Inverse approach to identification of material parameters of cyclic elasto-plasticity for component layers of a bimetallic sheet

The present paper proposes a novel approach to the identification of the mechanical properties of individual component layers of a bimetallic sheet. In this approach, a set of material parameters in a constitutive model of cyclic elasto-plasticity are identified for the two layers of the sheet simultaneously by minimizing the difference between the experimental results and the corresponding results of numerical simulation. This method has an advantage of using the experimental data (tensile load vs strain curve in the uniaxial tension test and the bending moment vs curvature diagram in the cyclic bending test) for a whole bimetallic sheet but not for individual component layers. An optimization technique based on the iterative multipoint approximation concept is used for the identification of the material parameters. This paper describes the experimentation, the fundamentals and the technique of the identification, and the verification of this approach using two types of constitutive models (the Chaboche-Rousselier and the Prager models) for an aluminum clad stainless steel sheet.     

Stress Reconstruction and Constitutive Parameter Identification in Plane-Stress Elasto-plastic Problems Using Surface Measurements of Deformation Fields

This paper deals with the identification of elasto-plastic constitutive parameters from deformation fields measured over the surface of thin flat specimens with the grid method. The approach for recovering the constitutive parameters is the virtual fields method. A dedicated algorithm is used for deriving the distribution of the 2D stress components from the measured deformation fields. A state of plane stress is assumed. Guesses of the constitutive parameters are input in the algorithm and updated until the stresses satisfy the principle of virtual work in the least squares sense. The advantage of this approach is that it can handle very heterogeneous plastic flows and it is much faster than classical finite element model updating approaches. An experimental application is provided to demonstrate it. Six mild steel double-notched specimens have been tested in a configuration combining tension and in-plane bending. The identified parameters are in good agreement with their reference counterparts. Stress fields are eventually reconstructed across the specimen all along the test for analyzing the evolution of the plastic flow.     

Identification of Material Damage Model Parameters: an Inverse Approach Using Digital Image Processing

A reliable prediction of ductile failure in metals is still a wide-open matter of research. Several models are available in the literature, ranging from empirical criteria, porosity-based models and continuum damage mechanics (CDM). One major issue is the accurate identification of parameters which describe material behavior. For some damage models, parameter identification is more or less straightforward, being possible to perform experiments for their evaluation. For the others, direct calibration from laboratory tests is not possible, so that the approach of inverse methods is required for a proper identification. In material model calibration, the inverse approach consists in a non-linear iterative fitting of a parameter-dependent load–displacement curve (coming from a FEM simulation) on the experimental specimen response. The test is usually a tensile test on a round-notched cylindrical bar. The present paper shows a novel inverse procedure aimed to estimate the material parameters of the Gurson–Tvergaard–Needleman (GTN) porosity-based plastic damage model by means of experimental data collected using image analysis. The use of digital image processing allows to substitute the load–displacement curve with other global quantities resulting from the measuring of specimen profile during loading. The advantage of this analysis is that more data are available for calibration thus allowing a greater level of confidence and accuracy in model parameter evaluation.     

IDENTIFICATION OF ELASTIC-PLASTIC MECHANICAL PROPERTIES FOR BIMETALLIC SHEETS BY HYBRID-INVERSE APPROACH

Analysis, evaluation and interpretation of measured signals become important components in engineering research and practice, especially for material characteristic parameters which can not be obtained directly by experimental measurements. The present paper proposes a hybrid-inverse analysis method for the identification of the nonlinear material parameters of any individual component from the mechanical responses of a global composite. The method couples experimental approach, numerical simulation with inverse search method. The experimental approach is used to provide basic data. Then parameter identification and numerical simulation are utilized to identify elasto-plastic material properties by the experimental data obtained and inverse searching algorithm. A numerical example of a stainless steel clad copper sheet is consid- ered to verify and show the applicability of the proposed hybrid-inverse method. In this example, a set of material parameters in an elasto-plastic constitutive model have been identified by using the obtained experimental data.     

