Maximum Strain Energy Density Research Articles

Numerical study of steady-state dynamic characteristic of non-pneumatic tire with local structural damage

Non-pneumatic tires (NPTs) fundamentally avoid the risk of tire blowout of traditional pneumatic tires, but the overall and key component performance inevitably degrades due to factors such as high temperature, variable load, variable working conditions and impact in its service process. Once this leads to failure, it will significantly impact on vehicle safety. To this end, this paper studied the influence of local structural damage on the dynamic response of NPTs, which lays the foundation for realizing health monitoring of intelligent non-pneumatic tires (INPTs). Firstly, a three-dimensional nonlinear finite element model of NPTs was established, and the failure locations of NPTs were determined by fracture mechanics and maximum strain energy density; Secondly, the influence of structural damage on the static and dynamic performance of NPTs was analyzed; Finally, the sensitivity of the acceleration signal and sensor position of the tire inner liner to the local structural damage was studied. The research results show that structural damage will cause the stress of the spokes and shear layer to increase, and as the number of broken spokes increases, the shear layer will bear a larger load. Compared with the circumferential and lateral acceleration, the radial acceleration has the highest sensitivity to the damage of NPTs. The sensor closest to the damage location is the most sensitive to the damage. The research results provide a reference for the structural optimization design and health monitoring of INPTs.

Probabilistic fatigue life prediction of notched specimens based on modified stress field intensity method under multiaxial loading

In practical engineering components, due to the existence of non-uniform stress and strain field near the notch, it brings severe challenges to fatigue life prediction when evaluating the integrity of notched components. In this study, a probabilistic fatigue life prediction model for notched specimens was established by coupling the stress field intensity (SFI) method and Weibull distribution. Firstly, the position of the dangerous point is determined by finite element calculation, and the maximum strain energy density plane through the dangerous point is defined as the critical plane. Secondly, from the perspective of 2D features, the traditional SFI method is modified based on the stress distribution on the critical plane, and a new concept of effective stress is proposed to predict the fatigue life of notched specimens by the experimental data of smooth specimens. Finally, a new non-proportional additional hardening factor is established to characterize the influence of material properties and loading path on fatigue life. The experimental data of Q345 low alloy steel and GH4169 nickel base alloy are used to compare and analyze the proposed model. The results show that the predicted life of the proposed model is in good agreement with the experimental life.

Study on Fracture Characteristics of Layered Sandstone under Asymmetric Loading.

In engineering practice, layered rock masses often display obvious anisotropy while deforming and failing, and the failure mode directly impacts the engineering construction stability. In this study, the fracture failure load, fracture toughness, crack deflection angle, and failure mode of a layered rock mass under different fracture modes were analyzed by utilizing improved asymmetric semi-circular disc specimens. According to the constitutive model of transversely isotropic materials, the maximum tensile stress (MTS), maximum energy release rate (MERR), and maximum strain energy density (MSED) calculation formulas were modified, and the calculation formulas of the three prediction criteria under anisotropic materials were derived. The calculation results were compared with the experimental results. The results show that the fracture toughness and crack deflection angle were significantly affected by the weak bedding plane. As a result of applying the MTS criterion, the results are closer to the experimental results, providing a solid foundation for engineering deformation, failure, and fracture analyses.

Evaluation of bone-related mechanical properties in female patients with long-term remission of Cushing's syndrome using quantitative computed tomography-based finite element analysis.

Hypercortisolism in Cushing's syndrome (CS) is associated with bone loss, skeletal fragility, and altered bone quality. No studies evaluated bone geometric and strain-stress values in CS patients after remission thus far. Thirty-two women with CS in remission (mean age [±SD] 51 ± 11; body mass index [BMI], 27 ± 4 kg/m2; mean time of remission, 120 ± 90 months) and 32 age-, BMI-, and gonadal status-matched female controls. Quantitative computed tomography (QCT) was used to assess volumetric bone mineral density (vBMD) and buckling ratio, cross-sectional area, and average cortical thickness at the level of the proximal femur. Finite element (FE) models were generated from QCT to calculate strain and stress values (maximum principal strain [MPE], maximum strain energy density [SED], maximum Von Mises [VM], and maximum principal stress [MPS]). Areal BMD (aBMD) and trabecular bone score (TBS) were assessed by dual-energy X-ray absorptiometry (2D DXA). Trabecular vBMD at total hip and trochanter were lower in CS as compared with controls (P < .05). Average cortical thickness was lower, and buckling ratio was greater in CS vs controls (P < .01). All strain and stress values were higher in CS patients vs controls (P < .05). 2D DXA-derived measures were similar between patients and controls (P > .05). Prior hypercortisolism predicted both VM (β .30, P = .014) and MPS (β .30, P = .015), after adjusting for age, BMI, menopause, delay to diagnosis, and duration of remission. Women with prior hypercortisolism have reduced trabecular vBMD and impaired bone geometrical and mechanical properties, which may contribute to an elevated fracture risk despite long-term remission.

