Strain Energy Model Research Articles

A Constitutive Model of Human Dermis Skin Incorporating Different Collagen Fiber Families

Abstract Skin tissue is a complex heterogeneous material abundant with fibers. Various models capturing its anisotropy, nonlinearity, and viscoelasticity have been developed. However, the existence of multiple fiber families and their differences have been largely ignored. Furthermore, inhomogeneous deformation over the thickness is observed in the skin under shear deformation, which the traditional skin models do not predict. In this paper, we propose that two fiber families with distinct mechanical and structural properties exist in the skin within the framework of a general structure tensor-based constitutive strain energy model. Our constitutive model considers fiber families’ distinct properties and the consequent inhomogeneous deformation in the skin, showing good agreement with in vivo measurements of human face skin.

Fatigue behavior of modified ZK60 magnesium alloy after pre-corrosion under stress-controlled loading

Three kinds of modified layers were prepared on the surface of ZK60 magnesium alloy (BM) by micro-arc oxidation (MAO), laser shock penning (LSP), and composite of LSP and MAO method. Four kinds of specimens (BM, MAO, LSP, LSP / MAO) were pre-corroded in a simulated body fluid (SBF) with pH7.4 for 12 h. Fatigue tests were performed for non-corroded and pre-corroded specimens under stress-controlled cyclic loading. The cyclic deformation behavior of the specimens at different stress ratios and different stress amplitudes involves four deformation mechanisms: dislocation slip, twinnig-detwinning transfer to dislocation slip, partial twinning-partial detwinning, complete twinning-complete detwinning. The correlation between the cyclic deformation mechanism and fatigue life is discussed using a proposed evaluation parameter, β. The fatigue life of the material decreases with the β values increasing when cyclic deformation is dominated by twinning-detwinning. The proposed total strain energy model can better predict the fatigue life of modified magnesium alloys under different loading conditions.

Fatigue behavior after pre‐corroded in a simulated body fluid for ZK60 magnesium alloy prepared by micro‐arc oxidation

AbstractA bio‐ceramic coating was prepared on the surface of ZK60 magnesium alloys by micro‐arc oxidation (MAO) method. The substrate (BM) and coated (MAO) specimens were pre‐corroded in a simulated body fluid (SBF) for 12 h. Strain‐controlled and stress‐controlled loading modes were used to conduct fatigue tests for the specimens with non‐corroded and pre‐corroded, and the cyclic deformation behavior of different specimens was studied. The fatigue life of pre‐corroded MAO specimen is higher than that of pre‐corroded BM specimen. The mechanism of cyclic deformation under different loading conditions is related to twinning and slip. For the same specimens, the higher the absolute value of ratcheting strain, the lower the fatigue life. A modified total strain energy model is proposed, and the precision of life prediction is higher than that of traditional fatigue model.

Modelling hollow thermoplastic syntactic foams under high-strain compressive loading

The mechanical response of syntactic foams comprising hollow thermoplastic microspheres (HTMs) embedded in a polyurethane matrix were experimentally examined under uniaxial compressive strain. Phenomenological strain energy models were subsequently developed to capture both the axial stress-strain and transverse strain response of the foams. HTM syntactic foams were found to exhibit increased small-strain stiffness with reduced density, revealing a highly-tuneable and extremely lightweight syntactic foam blend for applications. The foams were also found to become strongly compressible at large strains and possess a high threshold for plastic deformation, making them a robust alternative to hollow glass microsphere syntactic foams. The non-standard transverse strain relationship exhibited by HTM syntactic foams at high filling fractions was captured by Ogden-type strain energy models. The thermal characteristics of these syntactic foams were also explored with Differential Scanning Calorimetry testing which showed that HTMs have a negligible impact on the thermal characteristics of the matrix.