Conforming finite element computations applied to a spatially periodic,harmonic Navier-Stokes problem

In this paper computations in the two dimensional case of a harmonic Navier-Stokes problem with periodic boundary conditions are presented. This study of an incompressible viscous fluid leads to a non-symmetric linear problem (very low Reynolds number). Moreover unknown functions have complex values (monochromatic dynamic behaviour). Numerical treatment of the incompressibility condition is a generalization of the classical treatment of Stokes problem. A mixed formulation, where discrete pressure plays the role of Lagrange multipliers is used (Uzawa algorithm). Two conforming finite element methods are tested on different meshes. The second one uses a classical refinement in the shape function: the so-called bulb function. All computational tests show that the use of a bulb function on each element gives better results than refinement in the mesh without introducing too many degrees of freedom. Finally numerical results are compared to experimental data.     

Novel procedure for complete in-plane composite characterization using a single T-shaped specimen

This paper deals with the direct identification of the in-plane elastic properties of orthotropic composite plates from heterogeneous strain fields. The shape of the tested specimen is that of a T subjected to a complex stress state. As a result, the entire set of unknown parameters is directly involved in the strain and displacement responses of the sample. No exact analytical solution is available for such a geometry, and a specific strategy is used to identify the different stiffness components from the whole-field displacements measured over the tested specimen with a suitable optical method. The paper focuses mainly on the experimental aspects of the procedure, and an example of mechanical characterization of a fabric-reinforced composite plate is given.     

Implementation of Convergence in Adaptive Global Digital Image Correlation

In FE based global digital image correlation (DIC) a finite element mesh is used to describe the deformation of the region of interest (ROI). However, the identification of an optimal mesh is a difficult problem and is often obtained by using “mechanical” pre-knowledge of the solution. In Finite Element Analysis (FEA) an optimal mesh can be found without any pre-knowledge of the solution by using mesh adaptivity, where an initial (non optimal) mesh is refined until the optimal solution is obtained. Refinement of the mesh can be based on error and/or convergence estimators. Despite the fundamental differences between FEA and DIC, in the present article the convergence procedure is successfully used in a recently published global FE based DIC method. In the used global DIC method elements can receive higher order shape functions, also known as p-elements. Using the aforementioned algorithm, also called p-DIC, refinement to a non-uniform higher order mesh is possible. Using the non-uniform mesh, an optimal mesh can be obtained for each section of the ROI. The presented study shows that a convergence scheme can be used to automatically control the mesh refinement in a global DIC approach. The convergence boundary, in percentage, is a more intuitive boundary than the absolute error boundary used in the original p-DIC approach. The procedure is validated using numerical examples and the robustness to experimental variables is investigated. Finally, the complete procedure is tested against a wide range of practical examples.     

On the use of simulated experiments in designing tests for material characterization from full-field measurements

The present paper deals with the use of simulated experiments to improve the design of an actual mechanical test. The analysis focused on the identification of the orthotropic properties of composites using the unnotched Iosipescu test and a full-field optical technique, the grid method. The experimental test was reproduced numerically by finite element analysis and the recording of deformed grey level images by a CCD camera was simulated trying to take into account the most significant parameters that can play a role during an actual test, e.g. the noise, the failure of the specimen, the size of the grid printed on the surface, etc. The grid method then was applied to the generated synthetic images in order to extract the displacement and strain fields and the Virtual Fields Method was finally used to identify the material properties and a cost function was devised to evaluate the error in the identification. The developed procedure was used to study different features of the test such as the aspect ratio and the fibre orientation of the specimen, the use of smoothing functions in the strain reconstruction from noisy data, the influence of missing data on the identification. Four different composite materials were considered and, for each of them, a set of optimized design variables was found by minimization of the cost function.     

