Effects of large deformation and material nonlinearity on spherical indentation of hyperelastic soft materials

Up to now, the indentation of hyperelastic soft materials has not been completely understood. In this paper, the spherical indentation on hyperelastic soft solids was systematically investigated through theoretical analysis and finite element method (FEM). The validation and application of the Hertzian load-displacement relation for indentation of hyperelastic soft materials were clarified, the effects of large deformation and material nonlinearity on spherical indentation of hyperelastic soft materials were analyzed and discussed. It was found that the complicated indentation behaviors of hyperelastic soft solids mainly depended on the coupling interactions of large deformation and material nonlinearity. Besides, we proposed two new nonlinear elastic contact models to separate the effects of large deformation and material nonlinearity on spherical indentation responses of hyperelastic soft solids. Our efforts might help to enhance the understanding of hyperelastic indentation problems and provided necessary instructions for the mechanical characterization of hyperelastic soft materials.     

Experimental analysis of crack tip fields in rubber materials under large deformation

A three-nested-deformation model is proposed to describe crack-tip fields in rubber-like materials with large deformation.The model is inspired by the distribution of the measured in-plane and out-of-plane deformation.The inplane displacement of crack-tip fields under both Mode I and mixed-mode(Mode I-II) fracture conditions is measured by using the digital Moire’ method.The deformation characteristics and experimental sector division mode are investigated by comparing the measured displacement fields under different fracture modes.The out-of-plane displacement field near the crack tip is measured using the three-dimensional digital speckle correlation method.     

A theory of coupled diffusion and large deformation in polymeric gels

A large quantity of small molecules may migrate into a network of long polymers, causing the network to swell, forming an aggregate known as a polymeric gel. This paper formulates a theory of the coupled mass transport and large deformation. The free energy of the gel results from two molecular processes: stretching the network and mixing the network with the small molecules. Both the small molecules and the long polymers are taken to be incompressible, a constraint that we enforce by using a Lagrange multiplier, which coincides with the osmosis pressure or the swelling stress. The gel can undergo large deformation of two modes. The first mode results from the fast process of local rearrangement of molecules, allowing the gel to change shape but not volume. The second mode results from the slow process of long-range migration of the small molecules, allowing the gel to change both shape and volume. We assume that the local rearrangement is instantaneous, and model the long-range migration by assuming that the small molecules diffuse inside the gel. The theory is illustrated with a layer of a gel constrained in its plane and subject to a weight in the normal direction. We also predict the scaling behavior of a gel under a conical indenter.     

Large deformation and electrochemistry of polyelectrolyte gels

Immersed in an ionic solution, a network of polyelectrolytes imbibes the solution and swells, resulting in a polyelectrolyte gel. The swelling is reversible, and the amount of swelling is regulated by ionic concentrations, mechanical forces, and electric potentials. This paper develops a field theory to couple large deformation and electrochemistry. A specific material model is described, including the effects of stretching the network, mixing the polymers with the solvent and ions, and polarizing the gel. We show that the notion of osmotic pressure in a gel has no experimental significance in general, but acquires a physical interpretation within the specific material model. The theory is used to analyze several phenomena: a gel swells freely in an ionic solution, a gel swells under a constraint of a substrate, electric double layer at the interface between the gel and the external solution, and swelling of a gel of a small size.     

On the modelling of anisotropic elastic and inelastic material behaviour at large deformation

