Large Deformation Analysis Research Articles

Analytical and numerical investigation of second-order infinitesimal mechanism in rigid origami

This study investigates second-order infinitesimal mechanisms and bifurcation paths of rigid origamis with multiple-degree-of-freedom mechanisms. A truss model, consisting of pin-connected rigid bars, is employed for the infinitesimal mechanism analysis. The conditions for the existence of a second-order infinitesimal mechanism are analytically solved to investigate the combinations of the infinitesimal mechanism modes that are the potential finite mechanisms. Analytical solutions for simple crease patterns show the bifurcation of the deformation paths at the flat state, some disappeared combinations of the mechanism modes in a single path, and the relationship between the nodal displacement and axial force distribution. This comprehensive analysis, using analytical solutions, lays the foundation for understanding bifurcation and finite mechanism of rigid origami, which have not yet been fully explored. These properties are also verified in the finite deformation paths generated by large deformation analysis of a frame model consisting of frame members and hinges, which is suitable for the analysis using general-purpose finite element analysis software. The second-order infinitesimal mechanisms found in this study are confirmed to be able to be extended to the finite mechanisms.

A high‐order shell finite element for the large deformation analysis of soft material structures

SummaryThis work proposes a higher‐order unified shell finite element for the analysis of cylinders made of compressible and nearly incompressible hyperelastic materials. The nonlinear governing equations are derived employing the Carrera unified formulation (CUF), thanks to which it is possible to build shell elements with the capability to capture three‐dimensional (3D) transverse and out‐of‐plane effects. The material and geometric nonlinearities are expressed in an orthogonal curvilinear reference system and the coupled formulation of hyperelastic constitutive law is considered. The principle of virtual work and a total Lagrangian approach is used to derive the nonlinear governing equations, which are solved by a Newton–Raphson scheme. The numerical investigations deal with a curved arch and both thick and thin cylinders subjected to line and point loadings. The obtained results are validated by comparing them with those from the literature. They demonstrate the reliability of the proposed method to analyze compressible and incompressible hyperelastic shell structures.

Drilling technology of long horizontal section of shale oil

As an important supplementary energy resource, shale oil has attracted worldwide attention due to its huge reserves and rich comprehensive utilization levels. The world is rich in oil shale resources. According to statistics, if the oil shale of 33 countries and regions in the world is converted into shale oil, it will be about 400 billion tons. With the continuous maturity of horizontal well drilling and completion technology in shale oil gas reservoirs and the application of other advanced technologies in horizontal well drilling, mature shale oil gas drilling and completion matching technologies have gradually formed at home and abroad after years of research and drilling practice. In terms of measurement technology, China has been able to produce single-point, multi-point, wired, wireless inclinometers and MWD measuring instruments while drilling and has mastered their usage methods. In terms of control technology, various specifications and types of fixed-angle and ground-adjustable curved shell screw drilling tools have been produced in China. Large deformation analysis and trajectory prediction methods for lower drilling tool assemblies have been completed. Various lower drilling tool assemblies and their usage processes required for wellbore trajectory control have been improved and mastered. In the construction of inclined and horizontal sections, attention should be paid to the response law of drilling tool combinations to drilling pressure in different formations, especially the response law of composite drilling. Reasonable drilling tool combinations should be selected for the control of wellbore trajectory in stable and horizontal sections, especially in the long stable and horizontal sections.

Large Deformation Analysis of Hyperelastic Continuum with Hexahedral Adaptive Finite Elements

The use of hyperelastic materials capable of large deformations, such as elastomeric bearings used to reduce seismic effects, is quite common in civil engineering. Such environments are, in most cases, addressed by numerical solution techniques such as the finite element method. In case of large deformations, nonlinear analysis is used in the solution. In the study presented here, large deformations of a hyperelastic continuum expressed by the Mooney-Rivlin material model are calculated using hexahedral adaptive finite elements. A code was written in MATLAB using the total Lagrangian formulation for the nonlinear adaptive finite element solution. Comparisons were made with Abaqus software to check the consistency of the results obtained from this program. It has been observed that local refinements in the adaptive element mesh occur in the regions where they are needed. Considering the variation of maximum displacement and maximum stress with the number of elements, it has been observed that mesh refinement creates a convergent solution.

