The inverse finite element method (iFEM) reconstructs full-field displacements from strain data without prior knowledge of loads or material properties. However, unknown or time-varying boundary conditions can degrade shape-sensing accuracy. This work advances smart sensing and structural health monitoring for beam-like structures by coupling iFEM with an online identification of boundary-condition degradation. An aluminum beam instrumented with an fiber Bragg grating sensor network is tested under controlled degradations—rotational stiffness reduction and vertical support settlement—each modeled as a virtual spring with unknown stiffness. A nonlinear optimization routine estimates the spring parameters while iFEM performs real-time shape reconstruction. Results show high-accuracy displacement fields and reliable quantification of support degradation, with a maximum deviation of about 10% from ground truth for both rotational and vertical cases. The framework demonstrates practical feasibility for simultaneous shape sensing and boundary-condition assessment in operational environments.

Fracture toughness evaluation of zirconia ceramics using nonlinear dynamic finite element analysis.

The design of smart skin with lightweight requirements utilizes high-performance composite materials, resulting in thin structural characteristics. When subjected to complex aerodynamic loads, the smart skin structure experiences warping deformation, which significantly impacts both flight efficiency and structural integrity. However, this deformation behavior has been largely overlooked in current shape sensing methods embedded within the structural health monitoring (SHM) systems of smart skin, leading to insufficient monitoring capabilities. To address this issue, this paper proposes a novel shape sensing methodology for the real-time monitoring of warping deformation in smart skin. Initially, the structural displacement field of the smart skin and the warping function are mathematically defined, incorporating constitutive relations and considering the influence of material parameters on sectional strains. Subsequently, the inverse finite element method (iFEM) is employed to establish a shape sensing model. The interpolation function and the actual sectional strains, derived from discrete strain measurements, are calculated based on the current constitutive equations. Finally, to validate the accuracy of the proposed iFEM for monitoring warping deformation, numerical tests are conducted on curved skin structures. The results indicate that the proposed methodology enhances reconstruction capability, with a 10% improvement in accuracy compared to traditional iFEM methods. Consequently, the shape sensing algorithm can be seamlessly integrated into the SHM system of smart skin to ensure the predicted performance.

Constitutive models (CMs) are used to predict material-specific relationships, such as stress and strain, through computer simulation. Although constitutive models, such as Johnson-Cook, Cowper-Symonds, modified Johnson-Cook, and Arrhenius, were used to simulate the behavior of animal bones and surrogate materials, the outcomes predicted from such models cannot be directly applied to human bone, as they were developed from animal and bone surrogate materials. Therefore, this is the first study to identify the Johnson-Cook model (JC-M) parameters for human cortical bone using the inverse finite element method (FEM). As a procedure, the initial value with upper and lower bounds for each of the parameters involved in the Johnson-Cook model was assigned for the simulation, and then the parameter values that could best represent the human cortical bone were determined using the Levenberg-Marquardt optimization algorithm (LMOA). To evaluate the results, tensile test simulations were carried out at various strain rates (0.00001-1/s); the results obtained from the simulations were shown to agree well with the experiments. A case study to demonstrate the orthogonal bone cutting was also conducted, which justified the demand for the Johnson-Cook model parameters of the human cortical bone. The findings of this study could be used to simulate complex surgical operations, and thus, the surgical rehearsal and practice could be carried out in silico without conducting experiments on human or animal bones.

Shape sensing and strain field reconstruction of full-scale wind turbine blade in static tests based on the inverse finite element method

The method proposed in this article pertains to developing a technique for structural health monitoring of cable-stayed bridges based on the inverse finite element method (iFEM). This approach is built on distributed monitoring of strains by using a Brillouin scattering-based distributed optical fiber sensor. Using this method, both the deflections and changes in cable forces are computed to assess the structural health of bridges. In contrast to the existing distributed strain-based techniques, the computation of cable forces does not require prior knowledge of loads and their locations. This provides the opportunity for use under operational conditions of the bridge, where the bridge is subjected to moving vehicular loads. The capability of the proposed technique was evaluated in laboratory experiments by a scaled model of a cable-stayed bridge. The experiments involved static and dynamic loads and the acquisition of distributed strains by a PPP-BOTDA optical fiber interrogation unit. Other sensor types, such as LVDT and FBG sensors, were employed in the experiments to validate the results of the proposed computational approach. In addition, the differences between the proposed approach and previous techniques are compared in terms of the computational approach, their attributes, and percentage errors in the computation of cable force variations.