A strain energy density field method to predict the life of metallic notched components under multiaxial fatigue loading

A method based on strain energy density field (SEDF) has been proposed to predict the angle of fatigue critical points and multi-axial life of the notched parts under multi-axial cyclic loading. The point bearing the maximum strain energy density was taken as the fatigue crack initiation point (fatigue critical point). The influence of stress-strain gradient around the notches were considered via combining SEDF and the critical distance theory (TCD) to calculate the multi-axial notch life. The predictive results indicate that the maximum deviation of the fatigue critical point (FCP) was 7.0°. The most of the predictive life was within the 3-time error band.

A finite element study on the risk of bone loss around posterior short implants in an atrophic mandible.

This study aimed to evaluate the risk of bone loss around single short molar crown-supporting implants in an atrophic mandible. Implants of different lengths (L = 4 or 6 mm) and diameters (Ø = 4.1 or 4.8 mm) were placed in the molar area of an atrophic mandible. Additional control mandible models were simulated for 4.1 mm diameter implants (L = 4, 6, 8, and 10 mm). A vertical masticatory load of 200 N was applied to three or six occlusal contact areas (3ca or 6ca) of the prosthetic crown. The bone strain energy density (SED) of 109.6 µJ/mm3 was assumed to be the pathological threshold for cortical bone. The peri-implant bone resorption risk index (PIBRri) was calculated by dividing the maximum SED of the crestal cortical bone by the SED pathological threshold. Increasing the implant length from 4 to 6 mm, implant diameter from 4.1 to 4.8 mm, and number of contact areas from 3 to 6 reduced the SED and PIBRri values by approximately 20%, 35%, and 40%, respectively, when comparing pairs of models that isolated a specific variable. All models with 6ca had a low bone resorption risk (PIBRri<0.8), while the Ø4.1 short implant with 3ca had a medium (0.8≤PIBRri≤1.0) or high (PIBRri>1.0) resorption risk. Increasing the diameter or occlusal contact area of a 4 mm short implant in an atrophic mandible resulted in reduced bone resorption risks, similar to or lower than those observed in a regular mandible with standard-length implants.

A new criterion based on the ratio of strain energy density for mixed-mode crack initiation prediction in ductile materials

In consideration of the different mechanisms of microscopic separation governed by dilation and microscopic shearing controlled by distortion on crack initiation, a new criterion based on the ratio of two strain energy densities (RSED) is proposed by differentiating the dilatational and distortional parts in strain energy density. The influence of the weights of two strain energy densities under different stress states on fracture resistance of crack initiation is also considered in the RSED criterion. The size and shape of the core region do not affect the direction and fracture resistance of crack initiation predicted by the RSED criterion. Moreover, the direction predicted by the RSED criterion is theoretically demonstrated to be identical to the orientations predicted by the maximum stress triaxiality (MST) criterion and the T criterion on crack initiation. The crack initiation directions which are obtained by the experiments for different materials and predicted by various criteria are found to be mostly coincident near the mode-I crack, and so are the fracture resistances. In the vicinity of the mode-II crack, the direction of crack initiation predicted by the RSED criterion shows a superior consistency for the experimental results of the ductile materials reported by Theocaris et al. (1982) and Kong et al. (1995) over the three classical criteria, such as the maximum tangential stress (MTS), the maximum energy release rate (MERR) and minimum strain energy density (MSED). The RSED criterion also has the potential to amend the issue of the underestimation for KIIC/KIC in some typical materials, e.g., the face-centered-cubic (f.c.c) metals. Therefore, the RSED criterion prefers to predict the direction and fracture resistance of crack initiation in ductile materials.

Fatigue life prediction and structural optimization design of the bionic petal non-pneumatic tire with spokes

Fatigue durability of the non-pneumatic tire (NPT) has a decisive influence on vehicle safety and transport economy. This paper aims at the research on the fatigue life prediction method suitable for the flexible spokes of the NPT, and explores the influence of structural parameters on fatigue performance. By simultaneously taking consideration of fatigue performance, bearing capacity, and weight of the NPT, the optimal model parameters are obtained by the proposed structural optimization method. Firstly, based on the Thomas crack model, the fatigue life of the bionic petal non-pneumatic (BP-NPT) is predicted. Then, the influential mechanism of key structural parameters including the curvature, array period, and spoke thickness on tire fatigue durability is investigated by numerical simulation methods. Finally, an optimization method based on the Kriging model and modified NSGA-II is proposed to optimize the structure characteristics of the BP-NPT for better fatigue life and bearing capacity while ensuring lightweight. The results show that the predicted fatigue failure mileage of the BP-NPT is 2.54 × 104 km. By properly increasing the curvature and thickness of the spoke, the maximum strain energy density of the BP-NPT will be reduced, thus improving its fatigue durability. The performance of the optimized structure is significantly improved by the proposed optimization method. The total mass is reduced by 7.44%. The fatigue life and bearing capacity are improved by 9.75% and 4.16%, respectively. It is indicated that a more durable and safer tire configuration is provided for tire safety applications.