Dynamic collapse characteristics of the tunnel face induced by the shutdown of earth pressure balance shields (EPB): A 3D material point method study

The collapse of the tunnel face is a prevalent geological disaster in tunnelling. This study employs a three-dimensional (3D) material point method (MPM) to simulate the dynamic collapse process and post-failure mechanisms of the tunnel face. The specific focus is on the scenario where the auxiliary air pressure balanced shield with a partially filled chamber is shut down. To assess the suitability of the 3D MPM, numerical solutions are compared with the results from small-scale experimental tests. Subsequently, a series of large-scale numerical simulations is conducted to explore the dynamic collapse characteristics of the tunnel face induced by the shutdown of the EPB shield under various support air pressures and cutter head conditions. The temporal evolution of the accumulated soil masses in the soil chamber and ground responses under different support air pressures, cutter head types and opening ratios are discussed. In particular, the associated surface subsidence due to the tunnel face collapse is determined and compared with empirical solutions. Numerical results confirm the applicability of the 3D MPM for simulating the large-scale tunnel face collapse scenarios, spanning from small to large deformation analysis.

Weighted radial basis collocation method for large deformation analysis of rubber-like materials

A nonlinear formulation, based on the total Lagrange description of the weighted radial basis collocation method (WRBCM), is proposed for the large deformation analysis of rubber-like materials where the materials are hyperelastic and nearly incompressible. The WRBCM based on the strong form collocation is a genuinely meshfree method that eliminates the need for meshing. As a result, it effectively circumvents challenges associated with mesh distortion during large deformation analysis. The proper weights that should be imposed on the boundary collocation equations are first derived to achieve the optimal convergence in hyperelasticity. In the WRBCM, the support of the shape function remains unchanged throughout material deformation, thereby guaranteeing the absence of tension instability during large deformation analysis. Additionally, by combining WRBCM with a least-squares solution, volumetric locking in nearly incompressible hyperelastic problems can be suppressed. This is due to the infinite continuity possessed by the radial basis approximation, which ensures the divergence-free condition. Several numerical examples are examined, demonstrating the high accuracy and exponential convergence of WRBCM in hyperelastic large deformation analysis. Moreover, no volumetric locking can be observed which further substantiates the effectiveness of applying nonlinear WRBCM to nearly incompressible hyperelastic problems.

Large deformation analysis of functionally graded revolutionary shallow thin shells with bi-modular effect: Snap-through buckling under different boundary constraints

Functionally graded materials (FGMs) enable structures to achieve a smooth transition between different material properties, providing an optimized combination of functions to meet the diversity of engineering needs. However, the presence of bi-modular effect in FGMs is often neglected due to the complexity in the analysis. In this paper, the curvature correction equivalent method based on the von Kármán theory will be applied to the theoretical study for the large deformation problem and the resulting snap-through buckling of functionally graded revolutionary shallow thin shells with bi-modular effect under different boundary constraints. Furthermore, a bi-modular FGMs user material subroutine (UMAT) is developed for the first time to simulate the real material model, thus validating the theoretical solution. The results show that except for the bi-modular effect of materials, boundary constraints of shells also have important influences on the relationship of load vs. central deflection and snap-through buckling. The research of boundary constraints brings new conclusions to snap-through buckling: the rotation constraint and radial constraint at the shell edge have opposite effects on snap-through buckling. This work will contribute to the analysis of the snap-through buckling of functionally graded revolutionary shallow thin shells with an obvious bi-modular effect and under various boundary constraints.

Accretion–ablation mechanics

In this paper, we formulate a geometric nonlinear theory of the mechanics of accreting–ablating bodies. This is a generalization of the theory of accretion mechanics of Sozio & Yavari (Sozio & Yavari 2019 J. Nonlinear Sci. 29 , 1813–1863 (doi:10.1007/s00332-019-09531-w)). More specifically, we are interested in large deformation analysis of bodies that undergo a continuous and simultaneous accretion and ablation on their boundaries while under external loads. In this formulation, the natural configuration of an accreting–ablating body is a time-dependent Riemannian 3 -manifold with a metric that is an unknown a priori and is determined after solving the accretion–ablation initial-boundary-value problem. In addition to the time of attachment map, we introduce a time of detachment map that along with the time of attachment map, and the accretion and ablation velocities, describes the time-dependent reference configuration of the body. The kinematics, material manifold, material metric, constitutive equations and the balance laws are discussed in detail. As a concrete example and application of the geometric theory, we analyse a thick hollow circular cylinder made of an arbitrary incompressible isotropic material that is under a finite time-dependent extension while undergoing continuous ablation on its inner cylinder boundary and accretion on its outer cylinder boundary. The state of deformation and stress during the accretion–ablation process, and the residual stretch and stress after the completion of the accretion–ablation process, are computed. This article is part of the theme issue ‘Foundational issues, analysis and geometry in continuum mechanics’.