The purpose of this work is the formulation and discussion of an approach to the modelling of anisotropic elastic and inelastic material behaviour at large deformation. This is done in the framework of a thermodynamic, internal-variable-based formulation for such a behaviour. In particular, the formulation pursued here is based on a model for plastic or inelastic deformation as a transformation of local reference configuration for each material element. This represents a slight generalization of its modelling as an elastic material isomorphism pursued in earlier work, allowing one in particular to incorporate the effects of isotropic continuum damage directly into the formulation. As for the remaining deformation- and stress-like internal variables of the formulation, these are modelled in a fashion formally analogous to so-called structure tensors. On this basis, it is shown in particular that, while neither the Mandel nor back stress is generally so, the stress measure thermodynamically conjugate to the plastic “velocity gradient”, containing the difference of these two stress measures, is always symmetric with respect to the Euclidean metric, i.e., even in the case of classical or induced anisotropic elastic or inelastic material behaviour. Further, in the context of the assumption that the intermediate configuration is materially uniform, it is shown that the stress measure thermodynamically conjugate to the plastic velocity gradient is directly related to the Eshelby stress. Finally, the approach is applied to the formulation of metal plasticity with isotropic kinematic hardening.     

Orientation effect on the Boussinesq indentation of a transversely isotropic piezoelectric material

Three-dimensional finite element analysis was used to study the effect of the angle between the loading direction and the axisymmetric direction on the indentation behavior of a transversely isotropic piezoelectric half-space by a cylindrical indenter of flat end. Two cases were considered in the analysis, which included (a) the indentation by an insulating indenter, and (b) the indentation by a conducting indenter. Both the indentation load and the indentation-induced potential were found to be proportional to the indentation depth. Using the simulation results and the analytical relationship for the indentation by a rigid, insulating indenter, semi-analytical relationships were developed between the indentation load and the indentation depth and between the indentation-induced potential on the indenter and the indentation depth for the conducting indenter, respectively. The proportionality between the indentation-induced potential and the indentation depth is only a function of the angle between the loading direction and the poling direction, independent of the type of indenters, which may be used to measure the relative direction of the loading axis to the axisymmetric axis of transversely piezoelectric materials from the indentation test.     

Micromechanical modelling of the effect of plastic deformation on the mechanical behaviour in pseudoelastic shape memory alloys

Except for the recoverable strain induced by phase transformation, NiTi alloys are very ductile even in the martensite phase. The purpose of the present paper is to study the influence of permanent deformation, which results from plastic deformation of martensite, on the mechanical behaviour of pseudoelastic NiTi alloys. Based on phenomenological theory of martensitic transformation and crystal plasticity, a new three dimensional micromechanical model is proposed by coupling both the slip and twinning deformation mechanisms. The present model is implemented as User MATerial subroutine (UMAT) into ABAQUS/Standard to study the influences of plastic deformation on the stress and strain fields, and on the evolution of martensite transformation. Results show that with the increasing of plastic deformation the residual strain increases and the phase transformation stress–strain curves from the martensite to austenite become steeper and less obvious. Both characteristics, stabilisation of martensite and impedance of the reverse transformation, due to plastic deformation are captured.     

A viscoelastic constitutive model of rubber under small oscillatory load superimposed on large static deformation

Summary  A viscoelastic constitutive equation of rubber that is under small oscillatory load superimposed on large static deformation is proposed. The model is derived through linearization of Simo's nonlinear viscoelastic constitutive model and reference configuration transformation. Most importantly, in this model, static deformation correction factor is introduced to consider the influence of pre-strain on the relaxation function. Natural statically pre-deformed state is served as reference configuration. The proposed constitutive equation is extended to a generalized viscoelastic constitutive equation that includes widely used Morman's model as a special case using objective stress increment. The proposed constitutive model is tested for dynamic behavior of rubber specimens with different carbon black content. It is concluded from the test that the assumption that the effects of static deformation can be separated from time effects, which is the basis of Morman's model, is only applicable to unfilled rubber. The viscoelastic constitutive equation for filled rubber must include, therefore, the influence of the static deformation on the time effects. The suggested constitutive equation with static deformation correction factor shows good agreement with test values. Received 4 January 2001; accepted for publication 13 June 2001     

A viscoelastic constitutive model of rubber under small oscillatory load superimposed on large static deformation considering the Payne effect

The viscoelastic behavior of carbon-black-filled rubber under small oscillatory loads superimposed on large static deformation is dealt with. In this class of problems, as the strain amplitudes of the load increase, the dynamic stiffness decreases, and this phenomenon is known as the Payne effect. Besides the effects of the static deformation and the frequencies of the superimposed dynamic load, the Payne effect is considered in this study. Influence factors are introduced in this model in order to consider the influence of static predeformation, the dynamic-strain-dependent properties, and frequency-dependent properties. For simplicity, separation of the three dominant variables, frequency, prestatic deformation, and dynamic amplitude of strain, is assumed. The Kraus model is used for describing the Payne effect. Dynamic tension tests are executed to obtain the model parameters and also for the verification of the proposed model. The suggested constitutive equation shows reasonable agreement with test data.     

