Review of terramechanics models and their applicability to real-time applications

ISTVS embarked on a project in 2016 that aims at updating the current ISTVS standards related to nomenclature, definitions, and measurement techniques for modelling, parameterizing, and, respectively, testing and validation of soft soil parameters and vehicle running gear-terrain interaction. As part of this project, a comprehensive literature review was conducted on the parameterization of fundamental terramechanics models. Soil parameters of the empirical models to assess off-road vehicle mobility, and parameters of the models to characterize the response of the terrain interacting with running gears or plates from the existing terramechanics literature and other researchers’ reports were identified. This review documents and summarizes the modelling approaches that may be applicable to real-time applications of terramechanics in simulation, as well as in controller design.     

Reduced testing and modelling of the bearing capacity of rooted soil for wheeled forestry machines

The next generation of forestry machines must be developed to be gentler to soil and to the root mat than present machines, especially in thinning operations. The bearing capacity of the soil is a key property for determining the terrain trafficability and machine mobility. This asks for better and more general terramechanics models that can be used to predict the interaction between different machine concepts and real and complex forest soil.This paper presents results from terramechanics experiments of rooted soil with a new and small-scale testing device. The force–deflection results are analyzed and compared with analytical root reinforcement models found in literature. The presented study indicates that rooted soil properties obtained with the new laboratory test device can be used to create an augmented soil model that can be used to predict the bearing capacity of rooted soil and also to be used in dynamic machine–soil interaction simulations.     

Online terrain estimation for autonomous vehicles on deformable terrains

In this work, a terrain estimation framework is developed for autonomous vehicles operating on deformable terrains. Previous work in this area usually relies on steady state tire operation, linearized classical terramechanics models, or on computationally expensive algorithms that are not suitable for real-time estimation. To address these shortcomings, this work develops a reduced-order nonlinear terramechanics model as a surrogate of the Soil Contact Model (SCM) through extending a state-of-the-art Bekker model to account for additional dynamic effects. It is shown that this reduced-order surrogate model is able to accurately replicate the forces predicted by the SCM while reducing the computation cost by an order of magnitude. This surrogate model is then utilized in an unscented Kalman filter to estimate the sinkage exponent. Simulations suggest this parameter can be estimated within 4% of its true value for clay and sandy loam terrains. It is also shown in simulation and experiment that utilizing this estimated parameter can reduce the prediction errors of the future vehicle states by orders of magnitude, which could assist with achieving more robust model-predictive autonomous navigation strategies.     

Cross-country mobility on various snow conditions for validation of a virtual terrain

Realistic simulation of on- and off-road vehicle performance in all weather conditions is needed by the U.S. Army for virtual training of personnel on existing vehicles, and for new vehicle design. The virtual test site is a computer simulation representing an actual terrain defined as having spatially distributed terramechanics properties and terrain interaction with vehicles. We developed a virtual test site for Ethan Allen Firing Range (EAFR) in northern Vermont. The virtual test site for EAFR is composed of terramechanics properties including spatially distributed snow depth and density, soil type, drainage class, slope, and vegetation type. Snow depth and density were spatially distributed with regard to elevation, slope, and aspect using a surface energy balance approach. This paper evaluates whether the terramechanics representation of a virtual test site is improved by adding spatially distributed snow and soil properties, rather than using uniform properties. The evaluation was accomplished by conducting a cross-country vehicle performance analysis using the North Atlantic Treaty Organization (NATO) Reference Mobility Model (NRMM) to validate the new algorithms for realistic spatial distribution of snow properties. The results showed that the percentage of No-Go areas for uniform snow is lower than the distributed snow by 4% for the CIV (CRREL Instrumented Vehicle), 8% for the HMMWV (High Mobility Multipurpose Wheeled Vehicle), and 5% for the Stryker vehicle. For both light vehicles, approximately 12% of the No-Go areas are classified as such because of slopes 29%. These results imply that spatial distribution of snow properties provides realistic vehicle response as opposed to having the snow properties distributed uniformly throughout the entire terrain. This represents an improvement over previous versions of the terramechanics properties.     