New insight into large deformation analysis of stretch-based and invariant-based rubber-like hyperelastic elastomers

A nonlinear finite element formulation for large deformation analysis of hyperelastic membranes in Total Lagrangian framework is developed. In many cases, it is convenient to utilize the invariant-based strain energy density function to analyze the structures when employing the finite element method. However, in this contribution, both invariant-based and stretch-based formulations are developed. Formulations are completely general and not restricted to axisymmetric loading and geometry of membrane. Furthermore, initially flat and non-flat membrane can be investigated by this method. Incompressible as well as compressible materials can be modeled. A method for imposing the plane stress condition to the formulation for compressible materials is presented. Moreover, isotropic and anisotropic materials can be considered. Some problems are analyzed and results compared to the available ones in the literature. The comparison between solution based on invariant-based method and stretch-based method with exact fourth-order elasticity tensor obtained in this work demonstrates that the stretch-based method derived in this paper works very well. The presented examples demonstrate that the developed formulations have no restriction or simplification with respect to the modeled object geometry and inherent anisotropy.

Arbitrary mesh‐moving velocity‐based space‐time finite element method for large deformation analysis of solids

SummaryThis paper presents a new velocity‐based space‐time finite element method for computing the large deformation of solids over arbitrary Lagrange/Eulerian moving meshes. The proposed method is oriented toward quasi‐static deformation problems with hypoelastic and neo‐Hookean hyperelastic constitutive models. The Cauchy stress in the weak form of the linear momentum equation is explicitly described in terms of deformation velocity through consistent time integration of objective stress rates transferred in the arbitrary moving mesh. Consequently, the resultant system equation only contains the space‐time nodal velocity as the primary unknown. An iterative algorithm for solving the discretized system equation is implemented, whereby the nonlinearities induced by geometrical change in the computational domain as well as nonlinear constitutive equations are computed in an iterative manner updating the stress and the strain over the moving mesh of the deforming domain. Three benchmark problems, such as uniform beam compression, thick‐cylinder compression with superimposed rigid body rotation and extrusion of a column involving material loss, have been solved in order to examine the accuracy of the proposed numerical scheme. The numerical results have revealed the proper computation of the stress and the displacement of the solids undergoing the large deformation and rotation over the arbitrary Lagrange/Eulerian moving meshes, and have shown the validity and applicability of the proposed method with linear convergence of the iterative algorithm.

Circumventing volumetric locking in stabilized smoothed particle finite element method and its application to dynamic large deformation problems

AbstractThe smoothed particle finite element method (SPFEM) is an effective framework for large deformation analysis. The original SPFEM possesses the rank deficiency issue due to the direct nodal integration technique, which can be overcome by incorporating the strain gradient stabilization method. However, an extra volumetric locking due to the strain gradient stabilization term has been found. In this study, we propose a simple and efficient approach, the B‐dev approach, which only considers the deviatoric part of the smoothed strain gradient for stabilization to overcome the volumetric locking issue. First, the correctness of the stabilized SPFEM method is verified by an elastic cantilever beam vibration problem without considering incompressibility. Then, through the example of the strip footing penetration problem, the volumetric locking in the stabilized SPFEM is demonstrated and the capability of the proposed B‐dev approach in terms of overcoming the volumetric locking is verified. Furthermore, the stabilized SPFEM with B‐dev approach is applied to two types of elastoplastic problems in geotechnical engineering. All numerical results illustrate that the proposed approach can improve the performance of the stabilized SPFEM in dealing with incompressible and large deformation problems in geomechanics.

