An inverse method for determining elastic material properties and a material interface (original) (raw)
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Identification of Elastic Parameters by Treating the Inverse Problem
International Journal of Computer Applications, 2014
The aim of this work is to lay the groundwork for identifying digital mechanical parameters of materials with elastic. Most of the tests do not allow identifying these parameters automatically. The use of the finite elements of calculations for sizing works is thus limited by a poor understanding of the mechanical properties. In this context, it raises the issue of inverse analysis [1] [2]. From this information about the parameters of the laws of material behavior, is it possible to obtain the displacement field from in situ measurements and how does digital technology obtain a determination of these parameters accurately and systematically? In this work we present a new approach by providing a formulation is easily used by treating the inverse problem. It is based on the finite element method, which, in a direct problem, gives the displacement field knowing the mechanical properties and an inverse problem gives the mechanical knowledge of the field trips. The resolution of the direct problem has yielded results. The latter is in agreement with the simulation code of commercial calculation. This allowed us to address the inverse problem with no understanding by offering an alternative identification using a database previously determined [3].
International journal of solids and …, 1997
boundary element solution is developed for an inverse elasticity problem. In this inverse problem, boundary conditions are incompletely specified. Strains can be determined experimentally, in practice, at a number of internal points and used as input to completely resolve these boundary conditions. In this paper, these strains, including random errors, are numerically simulated. This inverse problem fmds applications in the evaluation of residual stress and contact stress. In contrast to previous studies, the construction of the sensitivity matrix is embedded in the boundary element formulation thereby avoiding the solution of a series of forward problems. Further, the effects of prescribed non-zero boundary conditions and body forces are included in the relation between measured strains and the primary traction unknowns. Unfortunately, the inverse problem is still ill-posed. Physical constraints are introduced to stabilize the solution. As a result, the algorithm presented here has reasonable tolerance to error in the measurement of strains. Numerical examples are given to validate the inverse algorithm. In these examples, the input strains are numerically simulated, and stable and accurate solutions are obtained with up to + 5% random error in the input. 0 1997 Elsevier Science Ltd.
3D Inverse Analysis Model Using Semi-Analytical Differentiation for Mechanical Parameter Estimation
Inverse Problems in Science and Engineering, 2003
An inverse method is developed in order to estimate constitutive parameters of a material from compression tests. The direct model used to simulate mechanical tests is FORGE3 ®. It solves a transient thermo-mechanical problem using a finite element method. From velocity, pression and temperature fields, any output of a mechanical test can be computed and compared with experimental data. A Gauss-Newton algorithm is implemented to solve the least-square problem associated with the inverse problem. The optimisation module is coupled with a semi-analytical sensitivity analysis method. This method is fast and stable when using a remeshing algorithm. A confidence interval estimator is proposed. The stability of the optimisation module and the confidence interval estimation are tested for numerical test cases. Finally, constitutive parameters of a steel grade are estimated for two elastic-viscoplastic constitutive laws.
Inverse Problems in Science and Engineering, 2012
The identification of contact forces applied on a solid body or structure is a special case of a general class of inverse problems. This problem is very complicated, especially when there is insufficient boundary information in the region where the contact forces need to be identified. In this paper, the unknown loads or contact forces are identified by reconstructing the finite element formula and minimizing the criterion function derived as the sum of squares of the differences between measurements and numerical results of the finite element method. A detail description of the formulation, analysis and solution of the inverse problems are given. Tikhonov-Phillips regularization technique is employed to reduce the influence of the measurement noise. Three examples are chosen to demonstrate the accuracy of the numerical algorithm.
Finite element solution of two-dimensional inverse elastic problems using spatial smoothing
International Journal for Numerical Methods in Engineering, 1990
A finite element method (FEM) is presented for calculating the surface tractions on a body from internal measurements of displacement at discrete sensor locations. The solution algorithm employs a sensitivity analysis which minimizes the difference between the calculated and measured displacements at each sensor location. Spatial regularization is one technique employed to stabilize the minimization process by imposing various degrees of smoothness on the solution. It also allows the problem to be solved with fewer sensors than traction boundary nodes. As an alternative to spatial regularization, a method based on 'keynodes' is introduced which assumes that each component of the boundary traction distribution can be described by a polynomial of specified order. The methods are applied to several two-dimensional examples including a rolling contact problem. The effects of parameters such as the number of sensors, the location of the sensors and the error in the sensor displacements are discussed.
Engineering Analysis with Boundary Elements, 2007
The purpose of this work is to study a class of inverse problems that arises in solid mechanics areas such as quantitative non-destructive testing (QNDT) or shape optimization. The technique is based on the boundary integral equations (BIEs) used in the classical boundary element method (BEM), which are differentiated semi-analytically with respect to variations of the boundary geometry and used in an iterative search algorithm. The extension of this strategy is presented here for the case of elasticity in dynamics using the displacement or singular BIE, which allows to apply this strategy to QNDT problems based on vibrations or ultrasonics. The central point is the evaluation of the capability of solving numerically a QNDT problem such as the location and characterization of cavity and inclusion-type defects by measuring the dynamic response at an accessible boundary of the specimen. To test this capability, comprehensive convergence tests are made for the badness of the initial guess, the amount of supplied measurements, and simulated errors on measurements, geometry, elastic constants and frequency.
TOPICAL REVIEW: Inverse problems in elasticity
Inverse Problems, 2005
This article is devoted to some inverse problems arising in the context of linear elasticity, namely the identification of distributions of elastic moduli, model parameters, or buried objects such as cracks. These inverse problems are considered mainly for threedimensional elastic media under equilibrium or dynamical conditions, and also for thin elastic plates. The main goal is to overview some recent results, in an effort to bridge the gap between studies of a mathematical nature and problems defined from engineering practice. Accordingly, emphasis is given to formulations and solution techniques which are well suited to general-purpose numerical methods for solving elasticity problems on complex configurations, in particular the finite element method and the boundary element method. An underlying thread of the discussion is the fact that useful tools for the formulation, analysis and solution of inverse problems arising in linear elasticity, namely the reciprocity gap and the error in constitutive equation, stem from variational and virtual work principles, i.e. fundamental principles governing the mechanics of deformable solid continua. In addition, the virtual work principle is shown to be instrumental for establishing computationally efficient formulae for parameter or geometrical sensitivity, based on the adjoint solution method. Sensitivity formulae are presented for various situations, especially in connection with contact mechanics, cavity and crack shape perturbations, thus enriching the already extensive known repertoire of such results. Finally, the concept of topological derivative and its implementation for the identification of cavities or inclusions are expounded.
International journal of …, 2007
Inverse methods offer a powerful tool for the identification of elasto-plastic material properties of metals. The basic principle of the inverse method we are studying, is to compare an experimentally measured strain field with a strain field computed by a finite element (FE) model. The material parameters in the FE model are iteratively tuned in such a way that the numerically computed strain field matches the experimentally measured field as closely as possible. One of the building blocks in this identification procedure is the optimization algorithm for the material parameters in the numerical model. The key problem of this optimization algorithm is the determination of a sensitivity matrix, which expresses the sensitivities of the strains with respect to the material parameters. This paper presents an analytical method for the calculation of this sensitivity matrix in the case of a tensile test with non-rotating principal axes of strain.
EPJ Web of Conferences
Inverse methods are a modern alternative technique to traditional standard testing for the identification of material parameters. The material parameters in the numerical model are the unknown parameters which will be aimed to identify. In this paper an alternative iterative strategy for material identification is proposed. The concept of the proposed strategy is based on the material behavior under an applied load which is described by the stress-strain curve. The material parameters can be identified based on observation strain field and numerically stress field.