Finite Deformation Research Articles

Bulging of dielectric elastomer tubes considering residual stress and viscoelasticity

This paper investigates the impacts of residual stress and viscoelasticity on the bifurcation and post-bifurcation behaviors of dielectric elastomer tube actuator (DETA) with finite thickness. A theoretical model with residual stress is developed to analyze the electromechanical (EM) behavior of a DETA under a combined effect of voltage, internal pressure, and axial force loadings. A mathematical derivation of the bifurcation condition for the DETA under EM coupling loadings is presented, and a coexistence phase transition condition for steady bugle propagation is established. The effects of voltage, axial force, and residual stress on the bifurcation and coexistence phase transition conditions are studied. To validate the theoretical predictions, finite element (FE) simulations are performed on a closed-ended DETA subjected to the EM loadings. The results reveal a competitive relationship between the localized bugling and electric breakdown (EB). The large residual stress can inhibit the localized bugling and enhance the stability of the tube. Additionally, we explore the bifurcation behavior of the viscoelastic DETA, revealing that the viscoelastic effect significantly influences the critical pressure of bifurcation and the loading/unloading paths. It is observed that snap-back instability can occur during the unloading process under high loading rates or voltages. This work provides valuable insights into the finite deformation and bifurcation behaviors of the DETA under complex EM coupling loadings.

Vertical drain aided consolidation and solute transport

Land and groundwater pollution is increasingly threatening public health and ecological safety. Vertical drain is recognised as an effective solution to clean up contaminated lands. Clean-ups often involve complicated hydro-chemical transport processes and are difficult to manage. This study presents a consolidation–solute transport model to assist with clean-up management. The model can predict coupled consolidation and chemical transport in diverse ground conditions, e.g., fully or partially saturated, less to highly deformable, or permeable to impermeable layers. To factor in the varied ground conditions, the model integrates the unsaturated flow characteristics, finite deformation theory and finite difference method into a set of governing equations and numerical solutions. The model was experimentally verified and then applied to examine effects of soil saturation conditions, solute transport conditions, and consolidation efforts on solute transport. The results show that the dispersion process contributes to the chemical clean-up, whereas the contribution becomes less noticeable in unsaturated conditions. The solute sorption process counteracts the solute transport and delays the clean-up. The consolidation accelerates the transport of reactive chemicals but shows limited effects on transport of non-reactive chemicals.

An interface-enhanced discrete element model (I-DEM) of bio-inspired flexible protective structures

Natural organisms have evolved protective structures that help them survive environmental threats without sacrificing flexibility. While the discrete element method (DEM) has been used to model bio-inspired flexible protective structures, existing DEM models struggle with modeling interactions between elements of complex geometries and finite deformation, making them unsuitable for describing interfacial interlocking and associated failure mechanisms observed in experiments. Here, we propose an interface-enhanced DEM (I-DEM) model that brings about a number of advantages over the existing methods. First, contact-induced geometric nonlinearity is incorporated via a nonlinear interaction function to model interfacial interlocking. Second, finite deformation of interfacial material is taken into account in modeling interfacial failure. Furthermore, contact detection and processing algorithms are utilized to model collision and post-contact behaviors. The utility of I-DEM is demonstrated in modeling bio-inspired flexible protective structures across three distinct interfaces, evidencing its broad applicability to varied interface geometries. FEM simulations of scaled armor structures with segmented helmet and space shield are performed to demonstrate an increase in computational efficiency of the proposed I-DEM model by about four orders of magnitude for static analysis and by two orders of magnitude for dynamic analysis, with numerical discrepancies within about 10%, compared to FEM.

Fracture resistance of polyacrylamide-alginate hydrogels

Polyacrylamide-alginate hydrogels are biphasic materials with double-polymeric structure and considerable percentage of water inside. They exhibit complex mechanical behaviour in which finite deformations, non-linearity and time dependence are mixed. Fracture behaviour is less known, and this work analyses the fracture resistance obtained via methodologies of non-linear elastic materials such as that developed by Rivlin and Thomas and that attained with Non-Linear Fracture Mechanics procedures based on the use of J-integral. Special attention is paid to the fracture parameters on both crack growth initiation and crack propagation stages. The validity of the methodologies was evaluated, and conclusions were drawn about the effect of the alginate content on the fracture resistance of polyacrylamide.

