A robust solution procedure for hyperelastic solids with large boundary deformation

Compressible Mooney–Rivlin theory has been used to model hyperelastic solids, such as rubber and porous polymers, and more recently for the modeling of soft tissues for biomedical tissues, undergoing large elastic deformations. We propose a solution procedure for Lagrangian finite element discretization of a static nonlinear compressible Mooney–Rivlin hyperelastic solid. We consider the case in which the boundary condition is a large prescribed deformation, so that mesh tangling becomes an obstacle for straightforward algorithms. Our solution procedure involves a largely geometric procedure to untangle the mesh: solution of a sequence of linear systems to obtain initial guesses for interior nodal positions for which no element is inverted. After the mesh is untangled, we take Newton iterations to converge to a mechanical equilibrium. The Newton iterations are safeguarded by a line search similar to one used in optimization. Our computational results indicate that the algorithm is up to 70 times faster than a straightforward Newton continuation procedure and is also more robust (i.e., able to tolerate much larger deformations). For a few extremely large deformations, the deformed mesh could only be computed through the use of an expensive Newton continuation method while using a tight convergence tolerance and taking very small steps.     

Optimal topology design for stress-isolation of soft hyperelastic composite structures under imposed boundary displacements

Soft hyperelastic composite structures that integrate soft hyperelastic material and linear elastic hard material can undergo large deformations while isolating high strain in specified locations to avoid failure. This paper presents an effective topology optimization-based methodology for seeking the optimal united layout of hyperelastic composite structures with prescribed boundary displacements and stress constraints. The optimization problem is modeled based on the power-law interpolation scheme for two candidate materials (one is soft hyperelastic material and the other is linear elastic material). The ?-relaxation technique and the enhanced aggregation method are employed to avoid stress singularity and improve the computational efficiency. Then, the topology optimization problem can be readily solved by a gradient-based mathematical programming algorithm using the adjoint variable sensitivity information. Numerical examples are given to show the importance of considering prescribed boundary displacements in the design of hyperelastic composite structures. Moreover, numerical solutions demonstrate the validity of the present model for the optimal topology design with a stress-isolated region.     

Creating and simulating a realistic physiological tongue model for speech production

Simulation of the tongue has important applications in biomechanics, medical science, linguistics, and graphics. The accuracy of the geometry, intrinsic structure and dynamic simulation of tongue are crucial for these applications. In this paper, we build a 3D anatomically and biomechanically accurate tongue model. For ensuring anatomical accuracy, the tongue mesh model is constructed based on accurate medical data and an interactive muscle marking method for specifying the muscle geometry and fiber arrangement. For ensuring biomechanical accuracy, a nonlinear, quasi-incompressible, isotropic, hyperelastic constitutive model is applied for describing the tongue tissues. Particularly, tongue muscles are additionally endowed with an anisotropic constitutive model, which reflects the active and passive mechanical behavior of muscle fibers. The dynamic simulation results of tongue movements subjected to certain muscle activations are presented and validated with experimental data, indicating the suitability for visual speech synthesis.     

Generalized Nonlinear Stiffness Identification on Controlled Mechanical Vibrating Systems

A new algebraic parametric identification method in time domain for multiple degrees‐of‐freedom mechanical vibrating systems with high‐order nonlinear stiffness is proposed. Parameters of mass, damping and linear and nonlinear stiffness are estimated on‐line and, simultaneously, using transient real‐time position measurements and active control force signals. Parametric identification can be applied for real‐time estimation of both symmetrical and non‐symmetrical stiffness. Parametric identification is combined with adaptive planned motion control on Multiple‐Input‐Multiple‐Output nonlinear mechanical vibrating systems. Analytical and numerical results prove the effectiveness and efficiency of the proposed on‐line algebraic parametric identification approach.     