Stability Index of Surrounding Rock during Deep Rock Excavation Considering Energy Release Speed

Rockburst is a kind of dynamic rock failure process that is easily induced by the excavation of a high-stress rock mass. However, from an energy perspective, the existing indexes for rockburst tendency have a limitation in that they do not consider the energy release speed. In this study, energy release effectiveness was proposed based on the local energy release rate while considering the influence of the energy release speed. The index can evaluate the stability of surrounding rock during the excavation of high-stress rock. The index can be obtained by recording the strain energy density of every element in the model during excavation and identifying the maximum strain energy density (Eimax), the minimum strain energy density (Eimin), the maximum time (timax), and the minimum time (timin) to calculate energy release speed and energy release effectiveness. A case study of the excavation of an experimental tunnel, namely, the URL of AECL, was adopted to validate the index. The results indicated that the proposed index can clearly identify the location and strength of the impact tendency area, and it can be effectively applied to the stability analysis during the excavation of deep tunnels.

Unraveling the ultrahigh modulus of resilience of Core-Shell SU-8 nanocomposite nanopillars fabricated by vapor-phase infiltration

Modulus of resilience, the maximum strain energy density that can be stored in an elastically deformed solid, is an important mechanical property for developing artificial muscles in robotics, soft electronics panels, and micro-/nano-electromechanical actuators. In this study, core–shell SU-8 nanocomposites were fabricated via vapor-phase infiltration of nanoscale amorphous aluminum oxides into SU-8 nanopillars and performed transmission electron microscopy, nanomechanical testing, analytical modeling, and atomistic simulations to gain a fundamental insight into the ultrahigh modulus of resilience much higher than that of most high-strength materials. This study shows that the ultrahigh modulus of resilience results from: the low aspect ratio of amorphous aluminum oxide nano-particulates; the particulate size thicker than the free volume size; and the thin aluminum oxide interconnecting links within nano-particulates. These unique microstructural features produce the unusual combination of low specific Young’s modulus (E), 4 MPa/(kg/m3), and high specific yield strength (σy), 0.2 MPa/(kg/m3), leading to the specific modulus of resilience, 5.21 ± 0.39 kJ/kg (σy2/(2E)) about ten times higher than materials with the similar yield strength. This study demonstrates that vapor-phase infiltration is an excellent fabrication method to produce a polymer nanocomposite that can absorb and release a large amount of elastic strain energy.

Fatigue damage criteria for antivibration systems with filled natural rubber under negative and positive R ratios

A shape change can initiate fatigue damage in rubber components, which has led to the development of the effective shear strain γt criterion in this investigation. Referring to the previous damage criterion, i.e., effective tensile strain εt, the relation between the two was revealed. To benchmark the effectiveness of different damage criteria, six damage criteria, including the commonly used maximum principal strain, stress, and strain energy density, were compared using cylindrical dumbbell samples in 30 fatigue cases under ± R ratios. A large scatter was generated using either the maximum principal strain or the stress criterion. The strain energy density was in excellent agreement in uniaxial tension loadings but failed in torsional loadings with R = −1. To save significant cost in producing a completed new S–N curve for each rubber material, the derived S–N base functions using both εt and γt have been successfully validated on three independent experiments, i.e., the cylindrical dumbbell specimens, the ring specimens, and the industrial mount MDS. To fully verify the applicability of both εt and γt, the prediction of the crack orientation was performed for the first time using the proposed criteria, to the knowledge of the author, and the results were consistent with the experimental observations. The proposed criteria are useful for antivibration product design.

Porous metal block based on topology optimization to treat distal femoral bone defect in total knee revision