Uniaxial stretch-release of rubber-plastic bilayers: Strain-dependent transition to stable helices, rolls, saddles, and tubes

Polymeric plastics deform irreversibly (i.e., inelastically) whereas rubbers deform reversibly, i.e., elastically. Thus, uniaxially stretching a rubber-plastic bilayer composite beyond its yield point can create an elastic strain mismatch between the two layers. Upon release, the bilayer may then bend out-of-plane. We quantify the mechanics of such stretch-release-induced shape changes in rectangular specimens of rubber-plastic bilayers. We show a remarkable dependence of the final shape upon the stretch applied prior to release. At small stretch, all bilayers bend into arch or roll shapes with the plastic on the convex face. At large stretch, the bilayers bend into half-tubes with the plastic, now heavily-wrinkled, becoming the concave face. Thus, the sign and direction of the curvature both flip as applied stretch increases. Between these two extremes, saddle shapes appear which have characteristics of both arches as well as half-tubes. Sufficiently narrow samples show different behavior: they transition from arches to helices as stretch increases. All these shapes are mono-stable. We document numerous ways in which the mechanics of rubber-plastic bilayers differs from that of fully-elastic bilayers. Most importantly, yielding of the plastic layer during the shape change strongly affects the mechanics of the elastic–plastic bilayers, and yielding accompanied by plastic wrinkling has an especially large effect. A strain energy model illustrates how the shape change is dictated by the change in the ratio of elastic strain mismatch in the two directions due to the formation of wrinkles at the rubber-plastic interface.

Experimental and numerical studies on free vibration of CFRP laminate with cutout

Carbon fiber reinforced plastic (CFRP) laminate with cutout is a lightweight structure in mechanical equipment design. In this paper, experiments and numerical analysis are conducted to study the free vibration of the CFRP laminate with cutout. The damping loss factor (DLF) of one-layer CFRP laminate is calculated reversely for providing the reliable material properties. The effect of the cutout shape on the free vibration of the CFRP laminate with cutout is studied. Meanwhile, by taking the circle cutout for instance, the effect of the cutout size, location, and number on the free vibration of the CFRP laminate with cutout are investigated. The software ABAQUS is used to perform the numerical modal analysis of the CFRP laminate with cutout, and the natural frequencies of mode I to mode III are obtained. According to the damping strain energy model, the stress and strain components are extracted for calculating the DLF by program written in MATLAB. Using B&K vibration testing system, experiments are carried out for the validation of the numerical modal analysis results by applying “single-input single-output” (SISO) approach. In addition, the stiffness of the CFRP laminate with cutout is studied by numerical analysis and experiments. How the affecting factors affect the free vibration of the CFRP laminate with cutout is discussed, and the relationship between the DLF and stiffness is explored. This study provides a reference for the application of the CFRP laminate with cutout.

Evaluating the response of a modified Gent-Thomas strain energy function having limiting chain extensibility condition in torsion and azimuthal shear

The purpose of this paper is to investigate the torsion and azimuthal shear of an incompressible hyperelastic cylinder having a modified Gent-Thomas strain energy with limiting chain extensibility condition. First, the torsional response of the modified Gent-Thomas model is obtained analytically and compared with those of Gent-Gent, Gent-Thomas, and Carroll strain energy models where the former model incorporates the limiting chain extensibility condition while the latter two are phenomenological models. The results show the modified Gent-Thomas model to be in better agreement with the experimental data of Rivlin and Saunders on torsion than the other three models. To further evaluate the response of the modified Gent-Thomas model, azimuthal shear deformation of an incompressible hyperelastic cylinder with the modified Gent-Thomas, Gent-Thomas, Gent-Gent, and Carroll strain energies is considered, where the angular displacement in azimuthal shear is determined analytically for the first three models and numerically for the fourth model. It is shown that the strain hardening effect, predicted either by the limiting chain extensibility condition for the modified Gent-Thomas and Gent-Gent models or phenomenologically by the Carroll model, is quite significant in the azimuthal shear response of the incompressible cylinder.

