Equilibrium analysis of finitely deformed elastic networks

A specialized membrane theory is used to analyze equilibrium configurations of finitely deformed elastic networks. The effects of wrinkling of the network are incorporated by using a certain relaxed strain energy function derived from minimum energy considerations. The stresses derived from this function are non-compressive at all values of the strain. In particular, a fibre strain associated with vanishing fibre stress may be viewed as resulting from fine-scale wrinkling of the fibre. In this way destabilizing compressive stresses are automatically excluded from the solution of an equilibrium boundary value problem.The properties of the relaxed strain energy are used to show that all equilibrium configurations are absolute minimizers of the total potential energy, for certain classes of boundary data. The equilibrium equations are discretized by a differencing method derived from Green's theorem, and artificial mass, damping and time are incorporated. Equilibrium configurations are then obtained in the long-time limit of a damped dynamical problem. Several examples of two- and three-dimensional deformations are presented, and comparisons with analytical solutions are made wherever possible.     

Cosserat point element (<Emphasis Type="Italic">CPE</Emphasis>) for finite deformation of orthotropic elastic materials

An eight node brick Cosserat point element (CPE) has been developed for the numerical solution of three-dimensional problems of hyperelastic nonlinear orthotropic elastic materials. In the Cosserat approach, a strain energy function for the CPE is proposed which satisfies restrictions due to a nonlinear form of the patch test. Part of the strain energy of the CPE is characterized by a three-dimensional strain energy function that depends on physically based nonlinear orthotropic invariants. Special attention has been focused on developing closed form expressions for constitutive coefficients in another part of the strain energy that characterizes the response to inhomogeneous deformations appropriate for orthotropic material response. A number of example problems are presented which demonstrate that the CPE is a robust user friendly element for finite deformations of orthotropic elastic materials, which does not exhibit unphysical locking or hourglassing for thin structures or nearly incompressible materials.     

A total strain energy density model of metal fatigue

In this paper a total cyclic strain energy density equal to the sum of plastic strain energy and tensile elastic strain energy densities is used as a damage parameter for metal fatigue. It is shown that the total cyclic strain energy density is a consistent damage parameter for low- and high-cycle fatigue in the conditions of both uniaxial and multiaxial cyclic loading. This parameter is also consistent with the concept of crack initiation and subsequent propagation. The approach described here is applicable for both ideal Masing and non-Masing material response. The predictions of the proposed criterion are compared with the experimental data for medium carbon steel St5. The comparison has shown good agreement.Published inProblemy Prochnosti, Nos. 1–2, pp. 53–64, January–February, 1995.     

Tunable Photocontrolled Motions Using Stored Strain Energy in Malleable Azobenzene Liquid Crystalline Polymer Actuators

A new strategy for enhancing the photoinduced mechanical force is demonstrated using a reprocessable azobenzene‐containing liquid crystalline network (LCN). The basic idea is to store mechanical strain energy in the polymer beforehand so that UV light can then be used to generate a mechanical force not only from the direct light to mechanical energy conversion upon the trans–cis photoisomerization of azobenzene mesogens but also from the light‐triggered release of the prestored strain energy. It is shown that the two mechanisms can add up to result in unprecedented photoindued mechanical force. Together with the malleability of the polymer stemming from the use of dynamic covalent bonds for chain crosslinking, large‐size polymer photoactuators in the form of wheels or spring‐like “motors” can be constructed, and, by adjusting the amount of prestored strain energy in the polymer, a variety of robust, light‐driven motions with tunable rolling or moving direction and speed can be achieved. The approach of prestoring a controllable amount of strain energy to obtain a strong and tunable photoinduced mechanical force in azobenzene LCN can be further explored for applications of light‐driven polymer actuators.     

Room-Temperature Synthesis of a COFs Membrane Via LBL Self-Assembly Strategy for Energy Harvesting

The covalent organic frameworks (COFs) membrane with ordered and confined one-dimensional channel has been considered as a promising material to harvest the salinity gradient energy from the seawater and river water. However, the application of the COFs in the field of energy conversion still faces the challenges in membrane preparation. Herein, energy harvesting is achieved by taking advantage of a COFs membrane where TpDB-HPAN is synthesized via layer-by-layer self-assembly strategy at room temperature. The carboxy-rich TpDB COFs can be expediently assembled onto the substrate with an environmental-friendly method. The increased open-circuit voltage (V_oc) endows TpDB-HPAN membrane with a remarkable energy harvesting performance. More importantly, the application perspective is also illuminated by the cascade system. With the advantages of green synthesis, the TpDB-HPAN membrane can be considered as a low-cost and promising candidate for energy conversion.     