A meshfree large-deformation analysis method for geotechnical engineering based on the RBF field variable mapping technology

In this paper, a practical meshfree large deformation method (MFLDM) is proposed for numerical analysis in geotechnical engineerings, including: soil foundation, slop, dam, etc. The MFLDM leverages both the flexible nodal distribution in the meshfree method and the high stability in the arbitrary Lagrangian–Eulerian (ALE) framework. In each calculation step, two sets of Gauss points, fixed and moving Gauss points, are generated in the background mesh. In addition, the radial basis function (RBF) is used to map field variables, including stress, stain, and constitutive variables, between the fixed and moving Gauss points to achieve the field variable redistribution during the large-deformation analysis. The proposed MFLDM, which is written in C++ using the object-oriented programming approach, can be completely integrated into the self-development calculating system named GEODYNA and coupled with the finite element method (FEM) at the matrix level, which significantly broadens its practical application. The proposed model is verified by several numerical examples and compared with different constitutive models, including the linear elasticity model, ideal elastic–plastic model, and generalized elastic–plastic model. The comparison results verify the high accuracy, fast convergence, and good robustness of the proposed MFLDM. Finally, the proposed MFLDM is applied to a local large deformation analysis between the cut-off wall and the core wall on a deep overburden.

Large deformation analysis of a backside-supported snap-fit with nonlinear behavior

In this study, the large deformation of a backside-supported snap-fit was analyzed. The backside snap-fit pair consisted of mating part and base part. The mating part was a simple cantilever, and the base part had an opening with a supporting bar. The reaction force of the supporting bar was found to be an important parameter for the assembly and separation of the snap-fit. During our analysis, the supporting bar experienced a large deformation with nonlinear elasticity or plastic damage. Finite element analysis was performed. Stress concentration was observed at the root of the supporting bar and at the bent edge of the base part. Three types of specimens were designed and fabricated for experimental verification. The first specimen was a reference design that was fabricated according to the same design concept as the actual product. The second specimen was designed to reduce the stress concentration. The third specimen had an enriched design to increase the supporting force. The reaction force corresponding to the applied displacement was measured using a testing machine. The load exhibited a highly nonlinear behavior and reached a maximum peak value without causing any apparent damage, after which it decreased with plastic damage. Through numerical and experimental analyses, it was found out that the design of the backside-supported snap-fit could be improved by reducing the stress concentration and increasing the stiffness of the supporting bar.

Large deformation analysis of functionally graded thermoviscoplastic beams under ductile damage via finite elements

Large deformation analysis of functionally graded thermoviscoplastic beams under ductile damage via finite elements

The elastoplastic large deformation analysis based on meshless radial basis reproducing kernel particle method

In this paper, the radial basis reproducing kernel particle method (RB-RKPM) is extended to solve the elastoplastic large deformation problem. The Galerkin weak form of the elastoplastic large deformation problem based on the full Lagrange scheme is used to establish the solution equation, which is then solved using the Newton–Raphson iterative method. The RB-RKPM is established for the elastoplastic large deformation problem. The effect of the penalty factor, the scale parameter, and the shape parameter on the calculation accuracy are introduced, and the optimal parameters are obtained. Several numerical examples were used in the simulation. The RB-RKPM solution is compared with the reproducing kernel particle method (RKPM) solution and the finite element method (FEM) solution, the effectiveness of the RB-RKPM in solving elastoplastic large deformation problem is verified, and the RB-RKPM has high computational accuracy.

Nodal integration-based particle finite element method (N-PFEM) for poro-elastoplastic modelling of saturated soils under large deformation

This paper presents the nodal integration-based particle finite element method (N-PFEM) for poro-elastoplastic analysis of saturated soils subject to large deformation, utilising the generalised Hellinger-Reissner variational principle to reformulate the governing equations for saturated soil dynamics into a min–max optimisation problem. With finite element discretisation and nodal integration over cells, the problem is transformed into a standard second-order cone programming problem, efficiently resolved using the advanced primal–dual interior point method. The N-PFEM method has several advantages, including the use of linear triangular elements without volumetric locking issues, the avoidance of regularisation techniques, and the elimination of tedious variable mapping after remeshing. The numerical model is validated for large deformation analysis of saturated soils with a series of benchmarks against available analytical and numerical solutions, with a case study of the deformation of an embankment considering stone column reinforcement also carried out. This N-PFEM framework offers an effective and efficient simulation approach for the evolutionary behaviour of saturated soils with large deformation in complex geotechnical configurations of practical relevance.