Estimation of net traction for differential-steered wheeled robots

We present a method for estimating the net traction and resistive wheel torques for a suspensionless, differential-steered robot on rigid or deformable terrain. The method, based on extended Kalman-Bucy filtering (EKBF), determines time histories of net traction and resistive wheel torques and wheel slips during steady or transient maneuvers. This method assumes good knowledge of the vehicle dynamics and treats the unknown forces and moments due to terrain response as random variables to be estimated. A proprioceptive sensor suite renders a subset of the unknown forces and associated wheel slip and slip angles observable. This methodology decouples semi-empirical terramechanics models from the net effect of the vehicle-terrain interaction, namely the net traction developed by the vehicle on the terrain. By collecting sensor data and processing data off-line, force-slip characteristics are identified irrespective of the underlying terramechanics. These characteristics can in turn support development or validation of terramechanics models for the vehicle-terrain system. For autonomous robots, real-time estimates of force-slip characteristics can provide setpoints for traction and steering control, increasing vehicle performance, speed, and maneuverability. Finally, force-slip estimation is the first step in identifying terrain parameters during normal maneuvering. The methodology is demonstrated through both simulation and physical testing using a 13-kg robot.     

Machine learning in planetary rovers: A survey of learning versus classical estimation methods in terramechanics for in situ exploration

For the design of space missions in the Moon and planets, analysis of mobility in robots is crucial and poor planning has led to abortion of missions in the past. To mitigate the risk of mission failure, improved algorithms relying intrinsically on fusing visual odometry with other sensory inputs are developed for slip detection and navigation. However, these approaches are significantly expensive computationally and difficult to meet for future space exploration robots. Hence, today the central question in the field is how to develop a novel framework for in situ estimation of rover mobility with available space hardware and low-computational demanding terramechanics predictors. Ranging from pure simulations up to experimentally validated studies, this paper surveys dozens of existing methodologies for detection of vehicle motion performance (wheel forces and torques), surface hazards (slip-sinkage) and other parameters (soil strenght constants) using classical terramechanics maps, and compare them with novel approaches introduced by machine learning, allowing to establish future directions of research towards distributed exteroceptive and proprioceptive sensing for visionless exploration in dynamic environments. To avoid making it challenging to collect all relevant studies expeditiously, we propose a global classification of terramechanics according most common practices in the field, allowing to form an structured framework that condense most works in the domain within three estimator categories (direct/forward or inverse terramechanics, and slip estimators). Likewise, from the experiences collected in previous MER (Mars Exploration Rover) missions, five overlooked problems are documented that will need to be addressed in next generation of planetary vehicles, along three research questions and few hypothesis that will pave the road towards future applications of machine learning-based terramechanics.     

Modeling viscoelastic dielectrics

Dielectric elastomers, as an important category of electroactive polymers, are known to have viscoelastic properties that strongly affect their dynamic performance and limit their applications. Very few models accounting for the effects of both electrostatics and viscoelasticity exist in the literature, and even fewer are capable of making reliable predictions under general loads and constraints. Based on the principles of non-equilibrium thermodynamics, this paper develops a field theory that fully couples the large inelastic deformations and electric fields in deformable dielectrics. Our theory recovers existing models of elastic dielectrics in the equilibrium limit. The mechanism of instantaneous instability, which corresponds to the pull-in instability often observed on dielectric elastomers, is studied in a general non-equilibrium state. The current theoretical framework is able to adopt most finite-deformation constitutive relations and evolution laws of viscoelastic solids. As an example, a specific material model is selected and applied to the uniform deformation of a dielectric elastomer. This model predicts the stability criteria of viscoelastic dielectrics and its dependence on loading rate, pre-stress, and relaxation. The dynamic response, as well as the hysteresis behavior of a viscoelastic dielectric elastomer under cyclic electric fields, is also studied.     