Finite Bending of Fiber-Reinforced Visco-Hyperelastic Material: Analytical Approach and FEM.

This paper presents a new anisotropic visco-hyperelastic constitutive model for finite bending of an incompressible rectangular elastomeric material. The proposed approach is based on the Mooney-Rivlin anisotropic strain energy function and non-linear visco-hyperelastic method. In this study, we aim to examine the mechanical response of a reinforced viscoelastic rectangular bar with a group of fibers under bending. Anisotropic materials are typically composed of one (or more) family of reinforcing fibers embedded within a soft matrix material. This operation may lead to an enhancement in the strength and stiffness of soft materials. In addition, a finite element simulation is carried out to validate the accuracy of the analytical solution. In this research, the well-known stress relaxation test, as well as the multi-step relaxation test, are examined both analytically and numerically. The results obtained from the analytical solution are found to be in good agreement with those from the finite element method. Therefore, it can be deduced that the proposed model is competent in describing the mechanical behavior of fiber-reinforced materials when subjected to finite bending deformations.

A Negative Thermal Expansion Metamaterial Inspired by the Sicilian and Manx Symbols

A negative thermal expansion (NTE) metamaterial is established herein by inspiration from the Sicilian and Manx symbols to form rigid units of the metamaterial. By attaching connecting material of positive thermal expansion to the rigid units, the resulting metamaterial exhibits NTE. Analytical forms for the effective coefficients of thermal expansions (CTE) were established using infinitesimal and finite deformation assumptions for small and large temperature changes, respectively. Results indicate that the negativity of this metamaterial’s thermal expansion is enhanced with the thickness of the connecting material but decreases with the dimensions of the rigid units. The transverse isotropy for this metamaterial’s CTE is useful if thermal expansion compensation is required in two orthogonal directions but zero thermal expansion is required in the remaining orthogonal direction.

Analysis of Stress and Deformation Characteristics of Different Dam Heights in Deep Overburden

Relying on an actual project, this paper carries out the application analysis and prediction research of the dam height 150m-200m concrete-faced rockfill dam on deep overburden. Through the finite element calculation results, the stress and deformation of the dam and the structural design of the seepage control system are analyzed. Several preliminary standards have been adopted to control its safety and provide a reasonable basis and technical support for the construction of a 150m-200m high dam on deep overburden.

Reconstruction of Cam-clay model based on multiplicative decomposition of the deformation gradient

This study formulated the Cam-clay model, an elastoplastic constitutive model for fully remolded and normally consolidated clay, using the multiplicative decomposition of the deformation gradient and a hyperelastic body to correspond to the finite deformation theory. Finite deformation elastoplastic theory in this framework has been developed for metallic materials that do not yield plastic volume change. If this theory is directly applied to a model that yields plastic volume change, the Cauchy stress cannot be determined only from the current elastic deformation. Therefore, the existing multiplicative decomposition Cam-clay models cannot accurately reproduce the experimental facts underlying the core of critical-state soil mechanics. Through thermodynamic considerations that consider the volume changes occurring in the intermediate configuration, this study determined a common stress suitable for describing the elastic and plastic components, in addition to forms of hyperelastic body and plastic flow rule. Consequently, the proposed model can draw the state boundary surface in the Cauchy stress-specific volume space, which previous models could not achieve. In addition, an implicit stress-update algorithm for the proposed model was constructed, and a tangent modulus consistent with the algorithm was derived. The proposed model demonstrated the same numerical calculation convergence as that of existing models.