无网格局部Petrov-Galerkin法求解板壳弹塑性大变形

无网格局部Petrov-Galerkin法构造的高阶光滑的形函数非常适合建立板壳结构场函数的逼近函数,是一种比较理想的研究板壳问题的方法。基于Mindlin板壳理论,采用更新拉格朗日原理和大变形条件下场量的无网格表达形式,实现了率型无网格局部Petrov-Galerkin方法对板壳弹塑性大变形的求解,算例分析表明了方法的有效性和较高的分析精度。     

Computer simulated analyses on deformation and fracture of non-cracked and cracked specimens

A unified damage and fracture model, the combinatory work density model, which is suitable for either non-cracked body or cracked body has been suggested^[t−7]. In the present paper, the deformation and fracture of the two kinds of tensile spceimen and TPB specimen made of 40Cr steel have been simulated by using the new model together with the large elastic-plastic deformation finite element method. The results give a good picture of the whole deformation and fracture processes of the specimens in experiments; especially, the results on the TPB specimen can be used to obtain the relationship between load and displacement at the loading pointP-Δ, and between crack extension and displacement at the loading point Δa-Δ, the resistance curveJ _R -Δa and the fracture toughnessJ _1C . All the results are in remarkable agreement with those obtained by experiments. Therefore the model suggested here can be used to simulate crack initiation and propagation in non-cracked body and fracture initiation and crack stable propagation in cracked body. The project supported by National Natural Science Foundation of China     

On a geometrically nonlinear damage model based on a multiplicative decomposition of the deformation gradient and the propagation of microcracks

We aim to derive a damage model for materials damaged by microcracks. The evolution of the cracks shall be governed by the maximum energy release rate, which was recently shown to be a direct consequence of the variational principle of a body with a crack (Arch. Appl. Mech. 69 (5) (1999) 337). From this, we get the path of the growing crack by introducing a series of thermodynamically equivalent straight cracks. The equivalence of the energy dissipated by microcrack growth and the damage dissipation leads to our damage evolution law. This evolution law will be embedded in a finite deformation framework based on a multiplicative decomposition into elastic and damage parts. As a consequence of this, we can present the anisotropic damaged elasticity tensor with the help of push and pull operations. The connection of this approach to other well known damage theories will be shown and the advantages of a finite element framework will be worked out. Numerical examples show the possibilities of the proposed model.     

The effect of indentation sequence on rock breakages: A study based on laboratory and numerical tests

Rock may response differently to external loads applied in different sequences. Thus, we conducted indentation tests to investigate the effect of the indentation sequence on rock breakages. Sequential indentations, consuming less indentation energy, usually resulted in larger and deeper grooves and then led to lower specific energies. Thus, we conclude that sequential indentations occur instead of simultaneous indentations form larger grooves with the same indentation energy. To further validate this conclusion, we performed a series of numerical tests. The numerical analysis of stress evolution shows that, for simultaneous indentations, the propagation of an internal crack from an inner rim restrained the propagation of the other internal crack from the other inner rim. However, the chipping pattern varied for sequential indentations. In the first indentation process, an internal crack, initiating from an inner rim, is usually connected with an internal crack caused by the second indentation. The deflection angles of the internal cracks for the sequential indentations were smaller because of the lower compressive stress in the horizontal direction. Then, these smaller deflection angles led to larger chips.     