近场动力学与有限元方法耦合求解热传导问题

求解含裂纹等不连续问题一直是计算力学的重点研究课题之一,以偏微分方程为基础的连续介质力学方法处理不连续问题时面临很大的困难. 近场动力学方法是一种基于积分方程的非局部理论,在处理不连续问题时有很大的优越性. 本文提出了求解含裂纹热传导问题的一种新的近场动力学与有限元法的耦合方法. 结合近场动力学方法处理不连续问题的优势以及有限元方法计算效率高的优势,将求解区域划分为两个区域,近场动力学区域和有限元区域. 包含裂纹的区域采用近场动力学方法建模,其他区域采用有限元方法建模. 本文提出的耦合方案实施简单方便,近场动力学区域与有限元区域之间不需要设置重叠区域. 耦合方法通过近场动力学粒子与其域内所有粒子(包括近场动力学粒子和有限元节点)以非局部方式连接,有限元节点与其周围的所有粒子以有限元方式相互作用. 将有限元热传导矩阵和近场动力学粒子相互作用矩阵写入同一整体热传导矩阵中,并采用Guyan缩聚法进一步减小计算量. 分别采用连续介质力学方法和近场动力学方法对一维以及二维温度场算例进行模拟,结果表明,本文的耦合方法具有较高的计算精度和计算效率. 该耦合方案可以进一步拓展到热力耦合条件下含裂纹材料和结构的裂纹扩展问题.      

基于弹性力学第一性原理的数据驱动力学建模

提出了一种基于弹性力学第一性原理的数据驱动力学建模方法,其能够从基于弹性力学方程的数值计算结果建立简洁且能准确捕捉变形机制的力学模型。基于有限元计算得到的高精度数据和无监督数据驱动控制方程识别方法Seq-SVF,从梁的载荷和位移数据中自动识别出了Timoshenko梁形式的弯曲控制微分方程,得到了三种不同加载条件下剪切影响系数关于结构尺寸和力学参数的函数表达式。揭示了经典模型适用的加载条件,同时还给出了一种未发现的新模型。通过将基于弹性力学的第一性原理计算与数据驱动范式相结合,克服了传统建模方法的局限性和对人类经验的强依赖性,为建立简洁的力学模型提供了一种新途径。     

A new hybrid technique for in-plane characterization of orthotropic materials

In this paper we present a novel hybrid procedure for the in-plane mechanical characterization of orthotropic materials. The material identification reverse engineering problem is solved by combining speckle interferometry and numerical optimization. The rationale behind the entire process is the following: for any specimen to be characterized and which has been subjected to some loading condition, it is possible to express the difference between experimental data and analytical/numerical predictions by means of an error function ψ, which depends on the elastic constants of the material. The ψ error will decrease as the elastic constants come close to their target values. Here, we build the ψ function as the difference between the displacement field measured with speckle interferometry and its counterpart computed by means of finite element analysis. Since the ψ function is highly non-linear, it has to be optimized with a global optimization algorithm, which perform a random search in the elastic constants design space. The hybrid material identification process finally allows us to determine values of the elastic constants. In order to prove the feasibility of the present approach, we have determined the in-plane elastic properties of an eight-ply composite laminate (woven fiberglass-epoxy) used as a substrate for printed circuit boards. The results indicate that the procedure proposed in this paper was able to accurately characterize the material under investigation. Remarkably, the elastic constants found by the identification procedure were less than 0.7% different from their target values, while the residual error between the displacements measured by speckle interferometry and those computed at the end of the optimization process was less than 3%. L. Lamberti is an Assistant Professor, and C. Pappalettere (SEM Member and President of the Italian Society of Stress Analysis) is Professor of Mechanical Engineering and Experimental Mechanics, Politecnico di Bari, Dipartimento di Ingegneria Meccanica e Gestionale, Viale Japigia 182, 70126 Bari, Italy     

Leveraging Full-Field Measurement from 3D Digital Image Correlation for Structural Identification

