Inverse Finite Element Modeling Research Articles

Local stress analysis on semiconductor devices by combined experimental–numerical procedure

Intrinsic stresses in bondpads may lead to early failure of IC’s. In order to determine the intrinsic stresses in semiconductor structures, a new procedure is set up. This procedure is a combined experimental/numerical approach which consists of the following steps: First, a conductive gold layer (20 nm thickness) is deposited on the power line surface; subsequently markers (small holes) for Digital Image Correlation (DIC) purposes are added using a Focused Ion Beam (FIB). Next, a scanning electron microscope (SEM) is used to image the original (‘before’) surface. The FIB is then used to mill a slot into the surface to release the intrinsic stresses, which results in contraction of the surface. Finally, a SEM image is made of the contracted (‘after’) surface. DIC is used to determine in-plane displacements due to FIB milling. DIC performance was verified by the traditional strain gauge approach. An inverse Finite Element (FE) modelling approach is used to determine the before mentioned stresses. The slot displacements found with DIC are inserted into an FE model of the product. Stresses which now emerge from closing the (virtual) FIB slot correspond to the intrinsic stresses which were originally present in the product. Favorable positions for FIB milling are near the edge of the structure and displacements are determined to be in the nanometer range. This indicates a presence of substantial (50–250 MPa) compressive stresses. Displacements near the center of the structure appear to be smaller than DIC resolution.

Poroviscoelastic characterization of particle-reinforced gelatin gels using indentation and homogenization

Hydrogels are promising materials for bioengineering applications, and are good model materials for the study of hydrated biological tissues. As these materials often have a structural function, the measurement of their mechanical properties is of fundamental importance. In the present study gelatin gels reinforced with ceramic microspheres are produced and their poroviscoelastic response in spherical indentation is studied. The constitutive responses of unreinforced gels are determined using inverse finite element modeling in combination with analytical estimates of material parameters. The behavior of composite gels is assessed by both analytical and numerical homogenization. The results of the identification of the constitutive parameters of unreinforced gels show that it is possible to obtain representative poroviscoelastic parameters by spherical indentation without the need for additional mechanical tests. The agreement between experimental results on composite gelatin and the predictions from homogenization modeling show that the adopted modeling tools are capable of providing estimates of the poroviscoelastic response of particle-reinforced hydrogels.

Tensile Mechanical Characterization of Cell Stiffness Improves Correlation to Metastatic Potential in Models of Osteosarcoma

A correlative link between decreased cancer cell stiffness and increased aggressiveness (metatstatic potential) has been established in a wide range of cancers, such as leukemia, breast cancer and chondrosarcoma. Nearly all studies establishing this link in adherent cells have utilized cell compression (indentation) or shearing (e.g. magnetic cyto-twisting). In this study we applied a novel tensile assay of cell stiffness to investigate the mechanical behavior of two osteosarcoma models (SAOS-2/LM5 and HUO9/M132), with each system comprising a parental cell line and its highly metastatic derivative form. The goal was to find a common trend linking cell stiffness and metastatic potential, further hypothesizing that a tensile assay could provide additional information compared to traditional compressive measures. Cells were therefore tested in two different mechanical configurations: in compression using atomic force micro-indentation; and in tension using a custom functional imaging platform that applies a controlled bi-axial deformation to the cell substrate while imaging and tracking substrate deformation at high spatial resolution. These measurements were coupled with an inverse finite element model to more precisely estimate cell tensile constitutive behavior.Both parental lines proved to be significantly (p<0.01) stiffer than their metastatic variants in tension: 2.5±1.6 kPa (SAOS-2) vs. 1.4±1.0 kPa (LM5) and 5.3±2.5 kPa (HUO9) vs. 2.5±0.7 kPa (M132). Although a compressive characterization of the SAOS-2/LM5 model confirmed this trend (3.5±1.7 kPa vs. 1.8±0.8 kPa, p<0.001), the compressive (cytosolic) stiffness of the HUO9/M132 was unexpectedly higher in the highly metastatic cells (2.0±0.7 kPa vs. 4.9±2.1 kPa, p<0.001). These results indicate that the relationship between “cell stiffness” and phenotypic aggressiveness is not straight forward, and that tensional mechanical characterization provides additional, and perhaps more pertinent, information linking cell mechanical behavior to metastatic potential.