Insight into the physics of foam densification via numerical simulation

Foamed materials are increasingly finding application in engineering systems on account of their unique properties. The basic mechanics which gives rise to these properties is well established, they are the result of collapsing the foam microstructure. Despite a basic understanding, the relationship between the details of foam microstructure and foam bulk response is generally unknown. With continued advances in computational power, many researchers have turned to numerical simulation to gain insight into the relationship between foam microstructure and bulk properties. However, numerical simulation of foam microscale deformation is a very challenging computational task and, to date, simulations over the full range of bulk deformations in which these materials operate have not been reported. Here a particle technique is demonstrated to be well-suited for this computational challenge, permitting simulation of the compression of foam microstructures to full densification. Computations on idealized foam microstructures are in agreement with engineering guidelines and various experimental results. Dependencies on degree of microstructure regularity and material properties are demonstrated. A surprising amount of porosity is found in fully-densified foams. The presence of residual porosity can strongly influence dynamic material response and hence needs to be accounted for in bulk (average) constitutive models of these materials.     

A complete and irreducible dynamic SGS heat-flux modelling based on the strain rate tensor for large-eddy simulation of thermal convection

In this paper, a general family of explicit algebraic tensor diffusivity functions based on the resolved temperature gradient vector and strain rate tensor is studied and applied to the construction of new constitutive relations for modelling the subgrid-scale (SGS) heat flux (HF). Based on Noll’s formulation, dynamic linear and nonlinear tensor diffusivity models are proposed for large-eddy simulation of thermal convection. The constitutive relations for these two proposed models are complete and irreducible. These two new models include several existing dynamic SGS HF models as special cases. It is shown that in contrast to the conventional modelling approach, the proposed models embody more degrees of freedom, permit non-alignment between the SGS HF and resolved temperature gradient vectors, reflect near-wall flow physics at the subgrid scale, and therefore, allow for a more realistic geometrical representation of the SGS heat flux for large-eddy simulation of thermal convection. Numerical simulations have been performed using a benchmark test case of a combined forced and natural convective flow in a vertical channel with a Reynolds number of and a Grashof number of Gr = 9.6 × 10⁵. The results obtained using the two proposed SGS HF models are compared with reported direct numerical simulation (DNS) data as well as predictions obtained using several conventional dynamic SGS HF models.     

强动载荷下金属材料塑性变形本构模型评述

爆炸、高速冲击等强动载荷作用下金属材料塑性流动的本构模型研究是冲击动力学领域备受关注的课题,近几十年来的研究成果极大地推动了冲击波物理、冲击动力学、材料科学等领域的发展. 本文对金属材料塑性变形动力学数值计算中重要的、得到普遍应用的本构模型进行了回顾和评述,进一步明确其适用范围、优点和不足,为冲击载荷下材料响应的数值模拟对本构模型的选取提供参考. 其中最新的、适用范围最广的PTW本构模型应给以特别地关注,其研究方法及应用前景都值得我们借鉴和期待.      

Anisotropic density growth of bone—A computational micro-sphere approach

Bones are able to adapt their local density when exposed to mechanical loading. Such growth processes result in densification of the bone in regions of high loading levels and in resorption of the material in regions of low loading levels. This evolution and optimisation process generates heterogeneous distributions of bone density accompanied by pronounced anisotropic mechanical properties. While several constitutive models reported in the literature assume the growth process to be purely isotropic, only few studies focus on the modelling and simulation of anisotropic functional adaptation we can observe in vivo. Some of these few computational models for anisotropic growth characterise the evolution of anisotropy by analogy to anisotropic continuum damage mechanics while others include anisotropic growth but assume isotropic elastic properties.The objective of this work is to generalise a well-established framework of energy-driven isotropic functional adaptation to anisotropic microstructural growth and density evolution. We adopt the so-called micro-sphere concept, which proves to be extremely versatile and flexible to extend sophisticated one-dimensional constitutive relations to the three-dimensional case. In this work we apply this framework to the modelling and simulation of anisotropic functional adaptation by means of a directional density distribution, which evolves in time and in response to the mechanical loading condition. Several numerical studies highlight the characteristics and properties of the anisotropic growth model we establish. The formulation is embedded into an iterative finite element algorithm to solve complex boundary value problems. In particular, we consider the finite-element-simulation of a subject-specific proximal tibia bone and a comparison to experimental measurements. The proposed model is able to appropriately represent the heterogeneous bone density distribution. As an advantage over several other computational growth models proposed in the literature, a pronounced local anisotropy evolution is identified and illustrated by means of orientation-distribution-type density plots.     

