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This paper aims to develop a mathematical method to analyze the assembly variation of the non-rigid assembly, considering the manufacturing variations and the deformation variations of the non-rigid parts during the assembly process.

First, this paper proposes a deformation gradient model, which represents the deformation variations during the assembly process by considering the forces and the self-weight of the non-rigid parts. Second, the developed deformation gradient models from the assembly process are integrated into the homogenous transformation matrix to model the deformation variations and manufacturing variations of the deformed non-rigid part. Finally, a mathematical model to analyze the assembly variation propagation is developed to predict the dimensional and geometrical variations due to the manufacturing variations and the deformation variations during the assembly process.

Through the case study with a crosshead non-rigid assembly, the results indicate that during the assembly process, the individual deformation values of the non-rigid parts are small. However, the cumulative deformation variations of all the non-rigid parts and the manufacturing variations present a target value (w) of −0.2837 mm as compared to a target value of −0.3995 mm when the assembly is assumed to be rigid. The difference in the target values indicates that the influence of the non-rigid part deformation variations during the assembly process on the mechanical assembly accuracy cannot be ignored.

In this paper, a deformation gradient model is proposed to obtain the deformation variations of non-rigid parts during the assembly process. The small deformation variation, which is often modeled using a finite-element method in the existing works, is modeled using the proposed deformation gradient model and integrated into the nominal dimensions. Using the deformation gradient models, the non-rigid part deformation variations can be computed and the accumulated deformation variation can be easily obtained. The assembly variation propagation model is developed to predict the accuracy of the non-rigid assembly by integrating the deformation gradient models into the homogeneous transformation matrix.

This study aims to propose a novel viscoelastic–viscoplastic combined constitutive model for glassy amorphous polymers within the framework of thermodynamics at finite strain that is capable of capturing their rate-dependent inelastic mechanical behavior in wide ranges of deformation rate and amount.

The rheology model whose viscoelastic and viscoplastic elements are connected in series is set in accordance with the multi-mechanism theory. Then, the constitutive functions are formulated on the basis of the multiplicative decomposition of the deformation gradient implicated by the rheology model within the framework of thermodynamics. Dynamic mechanical analysis (DMA) and loading/unloading/no-load tests for polycarbonate (PC) are conducted to identify the material parameters and demonstrate the capability of the proposed model.

The performance was validated in comparison with the series of the test results with different rates and amounts of deformation before unloading together. It has been confirmed that the proposed model can accommodate various material behaviors empirically observed, such as rate-dependent elasticity, elastic hysteresis, strain softening, orientation hardening and strain recovery.

This paper presents a novel rheological constitutive model in which the viscoelastic element connected in series with the viscoplastic one exclusively represents the elastic behavior, and each material response is formulated according to the multiplicatively decomposed deformation gradients. In particular, the yield strength followed by the isotropic hardening reflects the relaxation characteristics in the viscoelastic constitutive functions so that the glass transition temperature could be variant within the wide range of deformation rate. Consequently, the model enables us to properly represent the loading process up to large deformation regime followed by unloading and no-load processes.

Classical continuum models, i.e. continuum models that do not incorporate an internal length scale, suffer from excessive mesh dependence when strain‐softening models are used in numerical analyses and cannot reproduce the size effect commonly observed in quasi‐brittle failure. In this contribution three different approaches will be scrutinized which may be used to remedy these two intimately related deficiencies of the classical theory, namely (i) the addition of higher‐order deformation gradients, (ii) the use of micropolar continuum models, and (iii) the addition of rate dependence. By means of a number of numerical simulations it will be investigated under which conditions these enriched continuum theories permit localization of deformation without losing ellipticity for static problems and hyperbolicity for dynamic problems. For the latter class of problems the crucial role of dispersion in wave propagation in strain‐softening media will also be highlighted.

This paper describes the development and the numerical analysis of an electrochemical model for the analysis of a novel polymer/metal composite actuator. A general continuum model describing the transport and deformation processes of these actuators is briefly presented, along with a detailed description of the simulation scheme used to predict deformation, current, and mass transport. The predictions of the model are compared with experimental data, indicating a significant role of water transport in the large‐scale deformation. Comparison of the simulations and experimental data showed good agreement confirming the central role of water transport in the deformation process. For the sake of completeness the fabrication process and testing apparatus are also described.