Analyzing soft tissue stiffness of human upper arms during physical dynamic and quasi-static impacts in human–machine interaction

Knowledge of the changes in the behavior of human soft tissue stiffness during physical impact in human–machine interaction (HMI) plays a vital role in the development of biofidelity testing devices such as a human dummy. These testing devices are widely applied as an effective means to validate the safety of machinery during dynamic or static contact with humans in HMI. In this study, we assess changes in soft tissue stiffness in the upper arm of individuals under both dynamic (0.7 and 0.25 m/s) and quasi-static (QS) impacts under a constrained contact condition. Three impactor shapes (cylindrical, cubic, and spherical) are used in this study. Impact experiments are conducted using impactors attached to a pendulum. The soft-tissue displacement is determined using an ultrasound device. The impact force-displacement curves illustrate the nonlinear behavior of the soft tissue stiffness under both dynamic and QS impacts. By utilizing the “Linear Mixed Model” statistical analysis, we found that changes in the impact velocity significantly influenced the changes in the nonlinear behavior of soft tissue stiffness while there was no significant effect of the changes in the impactor shape on the nonlinear behavior of the soft tissue stiffness. Additionally, we revealed that the changes in the soft tissue stiffness are influenced by the size of the contact area. Moreover, we demonstrated a range of changes in soft tissue stiffness for different impact velocities, which provide valuable information for developing future validation test devices in HMI, such as the design and evaluation of dummy skin.     

Real‐time haptic manipulation and cutting of hybrid soft tissue models by extended position‐based dynamics

This paper systematically describes an interactive dissection approach for hybrid soft tissue models governed by extended position‐based dynamics. Our framework makes use of a hybrid geometric model comprising both surface and volumetric meshes. The fine surface triangular mesh with high‐precision geometric structure and texture at the detailed level is employed to represent the exterior structure of soft tissue models. Meanwhile, the interior structure of soft tissues is constructed by coarser tetrahedral mesh, which is also employed as physical model participating in dynamic simulation. The less details of interior structure can effectively reduce the computational cost during simulation. For physical deformation, we design and implement an extended position‐based dynamics approach that supports topology modification and material heterogeneities of soft tissue. Besides stretching and volume conservation constraints, it enforces the energy preserving constraints, which take the different spring stiffness of material into account and improve the visual performance of soft tissue deformation. Furthermore, we develop mechanical modeling of dissection behavior and analyze the system stability. The experimental results have shown that our approach affords real‐time and robust cutting without sacrificing realistic visual performance. Our novel dissection technique has already been integrated into a virtual reality‐based laparoscopic surgery simulator. Copyright © 2015 John Wiley & Sons, Ltd.     

Contact impedance estimation for robotic systems

In this paper, the problem of online estimation of the mechanical impedance during the contact of a robotic system with an unknown environment is considered. This problem is of great interest when controlling a robot in an unstructured and unknown environment, such as in telemanipulation tasks, since it can be easily shown that the exploitation of the knowledge of the mechanical properties of the environment can greatly improve the performance of the robotic system. In particular, a single-point contact is considered, and the (nonlinear) Hunt-Crossley model is taken into account, instead of the classical (linear) Kelvin-Voigt model. Indeed, the former achieves a better physical consistency and also allows describing the behavior of soft materials. Finally, the online estimation algorithm is described and experimental results are presented and discussed.     

微机械加速度计挠性梁机械刚度的实验研究

在使用开环频率响应实验求取微机械加速度计挠性梁机械刚度时,不可避免地受到静电负刚度的影响。通过分析预载电压和扫频信号幅值对静电负刚度的影响,提出了从系统刚度中分离出挠性梁机械刚度的计算方法。通过不同实验条件下得到的实验结果,验证了该方法的正确性。     

基于Marc的空气弹簧横向特性分析

为实现空气弹簧的横向特性和强度分析,基于有限元非线性接触技术,用Marc对空气弹簧的非线性横向刚度特性进行数值模拟,分析最大横向力作用下空气弹簧各部分的应力分布,横向刚度计算结果与试验结果基本一致,表明空气弹簧的建模与仿真方法的合理性,为空气弹簧优化设计和特性分析提供参考.     