Rate dependent compressive failure and delamination growth in multidirectional composite laminates

A novel intralaminar model has, for the first time, been applied and validated for the rate-dependent failure of multidirectional carbon/epoxy laminates. Quasi-static compressive failure is evaluated by the growth of intralaminar rate-dependent damage combined with the interaction of cohesive zones for interlaminar delamination. A special feature of the intralaminar model is the homogenised ply response, allowing simultaneous damage-degradation of the polymer matrix combined with the fibres. To model the observed quasi-brittle failure response of the plies under finite deformation, we have used a viscoelastic-viscoplastic matrix combined with damage and isotropic hardening behaviour. Elastic transverse isotropy is used to model the fibre reinforcement of the plies. Standard cohesive surfaces are used to model the initiation and propagation of delamination. Numerical simulations using ABAQUS/Explicit are performed to predict the growth and delamination of intralaminar damage under compression in different laminates with 56 plies of IM7/8552 carbon/epoxy. Predictions of stress versus strain and damage growth are shown to agree well with experimental results for a range of strain rates and stacking sequences.

Approaches to the Solution of the Lamé–Gadolin Problem for a Composite Hollow Ball Made of Nonlinear Elastic and Elasto-Plastic Materials Under Superimposed Finite Deformations

Approaches to the Solution of the Lamé–Gadolin Problem for a Composite Hollow Ball Made of Nonlinear Elastic and Elasto-Plastic Materials Under Superimposed Finite Deformations

The kinematic significance of subglacial bedforms and their use in palaeo-glaciological reconstructions

Subglacial bedforms are relevant geomorphic markers for palaeo-glaciological reconstructions. Due to the complexity of thermomechanical interactions between ice, till and water on subglacial beds, their formation processes and significance in palaeo-glaciology are still controversial. Based on the measurement and comparison of morphometric characteristics (length, width, amplitude, area and volume) of ∼250 000 bedforms formed below terrestrial ice sheets during the last glacial period, we propose a unified kinematic model, consistent with the ‘bed deformation model’, whereby bedform shapes and orientations depend on their degree of evolution and reflect the magnitude and orientation of finite bed deformation in response to motion of the overlying ice. Two application examples from the Low Land Ice Dome (British-Irish Ice Sheet) and Keewatin Ice Dome (Laurentide Ice Sheet) demonstrate how this model enables the derivation of palaeo-glaciological maps of finite bed deformation, which can then be used to better constrain ice flow directions, their relative velocities, and the location of subglacial drainage routes.

Coupling diffusion and finite deformation in phase transformation materials

We present a multiscale theoretical framework to investigate the interplay between diffusion and finite lattice deformation in phase transformation materials. In this framework, we use the Cauchy–Born Rule and the Principle of Virtual Power to derive a thermodynamically consistent theory coupling the diffusion of a guest species (Cahn–Hilliard type) with the finite deformation of host lattices (nonlinear gradient elasticity). We adapt this theory to intercalation materials – specifically Li1−2Mn2O4 – to investigate the delicate interplay between Li-diffusion and the cubic-to-tetragonal deformation of lattices. Our computations reveal fundamental insights into the microstructural evolution pathways under dynamic discharge conditions, and provide quantitative insights into the nucleation and growth of twinned microstructures during intercalation. Additionally, our results identify regions of stress concentrations (e.g., at phase boundaries, particle surfaces) that arise from lattice misfit and accumulate in the electrode with repeated cycling. These findings suggest a potential mechanism for structural decay in Li2Mn2O4. More generally, we establish a theoretical framework that can be used to investigate microstructural evolution pathways, across multiple length scales, in first-order phase transformation materials.

A multiscale electrochemo-mechanical model of porous electrode in lithium-ion batteries: The coupling of reaction and finite deformation

In this study, we present a novel multiscale electrochemo-mechanical model for porous electrodes in lithium-ion batteries (LIBs). Building upon the theory of finite deformation and the pseudo-two-dimensional framework introduced by Doyle et al. (Journal of the Electrochemical Society, 140, 6(1993)), our model incorporates the interaction between particle deformation and multiscale electrochemical processes, which has been lacking in previous research. The model is validated by the rate performance tests on SiO-based electrodes. By utilizing the model, we analyze the coupling effects among reaction distribution, porosity variation, and local geometrical distortion of the electrode at high current rates. We also investigate the relative importance of different electrochemo-mechanical coupling paths for materials with large volume expansion ratios. Comparing the comprehensive model with simplified versions, we find that diffusion stress is a priority due to its significant impact on ionic diffusion within particles. Porosity variation becomes equally significant at high current rates, as ionic transport in the electrolyte becomes the rate-limiting step. This work contributes to enhance understanding of the interplay between electrochemical and mechanical phenomena in LIB electrodes, especially for silicon-based materials.