Statics of integrated origami and tensegrity systems

This study presents an explicit form of the static equilibrium equations of integrated origami and tensegrity systems. The analytical approach allows one to model and analyze the isolated origami and tensegrity paradigms as a whole system. The tensegrity and origami members are described by the nodal coordinates and hinge angels between the origami panels. The nonlinear static equations of the integrated system are derived by the Lagrangian method. By Taylor’s expansion theory, we also presented its linearized form. The developed approach is capable of conducting the following comprehensive statics studies for any integrated origami and tensegrity systems: (1) Performing loading analysis, where bars and strings can have elastic or plastic deformations. (2) Conducting infinitesimal and large deformation analysis, which is helpful in understanding the stress in structural members and actuation strategies. (3) Dealing with various kinds of boundary conditions, for example, fixing or applying static loads at any nodes in any direction (i.e., gravitational force, some specified forces, or moments). (4) Conducting stiffness analysis, including eigenvalues and their modes. Three examples, a Miura origami unit, an integrated tensegrity origami shelter, and a cable-driven Kresling structure, are carefully selected and studied. This study provides a deep insight into structures, materials, as well as performances. The integration idea also promotes our ability to design and build deployable structures at large.

Numerical investigation of turbulent lid-driven flow using weakly compressible smoothed particle hydrodynamics CFD code with standard and dynamic LES models

Smoothed Particle Hydrodynamics (SPH) is a Lagrangian computational fluid dynamics method that has been widely used in the analysis of physical phenomena characterized by large deformation or multi-phase flow analysis, including free surface. Despite the recent implementation of eddy-viscosity models in SPH methodology, sophisticated turbulent analysis using Lagrangian methodology has been limited due to the lack of computational performance and numerical consistency. In this study, we implement the standard and dynamic Smagorinsky model and dynamic Vreman model as sub-particle scale models based on a weakly compressible SPH solver. The large eddy simulation method is numerically identical to the spatial discretization method of smoothed particle dynamics, enabling the intuitive implementation of the turbulence model. Furthermore, there is no additional filtering process required for physical variables since the sub-grid scale filtering is inherently processed in the kernel interpolation. We simulate lid-driven flow under transition and turbulent conditions as a benchmark. The simulation results show that the dynamic Vreman model produces consistent results with experimental and numerical research regarding Reynolds averaged physical quantities and flow structure. Spectral analysis also confirms that it is possible to analyze turbulent eddies with a smaller length scale using the dynamic Vreman model with the same particle size.

Large deformation analysis of a hyperplastic beam using experimental / FEM/ meshless collocation method

In the present study, nonlinear numerical and experimental static bending analyses of hyperelastic beams are surveyed. Timoshenko's beam theory is used to obtain the Cauchy-Green deformation tensor. The governing equations are extracted using the neo-Hookean strain energy and Euler–Lagrange relation. Afterward, the nonlinear governing equations are solved numerically using the meshless collocation method (MCM). To validate the present investigation, a comparison study is accomplished between the acquired results from MCM and the experimental test of digital image correlation (DIC) and finite element method (FEM). The hyperelastic beam is made of natural rubber. Also, loading and boundary conditions are considered as concentrated force and clamped–clamped, respectively. In addition, the displacement contour is extracted by the DIC. The uniaxial tensile test based on the ASTM D412 standard is performed to extract the mechanical properties of natural rubber. The hyperelastic theory and neo-Hookean strain energy function are utilized to model the nonlinear behavior of rubber in the FEM. The error for the maximum displacement of system obtained from both numerical methods is less than 12% compared to the DIC. Additionally, it can be observed that in large deformations, unlike the FEM, MCM is able to predict the system's response with high accuracy.

Large deformation and crack propagation analyses of hydrogel by peridynamics

In this paper, the large tensile deformation and Mode-I crack propagation of hydrogel are effectively simulated by the bond-associated (BA) non-ordinary state-based (NOSB) peridynamics (PD). Based on the nonlocal theory and meshless characteristic, the fracture involving large deformation of hydrogel is solved with simple implementations. In the analysis, the Gent model is first introduced into NOSB PD as the constitutive model to describe the stress-stretch response of hydrogel under a large tensile stretch. The bond-associated scheme is applied to overcome zero-energy modes and numerical oscillation in conventional NOSB PD. Effective stretch criterion is applied to capture the crack propagation. With the explicit dynamic solver, the tensile deformation of a hydrogel sheet with a hole and the crack propagation process of a hydrogel sheet with a pre-notch under pure shear are analyzed. The predicted stress-stretch responses are in good agreement with the experimental observations, which demonstrates the effectiveness and efficiency of the developed PD approach for predicting large deformation and crack propagation of hydrogel.