Real-Time Finite-Element Simulation of Linear Viscoelastic Tissue Behavior Based on Experimental Data

We propose an end-to-end solution to real-time and realistic finite-element modeling and simulation of viscoelastic soft tissue behavior. We provide an efficient numerical scheme for solving a linear viscoelastic FEM model derived from the generalized Maxwell solid, and present methods for measuring and integrating experimental data on the viscoelastic material properties of soft tissues into the model for realistic display of visual deformations and interaction forces. Our precomputation scheme and multilayer computational architecture enable the model's real-time execution with visual and haptic feedback to the user. Our approach includes time- and rate-dependent effects, which requires considering a node's loading history in our displacement computations at each cycle of the simulation     

基于神经网络的堆石料本构模型参数反演

为准确估计堆石料力学本构模型参数,根据堆石料三轴压缩实验观测数据,提出一种基于神经网络的堆石料非线性本构模型参数反演方法。通过对三轴压缩实验轴向和径向应变的分段线性化处理,建立求解垂直荷载与应变之间关系的解析表达式。应用神经网络法对堆石料的力学模型参数进行反演,建立三轴压缩实验轴向和径向应变与模型参数之间的非线性映射关系,并据此进行堆石料模型参数估计。为验证反演方法的有效性,采用施工现场的堆石料进行三轴压缩实验,结果表明,与基于梯度优化搜索的参数估计方法相比,该方法具有更高的预测精度,最大相对误差降低了17.8%。     

Dead‐Zone Model Based Adaptive Backstepping Control for a Class of Uncertain Saturated Systems

In this paper, a dead‐zone based model of saturation phenomena is proposed. This method is capable of modelling diverse kinds of saturation, including both hard‐limited and soft‐limited. Due to use of a linear parameter approach, the proposed model is consistent with the available adaptive control techniques in the literature. In addition, based on the proposed model, an adaptive controller is designed for a class of nonlinear saturated systems, where, the shape of the saturation phenomenon is assumed to be unknown. The effectiveness of the proposed method and its robustness against initial condition variation and reference signal is evaluated via simulated examples for both spring–mass–damper and ship steering autopilot systems.     

变刚度机构及其在协作型机器人中的应用

协作型机器人被广泛应用于自动化和物料搬运。为承载有效载荷并实现精确运动,协作型机器人需要具备足够的刚性。此外,为满足人机交互的安全性,协作型机器人还需要具备足够的灵活性,变刚度机器人则同时满足了安全性与刚性的要求。该文首先介绍了变刚度机器人的相关研究和几种基于机械结构的可变刚度方法,并对其工作原理进行分类;然后根据刚度范围、刚度比和响应时间等标准,对现有方法进行定量比较,简单总结各种方法的优缺点,并介绍了相关变刚度机构在协作型机械臂和抓手中的应用。     

Control of near‐grazing dynamics and discontinuity‐induced bifurcations in piecewise‐smooth dynamical systems

This paper develops a rigorous control paradigm for regulating the near‐grazing bifurcation behavior of limit cycles in piecewise‐smooth dynamical systems. In particular, it is shown that a discrete‐in‐time linear feedback correction to a parameter governing a state‐space discontinuity surface can suppress discontinuity‐induced fold bifurcations of limit cycles that achieve near‐tangential intersections with the discontinuity surface. The methodology ensures a persistent branch of limit cycles over an interval of parameter values near the critical condition of tangential contact that is an order of magnitude larger than that in the absence of control. The theoretical treatment is illustrated with a harmonically excited damped harmonic oscillator with a piecewise‐linear spring stiffness as well as with a piecewise‐nonlinear model of a capacitively excited mechanical oscillator. Copyright © 2009 John Wiley & Sons, Ltd.     