地面力学及其在行星探测研究中的应用

地面力学是研究越野行驶中机器与地面相互作用的一门力学学科,包括对机器通过性的预测和评价,行走机构的优化设计以及对地面可行驶性的预测判断等几个方面.首先简介地面力学的研究方法、试验仪器和设备以及主要的成果和结论,其中包括在这些方面的最新研究进展情况.之后重点介绍行星探测领域中所开展的地面力学研究,主要从行星探测器设计阶段对地面力学理论和方法的应用、行星模拟土壤研制和力学特性研究、行星就位土壤力学参数测量等几个方面进行了综述.最后对这一领域今后的研究方向进行了探讨.      

A thermodynamic approach to non-local damage modelling of concrete

This paper focuses on the development of a thermodynamic approach to constitutive modelling of concrete materials, with emphasis on the use of non-local damage models. Effort is put on the construction of a consistent and rigorous thermodynamic framework, which readily allows the incorporation of non-local features into the constitutive modelling. This is an important feature in developing non-local constitutive models based on thermodynamics. Examples of non-local constitutive models derived from this framework and numerical examples are given to demonstrate the promising features of the proposed approach.     

Experimental validation of a differential variational inequality-based approach for handling friction and contact in vehicle/granular-terrain interaction

The observation motivating this contribution was a perceived lack of expeditious deformable terrain models that can match in mobility analysis studies the level of fidelity delivered by today’s vehicle models. Typically, the deformable terrain-tire interaction has been modeled using Finite Element Method (FEM), which continues to require prohibitively long analysis times owing to the complexity of soil behavior. Recent attempts to model deformable terrain have resorted to the use of the Discrete Element Method (DEM) to capture the soil’s complex interaction with a wheeled vehicle. We assess herein a DEM approach that employs a complementarity condition to enforce non-penetration between colliding rigid bodies that make up the deformable terrain. To this end, we consider three standard terramechanics experiments: direct shear, pressure-sinkage, and single-wheel tests. We report on the validation of the complementarity form of contact dynamics with friction, assess the potential of the DEM-based exploration of fundamental phenomena in terramechanics, and identify numerical solution challenges associated with solving large-scale, quadratic optimization problems with conic constraints.     

General displacement and work bounds for dynamically loaded bodies

In recent years a number of writers have developed theorems which allow the evaluation of bounds on deformation properties of bodies subject to both static and dynamic loading. Some of these results have proved useful to structural designers in assessing structural performance, thereby obviating the need for a complete analysis. In this paper a general theory is described for small strains which brings together results for both quasi-static and dynamic loading, and also provides a theoretical framework within which a wide range of constitutive relationships may be discussed. The material behaviour is included through a functional property of the constitutive relationship which gives a generalization of the concept of maximum complementary work. A new result for impulsively loaded bodies is illustrated by examples involving elastic and elastic perfectly-plastic materials.     

基于深度强化学习算法的颗粒材料应力?应变关系数据驱动模拟研究

颗粒材料的宏观力学行为受颗粒组分等材料参数, 孔隙率、配位数等状态参数的影响, 同时又具备复杂的加载路径和加载历史相关性, 建立包含多个内变量以及各变量间相互关联的颗粒材料本构模型是一个重要的科学难题. 不同于传统的基于屈服面、流动法则和硬化函数框架下的唯象本构模型, 本文基于颗粒物质力学的研究基础, 以颗粒材料平均孔隙率、细观组构参数和弹性刚度参数作为内变量, 结合深度学习方法建立以有向图表征的数据本构模型. 有向图中以不同的链接网络表示不同的内变量信息流动方向, 各个内变量间的映射关系采用循环神经网络来建立, 将各个神经网络相互组合, 形成包含不同内变量且具有不同预测能力的本构模型. 该本构模型的建立过程等价于在众多可能的内变量链接关系空间中寻找最能描述实际材料宏观应力应变行为的优化问题. 因此, 可将有向图本构模型的建立过程看作“马尔可夫决策过程”, 采用深度强化学习算法构建有向图的内变量链接组合优化过程, 具体采用AlphaGo Zero算法自动寻找最优的颗粒材料数据驱动本构模型建模路径. 研究结果表明, 采用有向图和深度强化学习算法可建立起完全依靠“数据驱动”的颗粒材料应力?应变关系. 此外, 本方法提供了一种将不同理论模型从数据角度统一起来, 且基于人工智能算法发展更优模型的研究思路, 可为相似问题的研究提供借鉴.      