The effect of brittle interfacial compounds on deformation and fracture of molybdenum-aluminum fiber composites

The effect of brittle intermetallic compounds at the fiber-matrix interface on the deformation characteristics of molybdenum-aluminum fiber composites was investigated. If the filament is ductile and notch-insensitive, then composite strength degradation is relatively minor and composite strength can be predicted by a modified mixture-rule which neglects the strength contribution of the brittle compound. For the case of notch-sensitive filaments, severe filament degradation occurs upon compound formation. The degradation was shown to result from cracks formed during deformation at the roots of compound nodules. The presence of 10 per cent compound by volume results in a 50 per cent decrease in tensile strength, but larger amounts of compound cause little additional strength reduction. At filament volume fractions of 25 and 34 per cent and compound volume fractions less than 10 per cent, composite fracture occurs by the statistical accumulation of fiber necks or fractures depending on the notch sensitivity of the fiber. At high fiber or compound volume fractions, composite failure occurs upon the first or the second filament fracture.     

Surface stress effects on the resonant properties of metal nanowires: The importance of finite deformation kinematics and the impact of the residual surface stress

We utilize the recently developed surface Cauchy-Born model, which extends the standard Cauchy-Born theory to account for surface stresses due to undercoordinated surface atoms, to study the coupled influence of boundary conditions and surface stresses on the resonant properties of gold nanowires with surfaces. There are two major purposes to the present work. First, we quantify, for the first time, variations in the nanowire resonant frequencies due to surface stresses as compared to the corresponding bulk material which does not observe surface effects within a finite deformation framework depending on whether fixed/free or fixed/fixed boundary conditions are utilized. We find that while the resonant frequencies of fixed/fixed nanowires are elevated as compared to the corresponding bulk material, the resonant frequencies of fixed/free nanowires are reduced as a result of compressive strain caused by the surface stresses. Furthermore, we find that for a diverse range of nanowire geometries, the variation in resonant frequencies for both boundary conditions due to surface stresses is a geometric effect that is characterized by the nanowire aspect ratio. The present results are found to agree well with existing experimental data for both types of boundary conditions.The second major goal of this work is to quantify, for the first time, how both the residual (strain-independent) and surface elastic (strain-dependent) parts of the surface stress impact the resonant frequencies of metal nanowires within the framework of nonlinear, finite deformation kinematics. We find that if finite deformation kinematics are considered, the strain-independent surface stress substantially alters the resonant frequencies of the nanowires; however, we also find that the strain-dependent surface stress has a significant effect, one that can be comparable to or even larger than the effect of the strain-independent surface stress depending on the boundary condition, in shifting the resonant frequencies of the nanowires as compared to the bulk material.     

The effect of strain rate and heat developed during deformation on the stress-strain curve of plastics

Polymethylmethacrylate, cellulose acetate butyrate, polypropylene and nylon 6–6 have been characterized in compression at various strain rates from 10^?4 s^?1 to 10³ s^?1 at room temperature. A medium strain-rate machine and a split-Hopkinson-bar apparatus are used in conducting the experiments. The temperature rise developed during deformation is also measured by using a thermocouple. All four materials tested definitely show a viscous effect at the beginning of the deformation and a plastic flow follows thereafter. Test results also indicate that the temperature rise developed during deformation cannot be neglected in determining the dynamic response of those materials investigated in this study.     

The effect of ultrasonic treatment on mechanical behavior of titanium and steel specimens

The effect of surface ultrasonic treatment on plastic deformation and mechanical properties of polycrystalline titanium and low-carbon steel specimens under tension was studied. The deformation pattern was investigated using optical, transmission electron, scanning electron and scanning tunneling microscopy. It was shown that the material within hardened surface layers is characterized by ultrafine-grained structure. This structure results in plastic flow localization at different scale levels. Localized deformation meso-bands induce weak work hardening of the material. Plastic flow macro-localization causes a drop of the external deforming stress. The peculiar mechanisms of deformation localization within the specimen surface layer govern formation of a banded dislocation substructure in the bulk of the specimen.