Within the domain of structural health monitoring (SHM) measurement techniques have primarily relied on discrete sensing strategies using sensors physically attached to the structural system of interest. These sensors have proven effective in describing both global and local phenomena, but are limited to providing discrete response measurements of these systems. With the introduction of novel imaging tools and image analysis techniques, such as digital image correlation (DIC), the ability to measure the full-field response of these systems provides a novel approach to refining structural identification (St-ID) approaches used in SHM. This paper explores this proposed concept through a case study on a series of structural test specimens analyzed using 3D digital image correlation (3D-DIC) for St-ID. Finite element model updating (FEMU) was used as the technique for the structural identification. For the identification process, ABAQUS was interfaced with MATLAB to converge on the optimal unknown/uncertain system parameters of the experimental setup. 3D-DIC results provided a rich full-field dataset for the identification process, which was compared against measurements derived from traditional physical in-place sensors typically used in SHM. In this work a Hybrid Genetic Algorithm (HGA), which combines the genetic algorithm as a global optimization and a gradient-based method as a local optimization, was used for the FEMU based on 3D-DIC results of structural specimen subjected to variable loading. To minimize the error between the full field 3D-DIC measurements and FEA model updating results, an objective function was introduced that included the full-field contributions of strains and deformation response. The evolution of this objective function illustrated satisfactory convergence of the identified parameters and the excellent agreement of the experimental and numerical strain and displacement responses after the model updating process confirmed the success of the proposed approach. The results of this study highlight the advantage of this hybrid approach and provide the foundation for effective deployment of the proposed strategy for large-scale structural systems.     

Stiffness and Damping Identification from Full Field Measurements on Vibrating Plates

The paper presents an experimental application of a method leading to the identification of the elastic and damping material properties of isotropic vibrating plates. The theory assumes that the searched parameters can be extracted from curvature and deflection fields measured on the whole surface of the plate at two particular instants of the vibrating motion. The experimental application consists in an original excitation fixture, a particular adaptation of an optical full-field measurement technique, a data preprocessing giving the curvature and deflection fields and finally in the identification process using the Virtual Fields Method (VFM). The principle of the deflectometry technique used for the measurements is presented. First results of identification on an acrylic plate are presented and compared to reference values. Results are discussed and improvements of the method are proposed.     

Erratum to: Parameter identification of electronic throttle using a hybrid optimization algorithm

Aiming at the problems in parameter identification of an electronic throttle, this paper proposes a novel hybrid optimization algorithm to search the optimal parameter values of the plant. The parameter identification of an electronic throttle is considered as an optimization process with an objective function minimizing the errors between the measurement and identification, and the optimal parameter values of the plant are searched by using a hybrid optimization algorithm. The proposed hybrid optimization algorithm, effective combination of parallel chaos optimization algorithm (PCOA) and simplex search method, preserves both the global optimization capability of PCOA and the accurate search ability of simplex search method. Simulation and experiment results have shown the good performance of the proposed approach.     

Parameter identification of electronic throttle using a hybrid optimization algorithm

Aiming at the problems in parameter identification of an electronic throttle, this paper proposes a novel hybrid optimization algorithm to search the optimal parameter values of the plant. The parameter identification of an electronic throttle is considered as an optimization process with an objective function minimizing the errors between the measurement and identification, and the optimal parameter values of the plant are searched by using a hybrid optimization algorithm. The proposed hybrid optimization algorithm, effective combination of parallel chaos optimization algorithm (PCOA) and simplex search method, preserves both the global optimization capability of PCOA and the accurate search ability of simplex search method. Simulation and experiment results have shown the good performance of the proposed approach.     

ELASTO-PLASTIC CONSTITUTIVE MODEL OF SOIL-STRUCTURE INTERFACE IN CONSIDERATION OF STRAIN SOFTENING AND DILATION

The behavior of soil-structure interface plays a major role in the definition of soil-structure interaction. In this paper a bi-potential surface elasto-plastic model for soil-structure interface is proposed in order to describe the interface deformation behavior,including strain softening and normal dilatancy. The model is formulated in the framework of generalized potential theory,in which the soil-structure interface problem is regard as a two-dimensional mathematical problem in stress field,and plastic state equations are used to replace the traditional field surface. The relation curves of shear stress and tangential strain are fitted by a piecewise function composed by hyperbolic functions and hyperbolic secant functions,while the relation curves of normal strain and tangential strain are fitted by another piecewise function composed by quadratic functions and hyperbolic secant functions. The approach proposed has the advantage of deriving an elastoplastic constitutive matrix without postulating the plastic potential functions and yield surface. Moreover,the mathematical principle is clear,and the entire model parameters can be identified by experimental tests. Finally,the predictions of the model have been compared with experimental results obtained from simple shear tests under normal stresses,and results show the model is reasonable and practical.     