Advanced shape sensing of a full-scale composite UAV stabilizer under non-ideal boundary conditions using the inverse Finite Element Method

Abstract Timely and accurate acquisition of temperature distribution data in space solar arrays is critical for formulating scientific thermal management strategies and developing fault diagnosis methods to ensure the safe operation of spacecraft in orbit. To address this challenge, this study proposes a temperature field reconstruction method based on discrete temperature sensing and the inverse finite element method (iFEM), overcoming the difficulty of temperature inversion under conditions where prior knowledge of structural material properties and thermal load characteristics is unavailable. A radial basis function (RBF)-based approach was developed to construct a four-node temperature shape function matrix, resolving the issue of error accumulation and elimination in non-monitored points caused by parameter uncertainty in conventional interpolation methods. Furthermore, a temperature monitoring and distribution reconstruction system was established for honeycomb-core solar panels using quasi-distributed fiber Bragg grating (FBG) sensors. Experimental results demonstrate that the average relative error of reconstructed temperature distribution is 5.10% under single heat source conditions and 4.49% under dual heat source conditions. This research not only enables “digital twin” modeling of space solar array structures throughout their lifecycle but also provides crucial support for safety assessment, early warning, and condition-based maintenance of critical spacecraft components.

An improved inverse finite element method based on co-rotational coordinates for reconstructing geometrically nonlinear shell deformations

Dynamic response reconstruction technique investigation of catenary submarine cables based on inverse finite element method

In-vivo biomechanical characteristics analysis of ascending aortic aneurysm using multidimensional dynamic CTA.

Progress in inverse finite element method for aerospace structural health monitoring applications

Nonlinear inverse finite element method for large deformation reconstruction of hull structures

ABSTRACTMarine environment is a harsh environment that can cause major issues for marine structures while operating in this environment, including fatigue cracking and corrosion damage, which can yield catastrophic consequences, such as human life losses, financial losses, environmental pollution, and so forth. Therefore, it is critical to take necessary actions before undesired situations happen. One potential solution is to install structural health monitoring systems on marine structures. Structural health monitoring is a technology to enhance the safety, stability, and functionality of large engineering structures. The inverse Finite Element Method (iFEM) is a promising technique for this purpose. In this study, the corrosion damage detection capability of iFEM is presented by introducing two new damage parameters for plates under tension and bending loading conditions. The contribution of newly introduced parameters to the accuracy of iFEM on damage detection is demonstrated for multiple corrosion scenarios and sensor configurations.

Objective. Anatomically and functionally optimal tongue reconstruction after tumor removal presents significant challenges. Current virtual surgical planning (VSP) utilizes patient-specific data with geometric algorithms for free flap design. However, these geometric approaches often inadequately account for complex soft tissue biomechanics. This study introduces a biomechanics-informed VSP algorithm and computationally compares its flap designs against those derived from purely geometric methods.Approach. Hyperelastic inverse finite element method (hiFEM) was developed by integrating an Ogden hyperelastic constitutive model into a predecessor algorithm. The planar flap shape is determined by minimizing potential energy when tissue deforms to match patient-specific MRI-derived 3D defect geometry. Four clinically plausible tongue cancer cases were simulated, and resection regions were delineated. For each case, flap designs were generated using hiFEM, its predecessor iFEM, and two geometric flattening techniques: NURBS surface flattening and boundary first flattening (BFF). Intrinsic tissue deformation for these designs was compared across methods and quantified using area stretch metric.Main results. Across all simulated cases, hiFEM-generated flap designs required less intrinsic tissue deformation. Maximum area stretch ranged from 1.10-1.12 for hiFEM designs, versus 1.19-1.38 for NURBS flattening and 1.54-1.74 for BFF designs. Furthermore, hiFEM's area stretch distribution was tighter, centered around one (ideal, no stretch). Geometric comparison showed hiFEM yields flap designs similar to the clinically validated geometric algorithm, NURBS flattening, with an average Hausdorff distance of only 1.3 mm. hiFEM's distinct advantage is its core objective of minimizing tissue stretch, which has clinical relevance and suggests potential for improved patient outcomes. Computationally, hiFEM demonstrated robustness and efficiency. It converged rapidly (8 to 10 iterations; less than 0.3 s/case), even for complex geometries where iFEM failed.Significance. hiFEM offers a biomechanically informed and computationally robust tool for tongue VSP, showing potential for broader application in breast, nasal, and other soft tissue reconstructions.