A study of ultra-low cycle fatigue failure based on a fracture strain energy model

Ductile failure under ultra-low cycle fatigue (ULCF) loading is often the limit service state of a nuclear structure. In the paper, ULCF tests for a C-Mn-Si steel are carried out. It is observed that the fracture displacement decreases as the number of fatigue cycles increases. An energy-based model, which considers the effects of both stress triaxiality and cyclic loading on the critical fracture strain energy, is proposed. Coupled with the new model, finite element analyses of the round notched specimens can predict the equivalent plastic strain and the number of fatigue cycles to fracture within a scatter band of 1.5.

Dislocation creep modelling of Sanicro 25 based on microstructural evolution and particle hardening mechanism

A dislocation model for predicting creep deformation and long-term life of Sanicro 25 austenitic steel was proposed on the basis of microstructural evolution and particle hardening mechanism. This approach was integrated by four sub-models of (i) time- and strain-induced detachment stress model, (ii) Orowan strengthening model of two precipitates, (iii) void nucleation and growth model, and (iv) temperature-induced strain energy model. The validation of the proposed model was verified by the experimental data of different testing conditions of Sanicro 25. In addition, the microstructural fracture mechanism and the variation of detachment stress were discussed. The framework of the proposed model may provide a basis for evaluating the creep life of high temperature austenitic material.

Analytical solution of the peak bending moment of an M boom for membrane deployable structures

A deployable M cross section thin-walled boom (M boom) can be flattened and coiled elastically around a hub; and can then be self-deployed by releasing the stored strain energy. The M boom has been proposed as the key member of membrane deployable structures. First, the covariant base vectors of geometrical relation of the single type I tape spring were analyzed by establishing three coordinate systems. Second, the constitutive relation between stress and strain was expressed according to the Kirchhoff-Love hypothesis. Third, the equilibrium and controlling equations of the single tape spring were modeled based on Calladine shell theory. Fourthly, the total strain energy model of the single type I tape spring was built by integration. Fifth, the strain energy of the M boom was modeled by the sum of the strain energies of the six tape springs. Then, the strain energies of the single type II and III tape springs were analyzed. The sum of the strain energies of the six tape springs equals the total strain energy of the M boom. The bending moment model was established based on the minimum potential energy principle. The experimental equipment and four M boom samples were processed. The bending force value of the M booms was tested 20 times. Then, the average peak bending moment was calculated. The relative error between the theoretical and experimental results of the peak bending moment does not exceed 6.5% verifying the accuracy of the theoretical model.

Failure analysis of GFRP single lap joints tailored with a combination of tough epoxy and hyperelastic adhesives

Fibre reinforced polymeric composites bonded with epoxy adhesives often fail ungraciously, manifesting fibre-tear failure due to the edge peel stresses. This research work proposes phenol formaldehyde-based hyperelastic adhesive (AF32), as a compliant adhesive for tailoring the single lap joints consisting of GFRP adherends and well-toughened epoxy adhesive (AF3109 and EA9696) joints. The failure strength of the AF3109 and EA9696 adhesive joints is increased by 51.64% and 24.25%, respectively by having 20% volume of compliant adhesive in the bond line. Finite element simulations with Exponential Drucker-Prager (EDP) and Marlow strain energy models are carried out to simulate the experimental load-displacement response. Different failure mechanisms and the influence of adhesive intermingling are revealed by the failure analysis. Finally, a failure mode map for the tailored adhesive joints is proposed in terms of normalised strength ratio and the normalised volume of the compliant adhesive.

Ductile tearing analyses of cracked TP304 pipes using the multiaxial fracture strain energy model and the Gurson–Tvergaard–Needleman model

AbstractDuctile crack growth behaviours of TP304 pipes containing different circumferential defects were investigated in the study. Finite element (FE) damage analysis of the ductile fracture was carried out based on an uncoupled multiaxial fracture strain energy (MFSE) model with only two model parameters, which can be calibrated by data from tensile tests and fracture toughness tests. For the purpose of comparison, the Gurson–Tvergaard–Needleman (GTN) model was also employed in the FE damage analysis. It is observed that the MFSE model can reproduce the ductile tearing experiments as excellently as the GTN model does. Despite its simplicity, the MFSE model can reasonably predict the magnitudes of the crack initiation load and maximum load, the load‐line displacement, the crack mouth opening displacement, the crack extension and the crack profiles in the full‐scale cracked pipe tests.