A corotational interpolatory model for fabric drape simulation

Fabric drapes are typical large displacement, large rotation but small strain problems. In particle models for fabric drape simulation, the fabric deformation is characterized by the displacements of the particles distributed over the fabric. In this paper, a new particle model based on the corotational concept is formulated. Under the small membrane strain assumption, the bending energy can be approximated as a quadratic function of the particle displacements that are finite. In other words, the tangential bending stiffness matrix is a constant and only the tangential membrane stiffness matrix needs to be updated after each iteration or step. On the other hand, the requirement on the particle alignment is relaxed by interpolating the particle displacement in a patch of nine particles. To account for the membrane energy, a simple and efficient method similar to the three‐node membrane triangular element employing the Green strain measure is adopted. With the present model, the predicted drapes appear to be natural and match our daily perception. In particular, circular clothes and circular pedestal that can only be treated laboriously by most particle models can be conveniently considered. Copyright © 2008 John Wiley & Sons, Ltd.     

Energy-based prediction of low-cycle fatigue life of BS 460B and BS B500B steel bars

This paper develops energy-based models for predicting low-cycle fatigue life of BS 460B and BS B500B steel reinforcing bars. The models are based on energy dissipated in the first cycle, in average cycles and in total energy dissipated to failure for strain ratios R = −1, −0.5, and 0. Upon prediction of the low-cycle fatigue life, the total energy dissipated during the entire fatigue life of steel reinforcing bars can also be predicted based on the predicted fatigue life. The results indicated that the hysteresis plastic strain energy dissipated during fatigue loading is an important and accurate parameter for predicting the fatigue life of steel reinforcing bars and that the predictions based on energy dissipated on average cycles are more accurate than those based on energy dissipated in the first cycle. It is concluded that the strain ratio R has a clear effect on the energy dissipation for both materials where BS B500B dissipated more energy than BS 460B for R = −0.5 and 0 and about the same energy for R = −1 for certain range of fatigue life. Other conclusions and observations were also drawn based on the experimental results.     

Improved strain interpolation for curved C° elements

The strain energy of straight beam members derived from the isoparametric shape functions is known to be invariant with respect to the number of integration points as long as they exceed a minimum number. However, this invariant property is generally lost for curved members. For example, the two-point integrated, membrane strain energy of curved beams by employing the quadratic shape functions is different from the three-point integrated one. This paper presents an invariant strain interpolation scheme for quadratic curved beam elements, which can lead to improved membrane representations in curved shell elements, thus resolving the perplexing membrane-bending coupling difficulties in thin shell analysis.     

An energy‐based damage parameter for the life prediction of AISI 304 stainless steel subjected to mean strain

Abstract

This study extends the plastic strain energy approach to predict the fatigue life of AISI 304 stainless steel. A modified energy parameter based on the stable plastic strain energy density under tension conditions is proposed to account for the mean strain and stress effects in a low cycle fatigue regime. The fatigue life curve based on the proposed energy parameter can be obtained directly by modifying the parameters in the fatigue life curve based on the stable plastic strain energy pertaining to fully reversed cyclic loading. Hence, the proposed damage parameter provides a convenient means of evaluating fatigue life on the mean strain or stress effect. The modified energy parameter can also be used to explain the combined effect of alternating and mean strain/stress on the fatigue life. In this study, the mean strain effects on the fatigue life of AISI 304 stainless steel are examined by performing fatigue tests at different mean strain levels. The experimental results indicate that the combination of an alternating strain and a mean strain strongly influences the fatigue life. Meanwhile, it is found that the change in fatigue life is sensitive to changes in the proposed damage parameter under the condition of a constant strain amplitude at various mean strain levels. A good agreement is observed between the experimental fatigue life and the fatigue life predicted by the proposed damage parameter. The damage parameter proposed by Smith et al. (1970) is also employed to quantify the mean strain effect. The results indicate that this parameter also provides a reasonable estimate of the fatigue life of AISI 304 stainless steel. However, a simple statistical analysis confirms that the proposed damage parameter provides a better prediction of the fatigue life of AISI 304 stainless steel than the SWT parameter.     