New method for finding initial guess of original blank in inverse finite element of sheet metal forming

Traditionally, sheet metal forming processes are modelled using incremental Finite Element Modelling (FEM) methods. Although this is accurate, incremental FEM is very expensive in computation. Recently, the so‐called one‐step FEM, also called inverse FEM, has been developed. With acceptable accuracy, the one‐step FEM method can find the strain distribution and the initial blank shape in minutes instead of hours. However, the current versions of one‐step FEM suffer from a number of limitations, one of which is the ability to handle complex parts, such as those having multiple peaks and cavities. To solve this problem, the key is to find the initial blank profile. This study presents a new method, referred to as the modified arch‐length method. This new method is capable of finding the initial blank profile for any parts, including those having multiple peaks and cavities. The present study contains the technical details and two demonstration examples.

Inverse finite element modelling and identification of constitutive parameters of UHS steel based on Gleeble tensile tests at high temperature

The rheological behaviour of an ultra high strength (UHS) steel is investigated by Gleeble tensile tests at low-deformation rates and high temperature, from 1200°C to solidus temperature. Results show that large thermal gradients exist in specimens, resulting in heterogeneous deformation, which makes the identification of constitutive parameters difficult from the directly deduced nominal stress–strain curves. The advantages of an inverse identification method – associating a direct finite element model of Gleeble tests and an optimization module – are demonstrated in such conditions. The constitutive parameters identified by this technique have been successfully applied to additional tests, more complex in nature than those used for the identification of parameters. However, such tests combining successive loading and relaxation stages have revealed some limitations of the considered constitutive model.

Patient-Specific Modeling of Corneal Refractive Surgery Outcomes and Inverse Estimation of Elastic Property Changes

The purpose of this study is to develop a 3D patient-specific finite element model (FEM) of the cornea and sclera to compare predicted and in vivo refractive outcomes and to estimate the corneal elastic property changes associated with each procedure. Both eyes of a patient who underwent laser-assisted in situ keratomileusis (LASIK) for myopic astigmatism were modeled. Pre- and postoperative Scheimpflug anterior and posterior corneal elevation maps were imported into a 3D corneo-scleral FEM with an unrestrained limbus. Preoperative corneal hyperelastic properties were chosen to account for meridional anisotropy. Inverse FEM was used to determine the undeformed corneal state that produced <0.1% error in anterior elevation between simulated and in vivo preoperative geometries. Case-specific 3D aspheric ablation profiles were simulated, and corneal topography and spherical aberration were compared at clinical intraocular pressure. The magnitude of elastic weakening of the residual corneal bed required to maximize the agreement with clinical axial power was calculated and compared with the changes in ocular response analyzer (ORA) measurements. The models produced curvature maps and spherical aberrations equivalent to in vivo measurements. For the preoperative property values used in this study, predicted elastic weakening with LASIK was as high as 55% for a radially uniform model of residual corneal weakening and 65% at the point of maximum ablation in a spatially varying model of weakening. Reductions in ORA variables were also observed. A patient-specific FEM of corneal refractive surgery is presented, which allows the estimation of surgically induced changes in corneal elastic properties. Significant elastic weakening after LASIK was required to replicate clinical topographic outcomes in this two-eye pilot study.

A new sheet metal forming system based on the incremental punching, part 1: modeling and simulation

With the increasing demand for low-volume and customer-made products, incremental sheet metal forming (ISMF), a dieless sheet metal forming process, has become one of the leading RD then based on the fact that the energy will drive the sheet metal to attain its lowest energy position, the geometry of the final shape is derived. Then, another model is developed to predict the strain and stress distributions of the part using the inverse finite element modeling (FEM), also called the one-step FEM. Several numerical examples are provided. In the second part of the two papers, the design and the building of an incremental punching machine, as well as experiment results are given.