Continuum‐atomistic modeling denotes a mixed approach combining the usual framework of continuum mechanics with atomistic features like e.g. interaction potentials. Thereby, the kinematics are typically characterized by the so called Cauchy‐Born rule representing atomic distance vectors in the spatial configuration as an affine mapping of the atomic distance vectors in the material configuration in terms of the local deformation gradient. The application of the Cauchy‐Born rule requires sufficiently homogeneous deformations of the underlying crystal. The model is no more valid if the deformation becomes inhomogeneous. By virtue of the Cauchy‐Born hypothesis, a localization criterion has been derived in terms of the loss of infinitesimal rank‐1 convexity of the strain energy density. According to this criterion, a numerical yield condition has been computed for two different interatomic energy functions. Therewith, the range of the Cauchy‐Born rule validity has been defined, since the strain energy density remains quasiconvex only within the computed yield surface. To provide a possibility to continue the simulation of material response after the loss of quasiconvexity, a relaxation procedure proposed by Tadmor et al. [1] leading necessarily to the development of microstructures has been used. Alternatively to the above mentioned criterion, a stability criterion has been applied to detect the critical deformation. For the study in the postcritical region, the path‐change procedure proposed by Wagner and Wriggers [2] has been adapted for the continuum‐atomistics and modified.

Laser-based powder bed fusion (LPBF) is a new method for forming thin-walled parts, but large cooling rates and temperature gradients can lead to large residual stresses and deformations in the part. This study aims to reduce the residual stress and deformation of thin-walled parts by a specific laser rescanning strategy.

A three-dimensional transient finite element model is established to numerically simulate the LPBF forming process of multilayer and multitrack thin-walled parts. By changing the defocus amount, the laser in situ annealing process is designed, and the optimal rescanning parameters are obtained, which are verified by experiments.

The results show that the annealing effect is related to the average surface temperature and scan time. When the laser power is 30 W and the scanning speed is 20 mm/s, the overall residual stress and deformation of the thin-walled parts are the smallest, and the in situ annealing effect is the best. When the annealing frequency is reduced to once every three layers, the total annealing time can be reduced by more than 60%.

The research results can help better understand the influence mechanism of laser in situ annealing process on residual stress and deformation in LPBF and provide guidance for reducing residual stress and deformation of LPBF thin-walled parts.

This paper aims to measure the sensitivity of the structure’s deformation numerical model (NM) related to the various types of the design parameters, which is a suitable method for parameter selection to increase the time of model-updating.

In this research, a variance-based sensitivity analysis (VBSA) approach is proposed to measure the sensitivity of NM of structures. In this way, the contribution of measurements of the structure (such as design parameter values and geometry) on the output of NM is studied using first-order and total-order sensitivity indices developed by Sobol’. In this way the generated data set of parameters by considering different distributions such as Gaussian or uniform distribution and different order as input along with, the resulted deformation variables of NM as output has been submitted to the Sobol’ indices estimation procedure. To the verification of VBSA results, a gradient-based sensitivity analysis (SA), which is developed as a global SA method has been developed to measure the global sensitivity of NM then implemented over the NM’s results of a tunnel.

Regarding the estimated indices, it has been concluded that the derived deformation functions from the tunnel’s NM usually are non-additive. Also, some parameters have been determined as most effective on the deformation functions, which can be selected for model-updating to avoid a time-consuming process, so those may better to be considered in the group of updating parameters. In this procedure for SA of the model, also some interactions between the selected parameters with other parameters, which are beneficial to be considered in the model-updating procedure, have been detected. In this study, some parameters approximately (27 per cent of the total) with no effect over the all objective functions have been determined to be excluded from the parameter candidates for model-updating. Also, the resulted indices of implemented VBSA were approved during validation by the gradient-based indices.

The introduced method has been implemented for a circular lined tunnel’s NM, which has been created by Fast Lagrangian Analysis of Continua software.

This paper plans to apply a statistical method, which is global on the results of the NM of a soil structure by a complex system for parameter selection to avoid the time-consuming model-updating process.