Tunable topological phase transition in soft Rayleigh beam system with imperfect interfaces

Acoustic metamaterials, especially the topological insulators, have garnered substantial research attention due to their unique wave properties. Recent research emphasizes the crucial role of imperfect interfaces in accurately simulating and understanding wave propagation within these metamaterials. This paper studies the mechanical properties of soft imperfect interfaces and derives the effects of finite deformations on their stiffness. We present a comprehensive model of a soft Rayleigh beam system that incorporates these interfaces, allowing for the observation of the topological phase transition by altering the distance between them. Our investigation into the impacts of finite deformations and interface stiffness adjustment reveals that longitudinal waves' phase transition points are mainly influenced by interface stiffness. In contrast, transverse waves are predominantly affected by finite deformations. The decisive parameters driving these phenomena are also identified theoretically. The transmission studies of supercells further confirm the presence of topologically protected interface modes and their extensive tunability. Overall, this study offers a novel methodology and framework for managing topological phase transition in composite and soft topological insulator systems.

Modeling failure and instability of a single-jointed rock column based on finite deformation theory

The mechanical behaviour of rock columns is closely tied to factors such as joint development and height-to-width (H/W) ratio. Based on a recently developed finite deformation analysis scheme that can consider both material failure and structural instability of rock columns, uniaxial compression numerical tests of different H/W ratio rock columns containing a single-filled joint were carried out. It analyzes the effects of the strength of joint-filled material (joint strength) and H/W ratio on strength characteristics and failure modes of rock columns. The numerical results indicate that the joint strength controls the joint failure degree, macro-strength, stress distribution, and failure zone range of the rock column. Under different H/W ratios, the macro-strength of the rock column increases in an S-shaped curve with the increase in joint strength. Lower joint strength will accelerate joint failure, resulting in the failure mode of the rock column being joint failure-induced structural instability. As the joint strength and H/W ratio increase, the failure mode of the rock column evolves into the mode of cooperative material-structure-induced collapse and finally develops into structural instability-induced material failure. The research results have a particular reference significance for selecting grout materials for columnar jointed rock mass engineering.

Structural topology optimization of three-dimensional multi-material composite structures with finite deformation

In this work, an explicit three-dimensional (3D) topology optimization approach is presented for multi-material composite structures accounting the finite deformation effect. The proposed method employs different sets of 3D Moving Morphable Voids (MMVs) to identify each phase material, resulting in explicit geometric descriptions of the optimized composite structures and a reduction in the number of design variables. The decoupling between the topology description and finite element analysis of composite structures enables the removal of redundant degrees of freedom, thereby mitigating the convergence issue of finite deformation analysis caused by low-density elements and leading to significant computational savings. Numerical experiments of composite structures with two- and three-phase materials are optimized to validate the accuracy and efficiency of the proposed method. The results demonstrate that, under finite deformation, the distribution of each phase material in optimized 3D composite structures is significantly affected by the amplitude of external loads, and the optimized layout could be quite different from its counterpart under small deformation assumption.

Asymptotically correct 3D displacement of the Mooney–Rivlin model using VAM

The current work focuses on the nonlinear analytical analysis (dimensional reduction and recovery relations) of a hyperelastic plate governed by the compressible Mooney–Rivlin model using the Variational Asymptotic Method (VAM). The geometric nonlinearity is accommodated through finite deformations, and generalized 3D warping functions, while material nonlinearity through the hyperelastic material model. VAM mathematically splits the 3D nonlinear elastic problem into the 1D through the thickness analysis and 2D nonlinear plate analysis, using the inherent small parameters. These are the geometric small parameter (ratio of thickness to the characteristic dimension), and the physical small parameter (moderate strains). This work results include the derivation of closed-form analytical expressions of 3D warping functions, 2D nonlinear constitutive relation, and recovery relation to express the 3D displacement field for a plate. The 2D nonlinear constitutive relation is given as an input to the in-house developed 2D nonlinear finite element analysis of the reference surface to determine the 2D displacements and 2D strains. In order to validate the current theory, standard test cases are solved and compared with 3D nonlinear Finite Element Analysis (FEA).