Wrinkle/slack model and finite element dynamics of membrane

This paper reviews conventional wrinkle models for anisotropic membrane and shows the relation between the models. A new wrinkle model is proposed which assumes virtual shear as well as virtual elongation of the membrane to estimate the real strain in the wrinkled region. This model coincides with the other models if the virtual shear and elongation is determined so that the strain energy is minimized. Another wrinkle/slack model is proposed for the dynamic analysis of thin isotropic membrane undergoing large overall motion with wrinkle and slack. It can take into account the residual compressive stress in the wrinkled and slack regions, i.e. the stiffness in the post‐buckling state. It is shown that the proposed model is a generalization of the conventional ones. Finite element formulation of the proposed model is described. Furthermore, the energy momentum conservation framework is constructed for the proposed membrane element, which achieves the unconditionally stable time integration. The total of the proposed method enables us to compute the overall motion of thin isotropic membrane such as the deployment of folded membrane, which has been one of the most difficult problems in aerospace engineering. Copyright © 2005 John Wiley & Sons, Ltd.     

Study of force,strain, and energy criteria for the low-cycle strength of steel 5KhNM in the presence of stress concentrators

The stability of force, strain, and energy criteria for strength in zones of a structural concentrator in relation to the number of loadings, nominal stress intensity, and lowcycle strain curve kinetics is analyzed. It is shown that as a low-cycle failure criterion for a structural element it is desirable to use the local specific energy of elastoplastic deformation as the most stable physical parameter. Translated from Problemy Prochnosti, No. 5, pp. 5–15, May, 1996.     

An h-p- multigrid method for finite element analysis

The finite element method generates solutions to partial differential equations by minimizing a strain energy based functional. Strain energy based techniques for adaptive mesh refinements are not always effective, however. The adaptive refinement technique proposed in this paper uses strain energy but also incorporates advantages from the h- and p- finite element methods, the multigrid method and a Delaunay based mesh generation method. The refinement technique converged rapidly and was numerically efficient when applied to determining stress concentrations around the circular hole of a thick plate under tension.     

Stretching and bending deformations due to normal and shear tractions of doubly curved shells using third-order shear and normal deformable theory

ABSTRACT

We analyze static infinitesimal deformations of doubly curved shells using a third-order shear and normal deformable theory (TSNDT) and delineate effects of the curvilinear length/thickness ratio, a/h, radius of curvature/curvilinear length, R/a, and the ratio of the two principal radii on through-the-thickness stresses, strain energies of the in-plane and the transverse shear and normal deformations, and strain energies of stretching and bending deformations for loads that include uniform normal tractions on a major surface and equal and opposite tangential tractions on the two major surfaces. In the TSNDT the three displacement components at a point are represented as complete polynomials of degree three in the thickness coordinate. Advantages of the TSNDT include not needing a shear correction factor, allowing stresses for monolithic shells to be computed from the constitutive relation and the shell theory displacements, and considering general tractions on bounding surfaces. For laminated shells we use an equivalent single layer TSNDT and find the in-plane stresses from the constitutive relations and the transverse stresses with a one-step stress recovery scheme. The in-house developed finite element software is first verified by comparing displacements and stresses in the shell computed from it with those from either analytical or numerical solutions of the corresponding 3D problems. The strain energy of a spherical shell is found to approach that of a plate when R/a exceeds 10. For a thick clamped shell of aspect ratio 5 subjected to uniform normal traction on the outer surface, the in-plane and the transverse deformations contribute equally to the total strain energy for R/a greater than 5. However, for a cantilever shell of aspect ratio 5 subjected to equal and opposite uniform tangential tractions on the two major surfaces, the strain energy of in-plane deformations equals 95–98% of the total strain energy. Numerical results presented herein for several problems provide insights into different deformation modes, help designers decide when to consider effects of transverse deformations, and use the TSNDT for optimizing doubly curved shells.     

A Global/Local approach to lengthwise cracked beams: dynamic analysis

A simple model is developed for the calculation of dynamic stress intensity factors for lengthwise cracked beams subjected to impact or transient loading. The model is based on a Global/Local approach that separates the Global structural dynamics from the Local crack tip zone dominated by singular stresses. The Global model is that of connected waveguides while the Local model is based on a novel application of the J-integral that converts dynamic structural resultants directly into strain energy release rate. The accuracy of this approach is assessed by comparing it to a fully two-dimensional finite element analysis in which the modified crack closure integral is used to calculate the dynamic strain energy release rate. Both mode I and mode II examples are given, and situations with multiple wave reflections are emphasized.     