A unified framework for enhancing inverse finite element method through strain pre-extrapolation and sensor placement optimization

The study of wood acoustics is relevant to both understanding the biological functions of living trees and designing renewable sound-absorbing materials. This understanding can be enhanced through micromechanical models that relate wood microstructure to its acoustic properties. This paper begins by introducing three-dimensional modeling for microscale wood structures, confirming the elastic properties of wood cell wall layers. The equation of motion, incorporating element stiffness, mass matrices, and the force vector of a single substructure, is analyzed to assemble the global dynamic stiffness matrix of a wood cell. Free wave propagation characteristics are then examined by solving eigenvalue problems within both direct and inverse wave finite element method frameworks. The dispersion relations of positive-going waves are illustrated for a wood cell without a pit. Additionally, the forced response and displacement field of a wood cell without a pit are explored. Finally, wave diffusion, including reflection and transmission coefficients, is examined in a wood cell with a pit. The results demonstrate the proposed approach’s potential for investigating wave propagation and diffusion characteristics in microscale wood structures.

ABSTRACT There are various deformation field reconstruction techniques, of which the inverse Finite Element Method (iFEM) is considered to be one of the most effective. This research explores how iFEM, isogeometric analysis (IGA), and reduced basis methods can be applied to the nonlinear deformation field reconstruction of stiffened plate structures in ships. A novel methodology is introduced, which integrates reduced basis functions along with strain increments to devise a swift reconstruction technique for nonlinear deformation fields. The development of this algorithm is substantiated through numerical validation using finite element models. Ultimately, a typical stiffened plate structure is investigated by employing on-site strain data derived from model experiments as input for the nonlinear deformation field reconstruction algorithm. The findings indicate that the method introduced in this research surpasses standard iFEM in terms of accuracy and effectiveness for displacement reconstruction, strengthening the practical application of iFEM in shape sensing analysis of large-scale structures.

Abstract Mechanical characterisation of 3D-printed composite materials using conventional methods, such as tension and compression tests, faces several challenges, including precise machining of complex geometries, difficulties in testing materials with time-dependent properties, and extensive sample preparation to account for varying build orientations and raster angles. Accurately characterising the mechanical properties of composite constituents is further complicated by their anisotropic nature, visco-plastic behaviour, and phase interactions at the micro-scale. Traditional nano-indentation techniques often suffer from inaccuracies due to pile-up effects and time-dependent deformations in polymer matrices. To overcome these challenges, this study introduces an innovative methodology that integrates nano-indentation and micro-mechanical analysis of a representative volume element (RVE) to determine orthotropic engineering constants. Experimental nano-indentation, coupled with atomic force microscopy, is used to obtain load–displacement curves and residual indentation marks, whilst an inverse finite-element method accounting for neighbouring phase effects and polymer matrix creep properties enhances prediction accuracy. The stiffness properties of composite constituents derived from this method are employed in an RVE-based micro-mechanical model, with effective orthotropic engineering constants validated through experimental tensile and shear tests using the Digital Image Correlation technique. This approach not only enhances micro-mechanical characterisation accuracy but also reduces the need for extensive experimental testing, offering a cost-effective and scalable solution for evaluating 3D-printed composite materials. Additionally, it bridges the gap between microstructural and bulk property measurements, reducing test sample manufacturing costs and minimising the need for repetitive experimental trials.

A novel inverse extended finite element method for structural health monitoring of cracked structures