Considers the problem of stability of the enhanced strain elements in the presence of large deformations. The standard orthogonality condition between the enhanced strains and constant stresses ensures satisfaction of the patch test and convergence of the method in case of linear elasticity. However, this does not hold in the case of large deformations. By analytic derivation of the element eigenvalues in large strain states additional orthogonality conditions can be derived, leading to a stable formulation, regardless of the magnitude of deformations. Proposes a new element based on a consistent formulation of the enhanced gradient with respect to new orthogonality conditions which it retains with four enhanced modes volumetric and shear locking free behaviour of the original formulation and does not exhibit hour‐glassing for large deformations.

An accurate prediction of the deformation of retaining structures is critical for ensuring the stability and safety of braced deep excavations, while the high nonlinear and complex nature of the deformation makes the prediction challenging. This paper proposes an explainable boosted combining global and local feature multivariate regression (EB-GLFMR) model with high accuracy, robustness and interpretability to predict the deformation of retaining structures during braced deep excavations.

During the model development, the time series of deformation data is decomposed using a locally weighted scatterplot smoothing technique into trend and residual terms. The trend terms are analyzed through multiple adaptive spline regressions. The residual terms are reconstructed in phase space to extract both global and local features, which are then fed into a gradient-boosting model for prediction.

The proposed model outperforms other established approaches in terms of accuracy and robustness, as demonstrated through analyzing two cases of braced deep excavations.

The model is designed for the prediction of the deformation of deep excavations with stepped, chaotic and fluctuating features. Further research needs to be conducted to expand the model applicability to other time series deformation data.

The model provides an efficient, robust and transparent approach to predict deformation during braced deep excavations. It serves as an effective decision support tool for engineers to ensure the stability and safety of deep excavations.

The model captures the global and local features of time series deformation of retaining structures and provides explicit expressions and feature importance for deformation trends and residuals, making it an efficient and transparent approach for deformation prediction.

This paper aims to present a nonlocal gradient plasticity damage model to demonstrate the crack pattern of a body, in an elastic and plastic state, in terms of damage law. The main objective of this paper is to reconsider the nonlocal theory by including the material in-homogeneity caused by damage and plasticity. The nonlocal nature of the strain field provides a regularization to overcome the analytical and computational problems induced by softening constitutive laws. Such an approach requires C1 continuous approximation. This is achieved by using an isogeometric approximation (IGA). Numerical examples in one and two dimensions are presented.

In this work, the authors propose a nonlocal elastic plastic damage model. The nonlocal nature of the strain field provides a regularization to overcome the analytical and computational problems induced by softening constitutive laws. An additive decomposition of strains in to elastic and inelastic or plastic part is considered. To obtain stable damage, a higher gradient order is considered for an integral equation, which is obtained by the Taylor series expansion of the local inelastic strain around the point under consideration. The higher-order continuity of nonuniform rational B-splines (NURBS) functions used in isogeometric analysis are adopted here to implement in a numerical scheme. To demonstrate the validity of the proposed model, numerical examples in one and two dimensions are presented.

The proposed nonlocal elastic plastic damage model is able to predict the damage in an accurate manner. The numerical results are mesh independent. The nonlocal terms add a regularization to the model especially for strain softening type of materials. The consideration of nonlocality in inelastic strains is more meaningful to the physics of damage. The use of IGA framework and NURBS basis functions add to the nonlocal nature in approximations of the field variables.

The method can be extended to 3D. The model does not consider the effect of temperature and the dissipation of energy due to temperature. The method needs to be implemented for more real practical problems and compare with experimental work. This is an ongoing work.

The nonlocal models are suitable for predicting damage in quasi brittle materials. The use of elastic plastic theories allows to capture the inelastic deformations more accurately.

The nonlocal models are suitable for predicting damage in quasi brittle materials. The use of elastic plastic theories allows to capture the inelastic deformations more accurately.

The present work includes the formulation and implementation of a nonlocal damage plasticity model using an isogeometric discretization, which is the novel contribution of this paper. An implicit gradient enhancement is considered to the inelastic strain. During inelastic deformations, the proposed strain tensor partitioning allows the use of a distinct potential surface and distinct failure criterion for both damage and plasticity models. The use of NURBS basis functions adds to more nonlocality in the approximation.