State tracking model reference adaptive control for switched nonlinear systems with linear uncertain parameters

Model reference adaptive control(MRAC)is considered for a class of switched nonlinear systems in which the unknown parameters appear linearly.The linear uncertain parameters in each subsystem can be expressed as a vector and the uncertain vectors in different subsystems are estimated individually by different vector variables.Update laws are designed such that the parameter estimation will ’freeze’ until its corresponding subsystem is active.Controllers for subsystems are given to ensure asymptotic states tracking under arbitrary switchings.Two examples are presented to validate the proposed method.     

多轴承载下基于Mullins效应的非线性刚度的分析方法

轨道交通所用的橡胶减震元件在多向承载时通常会获得预压缩应力,这会使橡胶减震元件在多向承载过程中表现出Mullins效应.详细研究橡胶材料的Mullins效应原理、超弹本构模型的局限以及Mullins参数对橡胶软化行为的影响特性,为研究和分析带预应力的橡胶减震元件的非线性刚度计算提供一种新的思路和方法.     

A Bernstein-Bézier Based Approach to Soft Tissue Simulation

This paper discusses a Finite Element approach for volumetric soft tissue modeling in the context of facial surgery simulation. We elaborate on the underlying physics and address some computational aspects of the finite element discretization.
In contrast to existing approaches speed is not our first concern, but we strive for the highest possible accuracy of simulation. We therefore propose an extension of linear elasticity towards incompressibility and nonlinear material behavior, in order to describe the complex properties of human soft tissue more accurately. Furthermore, we incorporate higher order interpolation functions using a Bernstein-Bézier formulation, which has various advantageous properties, such as its integral polynomial form of arbitrary degree, efficient subdivision schemes, and suitability for geometric modeling and rendering. In addition, the use of tetrahedral Finite Elements does not put any restriction on the geometry of the simulated volumes.
Experimental results obtained from a synthetic block of soft tissue and from the Visible Human Data Set illustrate the performance of the envisioned model.     

低g值微惯性开关中阿基米德平面螺旋梁的设计

针对低g值微惯性开关对微弹簧的系统刚度达到(0.1~10)N/m数量级的要求,设计了一种阿基米德平面螺旋梁结构的微惯性开关。根据材料力学中的卡氏定理和线弹性理论,推导了阿基米德平面螺旋梁的弹性系数计算公式,并与ANSYS有限元仿真分析结果进行了对比。基于推导的弹性系数计算公式设计了一种三根阿基米德平面螺旋梁支撑的动作阈值5.5 gn 的微惯性开关,并采用SOI硅片以及玻璃－硅－玻璃键合技术进行了加工,在离心转台上对开关实际动作阈值进行测试,并将测试值与设计值进行对比。结果表明,采用推导到的阿基米德平面螺旋梁弹性系数计算公式计算结果与ANSYS仿真结果相近,基于推导的弹性系数计算公式设计的三根阿基米德平面螺旋梁支撑的微惯性开关动作阈值设计值与实测值相近,单根阿基米德平面螺旋梁弹性系数约0.8 N/m,能够满足低g值微惯性开关低刚度的要求,推导的弹性系数计算公式能够用于基于阿基米德平面螺旋梁的低g值微惯性开关的设计。     

An integrated physical model that characterizes creep and hysteresis in piezoelectric actuators

In this paper, a model that can precisely portray hysteresis and creep in piezoelectric actuators is proposed. The model, which is originally constructed using bond-graph representation, describes the actuator’s various physical effects and energy interaction between physical domains. Specifically, the model utilizes a parallel connection of Maxwell-slip elements and a nonlinear spring to describe hysteresis, and a series connection of Kelvin–Voigt units to describe creep. Using the experimental data, the constitutive relation of the nonlinear spring and the parameters of linear, physical elements in the model can be systematically identified via the linear programming method. To further account for the frequency-dependent hysteresis behavior, a dynamic damper is incorporated. By analyzing the model, the influence of initial strain/charges on the creep response is revealed and an initialization procedure is devised to eliminate such an influence. An inverse model control, in the sense of feedback linearization, is constructed based on the identified model to make the actuator track reference trajectories. Experiments show that both creep and hysteresis are effectively cancelled and accurate tracking of selected reference trajectories is achieved.