisfied by the available plate theories, even for the symmetric lamination schemes. Results show that the viscoelasticity and phase-transformation effects on the resulting dynamic responses are more pronounced for the low and high energy impacts, respectively.     

Time‐dependent algorithms for viscoelastic flow: Finite element/volume schemes

Hybrid finite volume/element methods are investigated within the context of transient viscoelastic flows. A finite volume algorithm is proposed for the hyperbolic constitutive equation, of Oldroyd‐form, whereas the continuity/momentum balance is accommodated through a Taylor‐Galerkin finite element method. Various finite volume combinations are considered to derive accurate and stable implementations. Consistency of formulation is key, embracing fluctuation distribution and median‐dual‐cell constructs, within a cell‐vertex discretisation on triangles. In addition, we investigate the effect of treating the time‐term in a finite element fashion, using mass‐matrix iteration instead of the standard finite volume mass‐lumping approach. We devise an accurate transient scheme that captures the analytical solution at short and long time, both in core flow and near shear boundaries. In this respect, some difficulties are highlighted. A new method emerges, with the Low Diffusion B (LDB, with or without mass‐matrix iteration) as the optimal choice. We progress to a complex flow application and demonstrate some provocative features due to the influence of true transient boundary conditions on evolutionary flow‐structure in a 4:1 start‐up rounded‐corner contraction problem. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

Alternative Kelvin viscoelastic procedure for finite elements

In this work, an alternative Kelvin viscoelastic formulation for the finite element method (FEM) is described. This formulation performs spatial approximations before considering time integration and makes use of differential viscoelastic relations. A matrix time differential equation arises from the proposed formulation. It is solved numerically by a time marching procedure. It is shown that, after a small simplification, this methodology can be employed together with existent dynamic FEM packages. The methodology is extended to dynamic analysis leading to a rheological explanation for the first order modal decomposition stiffness proportional damping matrix. Plates and shells applications are shown in order to demonstrate the proposed formulation accuracy and stability.     

Optimization of sandwich structures with damping properties

Maximum viscoelastic damping characteristics of sandwich structures are designed using finite element and informative planning methods. Two basic design problems were considered: addition of a damping coating to a given homogeneous structure and building a sandwich structure subjected to a given set of constraints. The methods of complex eigenvalues and direct calculation of the frequency characteristics were used. Numerical examples of optimizing sandwich beams are presented for both design problems.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 5, pp. 653–656, September–October, 1993.     

A New Reduced-Order fve Algorithm Based on POD Method for Viscoelastic Equations

A proper orthogonal decomposition (POD) technique is used to reduce the finite volume element (FVE) method for two-dimensional (2D) viscoelastic equations. A reduced-order fully discrete FVE algorithm with fewer degrees of freedom and sufficiently high accuracy based on POD method is established. The error estimates of the reduced-order fully discrete FVE solutions and the implementation for solving the reduced-order fully discrete FVE algorithm are provided. Some numerical examples are used to illustrate that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced-order fully discrete FVE algorithm is one of the most effective numerical methods by comparing with corresponding numerical results of finite element formulation and finite difference scheme and that the reduced-order fully discrete FVE algorithm based on POD method is feasible and efficient for solving 2D viscoelastic equations.     

A beam segment element for dynamic analysis of large aqueducts

Large aqueduct structure is a complex structure that is commonly used in hydraulic engineering, especially in large-scale water conveying projects. The analysis of dynamic response for an aqueduct structure is necessary if the aqueduct is built in an earthquake area. Traditional 3D finite element analysis is time consuming and the existing simplified response method cannot take into account all the effects, such as the bending-torsion coupling effect and the constrained torsion, of the deformations of the thin wall structure of the aqueduct body. For this special structure, a simple and yet accurate model for dynamic analysis is needed. In this paper, a beam segment element is developed and used for the calculation of dynamic response for aqueduct structures. With the frame of the aqueduct being modeled using beam element, the proposed model can calculate the dynamic response of the whole aqueduct structures. Results are compared with that of a general purpose finite element analysis software using 3D finite element model. Good agreement is achieved between the two models. However, the proposed model needs less elements and much less computing time.     

A boundary element methodology for viscoelastic analysis: Part II without cells

In this study Kelvin and Boltzmann viscoelastic models are implemented in a two-dimensional boundary element atmosphere. This general methodology is based on differential constitutive relations for viscoelasticity, avoiding the use of relaxation functions. In this part of the study, important algebraic operations are introduced into the formulation allowing analysing viscoelastic problems without using internal cells. This improvement is very important to model infinite and semi-infinite regions. The formulation is verified comparing the numerical results with analytical solutions. An extension of the formulation to consider soil–structure interaction is presented in order to demonstrate the vast applicability of the technique.     

Computational modeling of cardiac tissue with strongly coupled electromechanics and orthotropic viscoelastic effects

Modeling of complex mechanisms leading to the functioning of the heart has been an active field of research since decades. Difficulties associated with in vivo experiments motivate the utilization of computational models in order to gain a better appreciation of heart electromechanics. Although rate dependent behaviour of the orthotropic passive heart tissue has been comprehensively studied in the literature [1], effects of this phenomenon on fully coupled cardiac electromechanics are unrevealed yet. Therefore, this contribution is concerned with the investigation of viscous effects on the electromechanical response of the myocardium. To this end, we adopt the fully implicit finite element framework which strongly couples the mechanical and electrophysiological problem of the myocardium in a mono- and bi-domain setting [2,3], respectively. Viscous effects, however, are consistently embedded into this framework by making use of the orthotropic viscoelastic material model for the passive myocardium, which considers different relaxation mechanisms for the different orientation directions [5]. The performance of the proposed model is assessed by comparing finite element simulations of spiral waves in heart tissue for elastic and viscoelastic formulations. We further investigate the influence of viscosity on the defibrillation phenomenon by means of the finite element formulation of bidomain electrophysiology. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)