Modeling,Simulation and Parameter Identification for Rate-Dependent Magnetoactive Polymer Response

A finite deformation framework for nonlinear magneto-viscoelasticity is introduced and applied to the constitutive and structural modeling of magnetoactive polymer (MAP) response. In this thermodynamically-consistent formulation the free energy function consists of purely elastic, purely magnetic and coupling contributions, where the rate-dependence is fully attributed to the non-magnetizable matrix material. The model consistently accounts for saturation in the magnetic as well as the magnetostrictive behavior. The identification of material parameters from experimental data is briefly described. Finally, a finite element model for the large strain magneto-mechanical problem is established and tested considering MAP behavior. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Large-Deformation Phase-Field Approach for the Modeling of Magneto-Sensitive Elastomers

Magneto-sensitive materials show magneto-mechanical coupled response and are thus of increasing interest in the recent age of smart functional materials. Ferromagnetic particles suspended in an elastomeric matrix show realignment under the influence of an external applied field, in turn causing large deformations of the substrate material. The magneto-mechanical coupling in this case is governed by the magnetic properties of the inclusion and the mechancial properties of the matrix. The magnetic phenomenon in ferromagnetic materials is governed by the formation and evolution of domains on the micro scale. A better understanding of the behavior of these particles under the influence of an external applied field is required to accurately predict the behavior of such materials. In this context it is of particular importance to model the macro scopic magneto-mechanically coupled behavior based on the micro-magnetic domain evolution. The key aspect of this work is to develop a large-deformation micro-magnetic model that can accurately capture the microscopic response of such materials. Rigorous exploitation of appropriate rate-type variational principles and consequent incremental variational principles directly give us field equations including the time evolution equation of the magnetization, which acts as the order parameter in our formulation. The theory presented here is the continuation of the work presented in [1, 7] for small deformations. A summary of magneto-mechanical theories spanning over multiple scales has been presented in [4]. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Phase field simulation on mechanically induced 180 degree switching in nanomagnets

The mechanically induced 180° switching of the magnetization in cylindrical nanomagnets is demonstrated through the switching dynamics simulation by a constraint-free phase field model which is fully magneto-mechanical coupled. By using the overrun behavior of the magnetization during the mechanically induced precessional switching, a deterministic 180° switching can be achieved. It is found that the residual torque resulting from the azimuthal-angle dependence of the magneto-elastic coupling and the overrun and precessional dynamics are responsible for the switching mechanism. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Magneto-Mechanically Coupled Phase-Field Model at Large Deformation

The aggregate magneto-mechanical behavior of magneto-rheological elastomers (MREs) stems from the magnetic properties of the ferromagnetic inclusion and the mechanical properties of the matrix material. We propose a large deformation micro-magnetic theory, to predict the behavior and interaction of ferromagnetic particles inside an elastomeric matrix. A rate-type variational principle, with the magnetization as the order parameter is proposed. A large deformation Landau-Lifshitz-Gilbert equation for the time evolution of the magnetization, is obtained directly from the proposed variational principle. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Distribution of dislocation density and residual stresses in plastically deformed specimens: numerical studies

A two-scale approach to the simulation of mechanical properties of metallic materials is considered. On the macroscopic level, the material behavior is described by a phenomenological model of finite strain viscoplasticity with nonlinear kinematic hardening. In particular, the process-induced plastic anisotropy is captured by backstresses. On the microstructural level, the so called “load path sensitive two-population dislocation cell model” is implemented. It describes an evolving dislocation cell structure with dislocation populations for dislocation cell walls and the cell interior. Owing to the coupling with the phenomenological plasticity model, it can describe the evolution of the dislocation densities depending on the load path. The applicability of the multiscale approach to the FEM simulation of severe plastic deformation processes such as Equal Channel Angular Pressing is demonstrated. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical modelling of finite strain magneto-viscoelastic deformations

Large strain magneto-viscoelastic deformations in the presence of a finite magnetic field are modelled in this paper. Internal dissipation mechanisms are proposed using a multiplicative decomposition of the deformation gradient and an additive decomposition of the magnetic induction. Using thermodynamically consistent constitutive and evolution laws, numerical results showing stress relaxation and magnetic field evolution are presented to illustrate the theory. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Micro-mechanical modeling of anisotropic inelastic response of soft tissues under supra-physiological loading

Under supra-physiological loading, soft tissues exhibit many inelastic phenomena, such as stress softening, hysteresis and permanent set [1]. Knowledge of the mechanical response of soft tissues under such a large range of deformation is vital for optimizations of vascular medical devices or improvement of injury prevention techniques. In this work, a micro-mechanical model is proposed for soft collagenous tissues. Besides the anisotropy the model can also describe the aforementioned inelastic effects under extremal loadings. To this end, the dispersion of collagen fibers in the soft tissues is captured by a probability distribution of fiber orientations around preferred directions. The deformation induced damage inside the tissue is assumed to take place between collagen fibrils and is included within a statistical mechanical framework. Finally, the accuracy of the model is assessed by comparison with experimental data available in the literature. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The longtime behavior of a nonlinear Reissner-Mindlin plate with exponentially decreasing memory kernels