Izboljšan model za napoved gostote deformacijske energije glede na vpliv glavne napetosti

Izboljšan model za napoved gostote deformacijske energije glede na vpliv glavne napetosti

Modeling the initial-volume dependent approximate compressibility of porcine liver tissues using a novel volumetric strain energy model

Experimental observations in the open literature indicate that soft tissues are slightly compressible, and this characteristic affects not only their overall elastic response but also their damage evolution and failure mechanism. In this study, we find that the compressibility of liver tissues is also closely related to the initial specimen volume according to the confined compression tests: the samples with smaller initial volume exhibit more compressible behavior compared to the larger ones. To include this initial-volume dependent effect, we developed a novel volumetric strain energy model with two variables, i.e., the bulk modulus and the compressibility factor. A detailed scheme was proposed as well to identify these two parameters, and the relationship between the bulk modulus and the initial volume was clarified. Findings from this study will help to deepen the understanding of the biomechanical properties of soft tissues. Statement of significanceLiver is a highly vascular organ and traditionally assumed to be an incompressible medium. However, through the confined compression tests, we found that the samples with smaller initial volumes exhibit more compressible behavior. Hence, we developed a novel strain energy density model to characterize the initial-volume dependent hyperelastic response, and found that the bulk modulus of liver tissues is positively related to the initial volume. Our results suggest that the compressibility of liver tissues should be considered in the future study of liver biomechanics.

Expanding the Build Plate: Functional Morphing 3D Printed Structures Through Anisotropy

Certain types of patterned metamaterials - gridshells and honeycombs - are capable of bistable behaviour through a tailored combination of local and global geometric parameters. This is an alternative to prestressed or composite materials, which are typically used to induce multistability in thin structures. Globally bistable structures, contrary to arrays of bistable elements, allow large deformations in a single step. Furthermore, this category of structures offers greater manufacturability and scalability compared to laminate, prestressed or multimaterial shells, since only geometry has to be considered. The simplicity of the material and geometrical requirements afford the designer easy and direct embedding in larger functional structures. In this study, the local and global response of bistable gridshells is interrogated through a manageable strain energy model, as well as through numerical and experimental methods. In addition, construction of bistable gridshells by employing various additive methods is examined and prototypes are presented for a series of functional devices. Finally, the availability of printed parts much larger than the build plate using commercial 3D printers is demonstrated, effectively ``expanding'' the dimensions of the build plate.

Fracture Modeling Of Cracked Pipe Under Monotonic And Cyclic Loading

ABSTRACT The present work presents experiment and numerical modelling to quantify the effect of the loading type on ductile crack growth in circumferential through-wall cracked SA508 Gr.1a pipes. In tests, three types of loading conditions are considered; monotonic, displacement-controlled and load-controlled large-amplitude cyclic loading. Experimental data are compared with numerical crack growth simulation results based on the multiaxial fracture strain energy model. Simulated results show overall good agreements with experimental data for all loading types. Based on FE results, the effects of the loading type and cyclic hardening model on ductile crack growth are discussed.

Functional morphology of the jaw adductor muscles in the Canidae.