A general framework for identification of hyper-elastic membranes with moiré techniques and multi-point simulated annealing

This paper presents a hybrid procedure for mechanical characterization of hyper-elastic materials based on moiré, finite element analysis and global optimization. The characterization process is absolutely general because does not require any assumption on specimen geometry, loading or/and boundary conditions.The novel experimental approach followed in this research relies on a proper combination of intrinsic moiré and projection moiré which allows 3D displacement components to be measured simultaneously and independently using always the same experimental setup and just one single camera. In order to properly compare experimental data and finite element predictions, 3D displacement information encoded in moiré patterns which are relative to the deformed configuration taken by the specimen are expressed in the reference system of the unloaded state.A global optimization algorithm based on multi-level and multi-point simulated annealing which keeps memory of all best records generated in the optimization is used in order to find the unknown material properties through the minimization of the Ω functional built by summing over the differences between displacements measured experimentally and those predicted numerically.Feasibility, efficiency and robustness of the proposed methodology are demonstrated for both isotropic and anisotropic specimens subject to increasing pressure loads: a natural rubber membrane and a glutaraldehyde treated bovine pericardium patch, respectively. Remarkably, the results of the characterization process are in very good agreement with target data independently determined. For the isotropic specimen, the maximum error on hyper-elastic constants is less than 1% and the residual error on displacements is less than 3.5%. For the anisotropic specimen, the maximum error on material properties is about 3.5% while the residual error on displacements is less than 3%. The identification process fails or becomes less reliable if “local” displacement values are considered.     

Optimal control problems with incomplete and different integral time domains in the objective and constraints

Optimal control problem with incomplete and different integral time domains is a class of very common practical engineering problems. In traditional way, the integral items are transformed to the transient items and treated as artificial states to reduce the complexity of programming. However, its main disadvantage is time wasting for the considered problems. In this paper, an efficient computational method is therefore proposed for this type of problem, where the integral time domains can be either fixed or variable. By employing the control vector parameterization and a timescaling transformation, the original problem is converted to an approximate optimal parameter selection problem. Moreover, new gradient formulae for the cost and constraint functions are derived. With these gradient formulae, standard gradient-based optimization methods can be easily applied to solve the generated approximate problem. For illustration, three classical numerical examples are tested. The research results, which save 10–22 % of time, show the effectivity of the proposed approach.     

Macroscopic and Micromechanical Approaches to the Modelling of the Osmotic Swelling in Clays

The osmotic swelling in clays has been extensively studied at the physico-chemical scale. The present paper addresses the question of the modelling of this phenomenon from the mechanical point of view. First, the classical macroscopic thermodynamic framework for saturated porous continua is extended in order to take into account the solid-salt interaction through the concept of macroscopic activity coefficient of the salt. The micromechanical approach then incorporates this interaction through the concept of swelling pressure which is used for describing the internal forces in the fluid phase at the microscopic scale. The results of a physico-chemical theory for the solid-salt interaction, such as the e.d.l. theory, can be introduced in both approaches. Each of them leads to the identification of a deviation, of chemical origin, to Terzaghi's effective stress principle. Besides, the micromechanical approach allows us to clearly differentiate the mechanical and the chemical parts of clay materials elasticity.     

实验数据反演识别分析方法与力学表征

本文给出了两类基于实验(实测)数据的反演识别方法,简述了其在界面力学性能及工程实测数据分析中的应用.在粘接界面力学性能的反演识别实验研究中,基于不同加载速率的实验曲线,结合参数化界面力学模型,通过反演识别给出粘接界面力学性能参数,并对识别结果的适定性进行独立的实验验证;在基于工程实测数据的反演识别与力学建模方面,在分析盾构装备载荷特点的基础上,对海量的实测数据统计分类,提出了力学量纲分析的建模方法,并应用于盾构掘进载荷的反演识别研究.