In this paper we investigate the longtime behavior of the mathematical model of a homogeneous viscoelastic plate based on Reissner-Mindlin deformation shear assumptions. According to the approximation procedure due to Lagnese for the Kirchhoff viscoelastic plate, the resulting motion equations for the vertical displacement and the angle deflection of vertical fibers are derived in the framework of the theory of linear viscoelasticity. Assuming that in general both Lame's functions, λ and μ, depend on time, the coupling terms between the equations of displacement and deflection depend on hereditary contributions. We associate to the model a nonlinear semigroup and show the behavior of the energy when time goes on. In particular, assuming that the kernels λ and μ decay exponentially, and not too weakly with respect to the physical properties considered in the model, then the energy decays uniformly with respect to the initial conditions; i.e., we prove the existence of an absorbing set for the semigroup associated to the model.     

A Magneto-Visco-Elastic Model for Magnetorheological Elastomers

In this work we present the modular construction and FEM implementation of a material model for magnetorheological elastomers (MRE) that is firmly rooted in micromechanics and performs well against experimental data. Keeping in mind the composite nature at the microscale, we develop a constitutive formulation based on a multiplicative magneto-mechanical split of the deformation gradient. We consider both Lee- and Clifton-type right and left decompositions. In contrast to other recent formulations [6], this general approach allows the use of highly advanced micromechnically-based network models for polymers such as [4] and [5] in a modular format and to extend its application for coupled magnetomechanical response. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于非约束模态的中心刚体-Timoshenko梁动力学建模与分析北大核心CSCD

梁的横向变形会导致梁纵向缩短,建模过程中考虑梁横纵变形二次耦合项则存在动力刚化现象,这说明梁的纵向变形会对模型的广义刚度造成影响.对于做旋转运动的梁结构,旋转运动时还会受到离心力的作用而产生轴向拉力,轴向拉力同样也会引起梁的轴向变形,这种影响对粗短梁更加明显.以大范围运动中心刚体-Timoshenko梁模型为研究对象:首先,运用Timoshenko梁理论以及Hamilton原理建立含离心力的动力学模型;其次,引入非约束模态概念,采用Frobenius方法求解非约束模态振型函数以及固有频率;最后,通过数值仿真探究不同恒定转速时非约束模态与约束模态广义刚度的差异和非约束模态条件下离心力对模型的影响.     

无粘性土的应力矢量本构模型(Ⅱ)——应用

将史宏彦等提出的无粘性土的应力矢量本构模型应用于分析多种复杂应力路径下材料的变形问题。结果表明，此模型不仅能够很好地反映无粘性土的应力应变非线形、硬化性、剪缩剪胀性、与应力路径的相关性、主应力与主应变增量方向之间的非共轴性以及球偏应力与变形的耦合性等主要变形特性，而且也能够同时考虑主应力轴的旋转和中主应力对土的变形及强度的影响。模型预测结果与试验结果之间的良好吻合表明了该模型的广泛适用性。     

Damage and fracture behavior in dynamic tension tests: Modelling and numerical simulations

The continuum damage model is based on a general thermodynamic framework for the modeling of rate and temperature dependent behavior of anisotropically damaged elastic-plastic materials subjected to fast deformation. The introduction of damaged and fictitious undamaged configurations allows the definition of damage tensors and the corresponding free energy functions lead to material laws affected by damage and temperature. The damage condition and the corresponding damage rule strongly depend on stress triaxiality. Furthermore, the rate and temperature dependence is reflected in a multiplicative decomposition of the plastic hardening and damage softening functions. The macro crack behavior is characterized by a triaxiality dependent fracture criterion. The continuum damage model is implemented into LS-DYNA as user defined material model. Corresponding numerical simulations of unnotched and notched tension tests with high strain rates demonstrate the plastic and damage processes during the deformation leading to final fracture numerically predicted by an element erosion technique. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A variational approach towards the modeling of equilibrium twin interfaces in a single-crystalline magnetic shape memory alloy sample

In this work, a variational approach is proposed to study the magneto-mechanical response of a single-crystalline MSMA sample. By proposing a total energy functional for the whole magneto-mechanical system, the governing PDE system is derived by calculating the variations of the total energy functional with respect to the independent variables. An iterative numerical algorithm is proposed to solve the governing PDE system. As an example, a MSMA sample with cuboid shape and subject to perpendicularly applied magnetic and mechanical loadings is considered. It can be seen that the magneto-mechanical response of this sample can be predicted at a quantitative level. The whole procedure of variant reorientation in the sample can also be simulated. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Advanced finite element formulations for modeling thin piezoelectric structures