유한요소 모델 변수의 역 추정법을 이용한 생체의 물성 규명

An inverse finite element (FE) model parameter estimation algorithm can be used to characterize mechanical properties of biological tissues. Using this algorithm, we can consider the influence of material nonlinearity, contact mechanics, complex boundary conditions, and geometrical constraints in the modeling. In this study, biomechanical experiments on macro and micro samples are conducted and characterized with the developed algorithm. Macro scale experiments were performed to measure the force response of porcine livers against mechanical loadings using one-dimensional indentation device. The force response of the human liver cancer cells was also measured by the atomic force microscope (AFM). The mechanical behavior of porcine livers (macro) and human liver cancer cells (micro) were characterized with the algorithm via hyperelastic and linear viscoelastic models. The developed models are suitable for computing accurate reaction force on tools and deformation of biomechanical tissues.

Rapid coupling optimization method for a tube hydroforming process

This paper deals with the optimization of tube hydroforming parameters in order to reduce defects that may occur at the end of the forming process such as necking and wrinkling. A specific methodology is proposed based on the coupling between an inverse finite element model for the rapid simulation of the tube hydroforming process, and a response surface method based on diffuse approximation. The response surfaces are built using moving least-squares approximations and constructed within a moving region of interest, which moves across a predefined discrete grid of authorized experimental designs. An application of hydroforming of a bulge from aluminium alloy 6061-T6 tubing has been utilized to validate the methodology. The final design is validated with ABAQUS Explicit Dynamic commercial code.

Effect of indenter shapes on inverse materials characterization based on the dual indenters method

Abstract The indentation method is a useful tool for studying the onset of plastic flow and work hardening in small volumes. Several approaches based on either single and dual indenters have been reported to characterise a wide range of materials. In this work, the single and dual indenters approaches, with different indenter types, have been comparatively studied using an inverse finite element modelling program developed based on the Kalman filter method. The effect of indenter shapes on the accuracy and uniqueness of the predicted results, as well as convergence time of the program are systematically analysed by automatically mapping the results with a wide range of initial values.

Determination of plastic properties of metals by instrumented indentation using a stochastic optimization algorithm

A novel optimization approach, capable of extracting the mechanical properties of an elasto-plastic material from indentation data, is proposed. Theoretical verification is performed on two simulated configurations. The first is based on the analysis of the load–displacement data and the topography of the residual imprint of a single conical indenter. The second is based on the load–displacement data obtained from two conical indenters with different semi-angles. In both cases, a semi-analytical approach [e.g., Dao et al., Acta Mater.49, 3899 (2001) and Bucaille et al., Acta Mater.51, 1663 (2003)] is used to estimate Young’s modulus, yield stress, and strain hardening coefficient from the load–displacement data. An inverse finite element model, based on a commercial solver and a newly developed optimization algorithm based on a robust stochastic methodology, uses these approximate values as starting values to identify parameters with high accuracy. Both configurations use multiple data sets to extract the elastic-plastic material properties; this allows the mechanical properties of materials to be determined in a robust way.

3D strain measurement in soft tissue: Demonstration of a novel inverse finite element model algorithm on MicroCT images of a tissue phantom exposed to negative pressure wound therapy

This study describes a novel system for acquiring the 3D strain field in soft tissue at sub-millimeter spatial resolution during negative pressure wound therapy (NPWT). Recent research in advanced wound treatment modalities theorizes that microdeformations induced by the application of sub-atmospheric (negative) pressure through V.A.C. ® GranuFoam ® Dressing, a reticulated open-cell polyurethane foam (ROCF), is instrumental in regulating the mechanobiology of granulation tissue formation [Saxena, V., Hwang, C.W., Huang, S., Eichbaum, Q., Ingber, D., Orgill, D.P., 2004. Vacuum-assisted closure: Microdeformations of wounds and cell proliferation. Plast. Reconstr. Surg. 114, 1086–1096]. While the clinical response is unequivocal, measurement of deformations at the wound-dressing interface has not been possible due to the inaccessibility of the wound tissue beneath the sealed dressing. Here we describe the development of a bench-test wound model for microcomputed tomography (microCT) imaging of deformation induced by NPWT and an algorithm set for quantifying the 3D strain field at sub-millimeter resolution. Microdeformations induced in the tissue phantom revealed average tensile strains of 18%–23% at sub-atmospheric pressures of −50 to −200 mmHg (−6.7 to −26.7 kPa). The compressive strains (22%–24%) and shear strains (20%–23%) correlate with 2D FEM studies of microdeformational wound therapy in the reference cited above. We anticipate that strain signals quantified using this system can then be used in future research aimed at correlating the effects of mechanical loading on the phenotypic expression of dermal fibroblasts in acute and chronic ulcer models. Furthermore, the method developed here can be applied to continuum deformation analysis in other contexts, such as 3D cell culture via confocal microscopy, full scale CT and MRI imaging, and in machine vision.