Energy absorption mechanisms during dynamic fracturing of fibre-reinforced composites

Dynamic photoelastic experiments were conducted to study crack propagation in fibrereinforced materials and, in particular, to determine the energy losses occurring during the crack growth and arrest process. This study utilized modified compact tension specimens which were fabricated from polyester matrix and different reinforcing fibres. The effect of the fibre-matrix interface on energy absorbed was also studied. The energy absorbed was partitioned into two parts: that absorbed in the fracture process zone associated with the crack tip, and the energy lost outside this zone. Results show that fibre reinforcement reduces the energy absorbed in the fracture process zone by about 10% for well-bonded and 15% for partly debonded fibres. For the same initial strain energy, this reduction in fracture energy manifests itself in reduced K _ID and lower crack-jump distance as compared to monolithic specimens. Reinforced specimens are found to retain a higher strain energy after crack arrest. The energy absorbed outside the fracture process zone for monolithic and well-bonded fibres is about 45% of the initial strain energy, while for partly debonded fibres it is about 55%.     

Resolving membrane and shear locking phenomena in curved shear-deformable axisymmetric shell elements

A simple two-node axisymmetric shell element with shallowly curved meridian assumptions and the inclusion of shear deformation and rotary inertia is presented. The principal developments include: (a) consistent resolution of the membrane and shear related excessive stiffening (locking) via anisoparametric interpolations of the displacement variables; (b) further upgrading of strain energy by means of a shear relaxation (correction) parameter. The resulting element possesses an improved condition of the stiffness matrix, increased efficiency in explicit time integration and enhanced accuracy in coarse discretizations. Comprehensive vibration examples are carried out to assess the element performance. The numerical results demonstrate a wide applicability range with respect to element slenderness and curvature properties.     

Singular crack-tip fields for pressure sensitive plastic solids

Plain strain mode-I singular plastic fields are examined for cracks embedded in pressure sensitive solids. Material response is described by a small strain deformation theory in conjunction with elliptic yield criterion and plastic potential. Non-associativity is accounted for and a pure power law is assumed to characterize strain hardening. The material does not admit a strain energy function hence it is not possible to deduce a-priori the J-integral motivated stress singularities. A standard separation of variables representation of near-tip eigenfunctions has been evaluated numerically, over a range of material parameters. It has been found that stress singularities may deviate from J-integral predictions, with increasing non-associativity, by up to nearly 20%. Sample illustrations are provided for singular field profiles and some aspects of pressure sensitive non- associated plasticity are discussed.     

AN EFFICIENT CURVED BEAM FINITE ELEMENT

The plane two-node curved beam finite element with six degrees of freedom is considered. Knowing the set of 18 exact shape functions their approximation is derived using the expansion of the trigonometric functions in the power series. Unlike the ones commonly used in the FEM analysis the functions suggested by the authors have the coefficients dependent on the geometrical and physical properties of the element. From the strain energy formula the stiffness matrix of the element is determined. It is very simple and can be split into components responsible for bending, shear and axial forces influences on the displacements. The proposed element is totally free of the shear and membrane locking effects. It can be referred to the shear-flexible (parameter d) and compressible (parameter e) systems. Neglecting d or e yields the finite elements in all necessary combinations, i.e. curved Euler–Bernoulli beam or curved Timoshenko beam with or without the membrane effect. Applying the elaborated element in the calculations a very good convergence to the analytical results can be obtained even with a very coarse mesh without the commonly adopted corrections as reduced or selective integration or introduction of the stabilization matrices, additional constraints, etc., for the small depth–length ratio. © 1997 John Wiley & Sons, Ltd.     

Lattice-Strain Engineering of Homogeneous NiS0.5Se0.5 Core–Shell Nanostructure as a Highly Efficient and Robust Electrocatalyst for Overall Water Splitting

Developing highly-efficient non-noble-metal electrocatalysts for water splitting is crucial for the development of clean and reversible hydrogen energy. Introducing lattice strain is an effective strategy to develop efficient electrocatalysts. However, lattice strain is typically co-created with heterostructure, vacancy, or substrate effects, which complicate the identification of the strain-activity correlation. Herein, a series of lattice-strained homogeneous NiS_xSe_1−x nanosheets@nanorods hybrids are designed and synthesized by a facile strategy. The NiS_0.5Se_0.5 with ≈2.7% lattice strain exhibits outstanding activity for hydrogen and oxygen evolution reaction (HER/OER), affording low overpotentials of 70 and 257 mV at 10 mA cm⁻², respectively, as well as excellent long-term durability even at a large current density of 100 mA cm⁻² (300 h), significantly superior to other benchmarks and the precious metal catalysts. Experimental and theoretical calculation results reveal that the generated lattice strain decreases the metal d-orbital overlap, leading to a narrower bandwidth and a closer d-band center toward the Fermi level. Thus, NiS_0.5Se_0.5 possesses favorable H* adsorption kinetics for HER and lower energy barriers for OER. This work provides a new insight to regulate the lattice strain of advanced catalyst materials and further improve the performance of energy conversion technologies.