This contribution is concerned with mixed finite element formulations for modeling piezoelectric beam and shell structures. Due to the electromechanical coupling, specific deformation modes are joined with electric field components. In bending dominated problems incompatible approximation functions of these fields cause incorrect results. These effects occur in standard finite element formulations, where interpolation functions of lowest order are used. A mixed variational approach is introduced to overcome these problems. The mixed formulation allows for a consistent approximation of the electromechanical coupled problem. It utilizes six independent fields and could be derived from a Hu-Washizu variational principle. Displacements, rotations and the electric potential are employed as nodal degrees of freedom. According to the Timoshenko theory (beam) and the Reissner-Mindlin theory (shell), the formulations account for constant transversal shear strains. To incorporate three dimensional constitutive relations all transversal components of the electric field and the strain field are enriched by mixed finite element interpolations. Thus the complete piezoelectric coupling is appropriately captured. The common assumption of vanishing transversal stress and dielectric displacement components is enforced in an integral sense. Some numerical examples will demonstrate the capability of the presented finite element formulation. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Geometric Framework for Stochastic Shape Analysis

We introduce a stochastic model of diffeomorphisms, whose action on a variety of data types descends to stochastic evolution of shapes, images and landmarks. The stochasticity is introduced in the vector field which transports the data in the large deformation diffeomorphic metric mapping framework for shape analysis and image registration. The stochasticity thereby models errors or uncertainties of the flow in following the prescribed deformation velocity. The approach is illustrated in the example of finite-dimensional landmark manifolds, whose stochastic evolution is studied both via the Fokker–Planck equation and by numerical simulations. We derive two approaches for inferring parameters of the stochastic model from landmark configurations observed at discrete time points. The first of the two approaches matches moments of the Fokker–Planck equation to sample moments of the data, while the second approach employs an expectation-maximization based algorithm using a Monte Carlo bridge sampling scheme to optimise the data likelihood. We derive and numerically test the ability of the two approaches to infer the spatial correlation length of the underlying noise.

     

Buckling Analysis of Carbon Nanotubes

In this work, an atomistic-continuum model is applied to single-walled carbon nanotubes. The constitutive behaviour is described by the interatomic Tersoff-Brenner potential. The coupling between atomistic deformation and the deformation of the continuum is done by an expanded Cauchy-Born rule. With the help of this model, the buckling behaviour of carbon nanotubes under different loading conditions is studied. Numerical simulation results are given for two different types of loading (axial compression, torsion). (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

高温泵用液膜密封流热固耦合分析

利用Mesh软件建立动环、静环周期模型,基于Workbench对动环、静环进行了三维力耦合和力热耦合计算.探究了力耦合和力热耦合对端面变形的影响,探讨了影响端面变形的操作参数(转速、压差),并分析了力热耦合产生的应力.得出:力耦合引起周向波度变形和收敛型径向锥度变形,有利于间隙流体的稳定;力热耦合变形中热载荷引起的变形占主导地位;转速对力热耦合变形影响较明显.     

A stochastic multiscale model for electricity generation capacity expansion

Long-term planning for electric power systems, or capacity expansion, has traditionally been modeled using simplified models or heuristics to approximate the short-term dynamics. However, current trends such as increasing penetration of intermittent renewable generation and increased demand response requires a coupling of both the long and short term dynamics. We present an efficient method for coupling multiple temporal scales using the framework of singular perturbation theory for the control of Markov processes in continuous time. We show that the uncertainties that exist in many energy planning problems, in particular load demand uncertainty and uncertainties in generation availability, can be captured with a multiscale model. We then use a dimensionality reduction technique, which is valid if the scale separation present in the model is large enough, to derive a computationally tractable model. We show that both wind data and electricity demand data do exhibit sufficient scale separation. A numerical example using real data and a finite difference approximation of the Hamilton–Jacobi–Bellman equation is used to illustrate the proposed method. We compare the results of our approximate model with those of the exact model. We also show that the proposed approximation outperforms a commonly used heuristic used in capacity expansion models.     

Thermodynamically consistent temperature prediction in dissipative solids

The present work deals with the thermomechanical coupling in dissipative solids and the consistent temperature prediction. One of the first works dealing with this subject was written by Taylor & Quinney (TQ) where the fraction between dissipated energy eventually transformed to heat and plastic work is assumed as constant (typically between 0.8-1.0 for metals). Although this assumption often leads to reasonable temperature predictions, it is not always in agreement with experimental observations. Furthermore, the TQ model does not comply with the first and second law of thermodynamics in general. Unfortunately, a standard thermodynamically consistent framework is not convincing either, since it usually leads to a significant overprediction of the temperature increase during dissipative processes. Within the present work, a novel framework suitable for the modeling of thermomechanically coupled processes is discussed. It will be shown that this framework is thermodynamically consistent and leads to a temperature increase, as a result of plastic deformation, in good agreement with the underlying experiments. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Instability in a delay-PDE model of earthquake occurrence

Summary Ductile deformation prior to brittle fracture in rocks causes fracture to take place with a time delay after the critical stress for fracture is reached, in the presence of an increasing load stress. We discuss the stability of a stochastic model of interactive earthquake occurrence under the influence of time delays resulting from the ductile process. A threshold for oscillatory behavior is found for large enough coupling and discrete time delays. The system is stable if the time delays are spread over a broad time interval, even for large coupling.