Constitutive modeling of porcine liver in indentation using 3D ultrasound imaging

In this work we present an inverse finite-element modeling framework for constitutive modeling and parameter estimation of soft tissues using full-field volumetric deformation data obtained from 3D ultrasound. The finite-element model is coupled to full-field visual measurements by regularization springs attached at nodal locations. The free ends of the springs are displaced according to the locally estimated tissue motion, and the normalized potential energy stored in all springs serves as a measure of model-experiment agreement for material parameter optimization. We demonstrate good accuracy of estimated parameters and consistent convergence properties on synthetically generated data. We present constitutive model selection and parameter estimation for perfused porcine liver in indentation, and demonstrate that a quasilinear viscoelastic model with shear modulus relaxation offers good model-experiment agreement in terms of indenter displacement (0.19 mm RMS error) and tissue displacement field (0.97 mm RMS error).

Combining Galerkin Methods and Neural Network Analysis to Inversely determine Thermal Conductivity of Living Green Roof Materials

Use of living biological materials for roof greening is an effective strategy for Urban Heat Island (UHI) mitigation. Sunagoke moss mat is a living composite material with good potential for active roof greening. However, the determination of its thermal conductivity is difficult because it is fabricated from organic (live Sunagoke moss and cotton wool) and inorganic (polyvinyl chloride (PVC) netting) constituents. Thermal conductivity of this living composite material was determined using inverse finite-element modelling and neural network optimisation. The research hypothesis was that this property can be modelled as a weighted average of thermal conductivities of its constituents. Temperature regimes on either side of a Sunagoke moss mat (dimension 110 mm by 100 mm by 18·1 mm) in a thermally insulated transmission system were measured at different dry basis (db) water contents. Temperature regimes at 0%, 50% and 100% water contents (db) were input into a finite-element model and used to calculate nodal temperatures at six nodes across the thickness of the material. A weighted average model was used to compute effective conductivity for each element from the thermal conductivities of its constituents. Four multi-layer Perceptron (MLP) neural network models were developed and used to optimise effective thermal conductivity of the material at 0%, 50% and 100% water contents (db). The effective thermal conductivity of the material was 0·1 W m−1 K−1at 0%; 0·24 at 50% and 0·28 at 100% water contents (db). Nodal temperature profiles showed that the material exhibits steady-state heat transfer at 0% and 100% water contents (db) and transient-state heat transfer at water contents in between. It was concluded that inverse finite-element modelling is a feasible alternative technique for evaluating the thermal conductivity of living roof and wall greening materials and other biomaterials where use of conventional methods is difficult or highly erroneous.

Granular layers on vibrating plates: Effective bending stiffness and particle-size effects

Acoustic methods of land mine detection rely on the vibrations of the top plate of the mine in response to sound. For granular soil (e.g., sand), the particle size is expected to influence the mine response. This hypothesis is studied experimentally using a plate loaded with dry sand of various sizes from hundreds of microns to a few millimeters. For low values of sand mass, the plate resonance decreases with added mass and eventually reaches a minimum without particle size dependence. After the minimum, a frequency increase is observed with additional mass that includes a particle-size effect. Analytical nondissipative continuum models for granular media capture the observed particle-size dependence qualitatively but not quantitatively. In addition, a continuum-based finite element model (FEM) of a two-layer plate is used, with the sand layer replaced by an equivalent elastic layer for evaluation of the effective properties of the layer. Given a thickness of sand layer and corresponding experimental resonance, an inverse FEM problem is solved iteratively to give the effective Young's modulus and bending stiffness that matches the experimental frequency. It is shown that a continuum elastic model must employ a thickness-dependent elastic modulus in order to match experimental values.