Micromechanics of kink-band formation in bimetallic layered composites

Bimetallic layered composites with ultrathin layers possess high strength and hardness, and excellent shock resistance and radiation damage tolerance. However, they are prone to deformation localization and readily form kink-bands when subjected to layer parallel compression. Following this, we carried out extensive plane strain finite element finite deformation analyses to understand and rationalize the experimentally observed kink-band formation in these composites. In the calculations, both constituent materials were assumed to follow a rate-independent isotropic elastic-plastic constitutive relation with an ad-hoc thickness dependent yield strength. Our results demonstrate that in these composites, layer refinement, together with the strength differential between the layers of the constituent materials, is sufficient to trigger kink-banding. Importantly, this phenomenon occurs even in the absence of elastically stiff layers, geometrical imperfections (such as waviness of the layers), and extreme plastic anisotropy within the layers. Additionally, we performed parametric studies to investigate the individual effects of layer thickness, strength differential between the two constituent materials, and strain-hardenability of the materials on kink-band formation. The outcomes of our parametric studies reveal that the strain-hardenability of the constituent materials stabilizes the formation of kink-bands. Furthermore, it leads to a transition from the abrupt formation of through-width kink-bands to the onset and propagation of stable inclined wedge-shaped kink-bands, similar to the experimental observations.

Design and Characterization of Deformable Superstructures Based on Amine-Acrylate Liquid Crystal Elastomers.

Deformable superstructures are man-made materials with large deformation properties that surpass those of natural materials. However, traditional deformable superstructures generally use conventional materials as substrates, limiting their applications in multi-mode reconfigurable robots and space-expandable morphing structures. In this work, amine-acrylate-based liquid crystal elastomers (LCEs) are used as deformable superstructures substrate to provide high driving stress and strain. By changing the molar ratio of amine to acrylate, the thermal and mechanical properties of the LCEs are modified. The LCE with a ratio of 0.9 exhibited improved polymerization degree, elongation at break, and toughness. Besides an anisotropic finite deformation model based on hyperelastic theory is developed for the LCEs to capture the configuration variation under temperature activation. Built upon these findings, an LCE-based paper-cutting structure with negative Poisson's ratio and a 2D lattice superstructure model are combined, processed, and molded by laser cutting. The developed superstructure is pre-programmed to the configuration required for service conditions, and the deformation processes are analyzed using both experimental and finite element methods. This study is expected to advance the application of deformable superstructures and LCEs in the fields of defense and military, aerospace, and bionic robotics.

Experimental Study on Vertical Bearing and Deformation Characteristics of Qiantang River Ancient Seawall

Situated on the northern bank of the Qiantang River estuary, the ancient seawall serves not only as a national cultural relic but also as an active agent in flood and tide prevention. This seawall features a trapezoidal cross-section and is constructed with layered stone blocks and a sticky rice mortar. To investigate the load-bearing and deformation attributes of this ancient structure, a scaled-down specimen with a ratio of 1:4 was created. Monotonic and cyclic vertical loadings were then applied to the wall’s top surface. During these loading procedures, measurements of the loading force, seawall displacement, and front and side deformation fields were taken. Experimental findings reveal that the seawall tends to lean towards the soil-retaining side under vertical loading. After ten loading cycles, the vertical rigidity of the wall was reduced by 10%. Upon application of a uniformly distributed vertical load of 1.6 MPa at the top of the wall, significant cracks began to materialize in the blocks at the base of the seawall. When the loading at the top increased to 2 MPa, a vertical crack that cut through the mortar layer at the wall’s center was observed. By comparing it to a three-dimensional finite element model, the load-bearing and deformation characteristics of the ancient seawall observed in the experiments were confirmed, which could contribute to the scientifically informed conservation and protection of the seawall.