Cranial form is closely allied to diet and feeding behavior in the Canidae, with the force and velocity of jaw-closing depending on the bony morphology of the skull and mandible, and the mass, architecture, and siting of the jaw adductor muscles. Previously, little has been reported on the details of the form and function of canid jaw adductor muscles, with earlier studies basing functional hypotheses on data derived from dry skull specimens. Here we use empirically derived muscle data from fresh-frozen specimens to explore the architecture of the muscles, and to inform finite element analyses models that predict bite force and strain energy in 12 species of wild canid. The inclusion of muscle architectural detail is shown to influence masticatory muscle force production capability calculations, indicating that muscles with longer fascicles were disadvantaged compared to muscles with shorter fascicles. No clear patterns of allometry were detected. Dietary groups were differentiated by temporalis fascicle angles, which, when allied with the differentiation of rostral length reported in previous studies, may further contribute to specializations of fast jaw-closing or forceful jaw-closing species. The most biomechanically demanding masticatory function is canine biting, and the highest strain energy values were reported in this loading condition, particularly in the zygomatic arches and caudal rostrum. Specific head shapes may be constrained by size, with scaled strain energy models predicting that some bony morphologies may only be viable in species with small body masses.

Effect of constraint factor on the thermo-mechanical fatigue behavior of an Al-Si eutectic alloy

The thermo-mechanical fatigue (TMF) behaviors and corresponding damage mechanisms of Al-Si piston alloy were investigated in the temperature range of 120~425 °C under different constraint factors (η). The TMF hysteresis loops exhibit asymmetrical, because the yield strength and elastic modulus decrease significantly with the increasing temperature. Taking the phase angles into consideration, the mean tensile stress for out of phase TMF (OP-TMF, η<0) and mean compressive stress for in-phase TMF (IP-TMF, η>0) can be found. The fatigue life of IP-TMF is longer than that of OP-TMF except for higher constraint factor, and the life of TMF decreases with the increasing absolute value of η. There are two different crack initiation mechanisms under the constrain TMF: primary phases broken mainly for OP-TMF and matrix deboned mainly for IP-TMF. The oxidation may have only little influence on the crack behavior and TMF life, considering the obvious damage by deboned or broken primary phases. The tensile stress is key factor for fatigue crack initiation and growth in primary phases (Si and intermetallic) under cyclic deformation. The TMF life under different constrain factors can be predicted by the strain energy model with good precision.

Yield Criterion for Rocklike Geomaterials Based on Strain Energy and CMP Model

The yield criterion of rock is significant for the identification of the whole failure process and the stability analysis of rock engineering. Studies of yield criteria from energy aspects are critical but rare. This paper investigated the yield criterion using strain energy and a modified compounded mobilized planes (CMP) model. The yield strain energy and strength criterion were formulated with different combinations of stress variables. Based on conventional triaxial and true triaxial tests, the evolution laws of mechanical parameters, including elastic parameters and strength parameter, were quantitatively determined. Accordingly, a new parameter correlation model, intermediate principal stress effect, and prerequisite for convex yield surface were investigated with theoretical and experimental approaches, respectively. With respect to previous criteria, the studied criterion has some advantages. Firstly, parameter correlations can be characterized with this criterion. Secondly, the shape of the yield surface is criterion-dependent and relies on rock properties, and can be applied to wide range of rocks. Thirdly, the estimation of yield stress is quasi-independent of the sample variability, which resulted in good agreement with test data. Fourthly, the criterion can be transformed into some classic criteria widely used in civil engineering. The criterion in this study offers an alternative viewpoint. In addition, it has high calculation precision and wide application for varied rocklike geomaterials.

Recrystallization Texture of Electrodeposited Zinc

Electrodeposited zinc layers help prevent the corrosion of steel surfaces. The microstructure, surface morphology, and texture of the electrodeposits are related to the deposition variables. Herein the surface morphology and microstructure are investigated as functions of the special electrodeposition variables, such as electrolyte composition, over-potential, current density, electrolyte temperature and pH. Upon heat treatment, the texture of the electrodepositd layers changes into a recrystallization texture. The texture of the as-electrodeposited and recrystallized zinc layers are studied. The //normal direction (ND) texture of the zinc electrodeposit can be obtained from zinc oxide, sodium hydroxide, potassium chloride, and sodium cyanide solution baths. The //ND texture of the zinc electrodeposit did not change even after recrystallization. This phenomenon of zinc eletrodeposits could be described by the strain-energy release maximization model.