Characterization of Elastoplastic Properties Based on Inverse Analysis and Finite Element Modeling of Two Separate Indenters

A method that can determine uniquely the elastoplastic properties from indentation loading and unloading curves has been developed. It is based on finite element modeling and inverse analysis of two separate indenters. The approach was validated by numerical experiments using a fictitious material. It was demonstrated that the proposed method can uniquely recover the elastoplastic properties using only indentation load-displacement curves of two indenters. Although the proposed procedure has been used to predict elastoplastic strain hardening behavior, it is also applicable to estimate other mechanical properties where there are more than two unknown parameters, such as rate-dependent behavior.

An inverse finite element algorithm to identify constitutive properties using dumb-bell miniature specimen

An inverse finite element algorithm is established to extract the tensile constitutive properties such as Young's modulus, yield strength and true stress–true strain diagram of a material in a virtually non-destructive manner. Standard test methods for predicting mechanical properties require the removal of large size material samples from the in-service component, which is impractical. To circumvent this situation, a new dumb-bell shaped miniature specimen has been designed and fabricated which can be used for evaluation of properties for a material or component. Also test fixtures were developed to perform a tension test on this proposed miniature specimen in a testing machine. The studies have been conducted in low carbon steel, die steel and medium carbon steel. The output from the miniature test, namely, load–elongation diagram, is obtained and used for the proposed inverse finite element algorithm to find the material properties. Inverse finite element modelling is carried out using a 2D plane stress analysis. The predicted results are found to be in good agreement with the experimental results.

Matrix-presentation linear least square error method of inverse elastic-plastic large deformation finite element model for upsetting

The main purpose of this paper is to develop the matrix presentation linear least square error method of inverse elastic-plastic large deformation finite element model for upsetting to obtain the friction coefficients during the upsetting process. This inverse model assumed the linear material and based on the modified experimental loading increments using the linear modified experimental upsetting loading standard proposed in this paper. Then the friction coefficients of contact boundary between the workpiece and the die at specific finite element analysis stages can be derived. Finally, using the cubic spline fitting, the history of friction coefficient during the upsetting process can be obtained. It is demonstrated that the workpiece profile of upsetting experiment is quite identical to the workpiece profile of simulation using the result obtained in this paper as the history of friction coefficient of contact boundary, and furthermore the distribution of stress and strain of the workpiece during upsetting process can be understood.

Thermal conductivity investigation for upsetting with a procedure of combining inverse model and the proposed regularization of Tikhonov method

The main purpose of this paper is to establish an inverse method, where by using this inverse method the history of the change in thermal conductivities of the workpiece material and the change in average temperatures of workpiece during upsetting process can be obtained. The inverse method is based on the measurement temperatures of an upsetting experiment and combines the matrix-presentation linear least-squares error method of an inverse heat-transfer finite element model proposed in this paper with the regularization of the Tikhonov method. Since the change of the thermal conductivities between the successive finite element analysis stages is very slight and continuous, the square of the difference of the thermal conductivities between successive finite element analysis stages is adopted as the stabilizing function of the regularization of the Tikhonov method in this paper. From the results, it can be shown and demonstrated that the inverse method proposed in this paper can make the history of the change in thermal conductivities during upsetting process has a better stability.

Sea surface velocities from sea surface temperature image sequences: 1. Method and validation using primitive equation model output

An inverse variational finite element model is developed for the purpose of estimating ocean surface velocity fields from sequences of temperature fields. The cross‐isotherm component of the velocity is controlled by a mixed layer integrated formulation of the heat balance. The aperture problem imposes additional constraints on the flow field: we control the divergence and the vorticity of the horizontal velocity. The method is then applied to sequences of sea surface temperature (SST) fields from a fine‐mesh numerical simulation over the Brazil‐Malvinas Confluence region. The difference between the actual velocity and the SST inverted velocity is 11% rms in magnitude and 17° rms in direction. These differences are analyzed; divergence and vorticity are computed. The hypothesis of neglecting the source terms made in the formulation of the mixed layer integrated heat balance is verified. The sensitivity of the solution to the influence of the constraints is examined. Perturbations are performed yielding fields of ellipses of covariance. We obtain on average 15% uncertainties in magnitude and 25° in direction of the velocity. Differences between the actual and SST inverted velocities fall into those covariance ellipses, except over regions where temperature does not change from one image to the other.