On the relative impact of subgrid‐scale modelling and conjugate heat transfer in LES of hot jets in cross‐flow over cold plates

This work describes numerical simulations of a hot jet in cross‐flow with applications to anti‐ice systems of aircraft engine nacelles. Numerical results are compared with experimental measurements obtained at ONERA to evaluate the performances of LES in this industrial context. The combination of complex geometries requiring unstructured meshes and high Reynolds number does not allow the resolution of boundary layers so that wall models must be employed. In this framework, the relative influence of subgrid‐scale modelling and conjugate heat transfer in LESs of aerothermal flows is evaluated. After a general overview of the transverse jet simulation results, a LES coupled with a heat transfer solver in the walls is used to show that thermal boundary conditions at the wall have more influence on the results than subgrid scale models. Coupling fluid flow and heat transfer in solids simulations is the only method to specify their respective thermal boundary conditions. Copyright © 2011 John Wiley & Sons, Ltd.     

泥石流本构模型及动力学模拟研究现状综述

由于泥石流动力学过程的复杂性,其本构模型及数值模拟研究仍然存在众多的难点问题。本文根据大量的文献资料和实例研究,对目前泥石流本构模型和动力学模拟研究现状和存在的问题进行了综合论述,主要包括:(1)已有泥石流动力学本构模型原理及适用性问题;(2)已有数值模拟方法的实现及选择应用;(3)泥石流动力学复杂环境效应研究,复杂地形和水文环境条件下的泥石流应力分布、动能传递等。最后对泥石流动力学G IS模拟的前景进行了讨论。     

A method for on-line soil parameters modification to planetary rover simulation

In planetary exploratory rover simulation, the contact model between wheel and terrain inevitably has some differences in contrast with the real one, which can make rover depart the planned track. To eliminate the dynamic errors caused by it, this paper presents a method for on-line soil parameters modification. This paper classifies data errors between virtual rover and real rover as model errors and asynchronous errors. Before modification, data identification is utilized to eliminate asynchronous errors and get a group of effective data with least additional errors. Based on the simplified terramechanics model, the origins of model errors are analyzed in detail from static status and kinetic status; meanwhile, some soil parameters are decoupled from the complicated model, and it makes on-line soil parameters modification feasible. An effective coefficient is also proposed to maintain the stability and convergence of modification. Lastly, through simulations on ROSTDyn (ROver Simulation based on Terramechanics and Dynamics), it is demonstrated that the soil parameters modification method is effective and useful for rover simulation to eliminate dynamic errors of predictive model.     

A general optimal formulation for the dynamic Smagorinsky subgrid‐scale stress model

In this paper, a general optimal formulation for the dynamic Smagorinsky subgrid‐scale (SGS) stress model is reported. The Smagorinsky constitutive relation has been revisited from the perspective of functional variation and optimization. The local error density of the dynamic Smagorinsky SGS model has been minimized directly to determine the model coefficient C_S. A sufficient and necessary condition for optimizing the SGS model is obtained and an orthogonal condition (OC), which governs the instantaneous spatial distribution of the optimal dynamic model coefficient, is formulated. The OC is a useful general optimization condition, which unifies several classical dynamic SGS modelling formulations reported in the literature. In addition, the OC also results in a new dynamic model in the form of a Picard's integral equation. The approximation tensorial space for the projected Leonard stress is identified and the physical meaning for several basic grid and test‐grid level tensors is systematically discussed. Numerical simulations of turbulent Couette flow are used to validate the new model formulation as represented by the Picard's integral equation for Reynolds numbers ranging from 1500 to 7050 (based on one half of the velocity difference of the two plates and the channel height). The relative magnitudes of the Smagorinsky constitutive parameters have been investigated, including the model coefficient, SGS viscosity and filtered strain rate tensor. In general, this paper focuses on investigation of fundamental mathematical and physical properties of the popular Smagorinsky constitutive relation and its related dynamic modelling optimization procedure. Copyright © 2005 John Wiley & Sons Ltd.