Metal block augmentations are common solutions in treating bone defects of total knee revision. However, the stress shielding and poor osteointegration resulted from metal block application could not be neglected in bone defects restoration. In this study, a novel porous metal block was designed with topology optimization to improve biomechanical performance. The biomechanical difference of the topologically optimized block, solid Ti6Al4V block, and porous Ti6Al4V block in treating bone defects of total knee revision was compared by finite element analysis. The inhomogeneous femoral model was created according to the computed tomography data. Combined with porous structures, minimum compliance topology optimization subjected to the volume fraction constraint was utilized for the redesign of the metal block. The region of interest was defined as a 10 mm area of the distal femur beneath the contacting surface. The biomechanical performance of daily motions was investigated. The von Mises stress, the strain energy density of the region of interest, and the von Mises stress of metal blocks were recorded. The results were analyzed in SPSS. In terms of the region of interest, the maximum von Mises stress of the topological optimized group increased obviously, and its average stress was significantly higher than that of the other groups (p < 0.05). Moreover, the topologically optimized block group had the highest maximum strain energy density of the three groups, and the lowest maximum stress of block was also found in this group. In this study, the stress shielding reduction and stress transfer capability were found obviously improved through topology optimization. Therefore, the topological optimized porous block is recommended in treating bone defects of total knee revision. Meanwhile, this study also provided a novel approach for mechanical optimization in block designing.

Alleviating expansion-induced mechanical degradation in lithium-ion battery silicon anodes via morphological design

The mechanics of films undergoing volume expansion on curved substrates plays a key role in a variety of technologies including biomedical implants, thermal and environmental barrier coatings, and electrochemical energy storage systems. Silicon anodes for lithium-ion batteries are an especially challenging case because they can undergo volume variations up to 300% that results in cracking, delamination, and thus significant loss in performance. In this study, we use finite element analysis to model the volume expansion during lithiation for silicon coated on spinodal, inverse opal, gyroid, and Schwartz primitive nickel backbones and compare the distributions of maximum principal stress, strain energy density, and von Mises stress, which we use as indicators for propensity for cracking, delamination, and yielding, in order to explore the effect of backbone morphology on mechanical degradation during expansion. We show that, when compared to the inverse opal, the spinodal morphology reduces and uniformly distributes the maximum principal stress and strain energy density in the silicon layer, and delays the onset of expansion-induced yielding at all silicon layer thicknesses, which we ascribe to the unique interfacial curvature distribution of spinodal structures. This work highlights the importance of morphology on coatings undergoing volume variations and unveils the particular promise of spinodally derived materials for the design of next generation lithium-ion battery electrodes.

How suture networks improve the protective function of natural structures: A multiscale investigation

Myriad natural protective structures consist of bone plates joined by convoluted unmineralized (soft) collagenous sutures. Examples of such protective structures include: shells of turtles, craniums of almost all animals (including humans), alligator armour, armadillo armour, and others. The function of sutures has been well researched. However, whether, and if so how, sutures improve protective performance during a predator attack has received limited attention. Sutures are ubiquitous in protective structures, and this motivates the question as to whether sutures optimize the protective function of the structure. Hence, in this work the behaviour of structures that contain sutures during predator attacks is investigated. We show that sutures decrease the maximum strain energy density that turtle shells experience during predator attacks by more than an order of magnitude. Hence, sutures make turtle shells far more resilient to material failure, such as, fracture, damage, and plastic deformations. Additionally, sutures increase the viscous behaviour of the shell causing increased dissipation of energy during predator attacks. Further investigations into the influence of sutures on behaviour during locomotion and breathing are also presented. The results presented in this work motivate the inclusion of sutures in biomimetically designed protective structures, such as helmets and protective clothing. Statement of significanceMyriad bony protective structures contain networks of sutures, that is con- voluted soft collagenous tissue. Their ubiquity motivates the question, whether, and if so how, sutures improve protective performance. Hence, this work inves- tigates how sutures affect protective performance using computational experi- ments. Due to the length scale of sutures being far smaller than the structures in which they reside, classical modelling approaches are prohibitively expensive. Hence, in this work, a multiscale approach is taken. To our knowledge, this is the first multiscale investigation of structures that contain sutures.Among other insights, we show that sutures decrease the maximum strain energy density in structures during predator attacks by over an order of mag- nitude. Hence, sutures make structures far more resilient to failure.

Analytical and experimental investigation on the effect of loading rate on the fracture toughness and fracture envelope in brittle rocks

Fracture toughness of brittle rocks is an essential factor for analyzing and designing many problems in rock mechanics such as crack initiation and propagation in rock masses, hydraulic fracturing, geothermal energy, etc. This parameter is closely related to the strain rate to which the rock mass is subjected. Therefore, the effect of strain rate on the fracture toughness under three loading modes (pure mode I, mixed mode loading I/II and pure mode II) by taking into account crack propagation speed was investigated in this work. Experiments were conducted on rectangular specimens of hornfels rock and two fracture criteria that include maximum tangential stress criterion (ϭ-criterion) and minimum strain energy density criterion (S-criterion) were adopted to verify their ability to predict the fracture envelope as a function of the strain rate. Results indicated that by increasing the strain rate from 6 × 10−4 to 6 × 10−2 S−1, fracture toughness under pure mode I, mixed mode loading I/II and pure mode II increased by 1.6, 1.8 and 1.9 orders of magnitudes, respectively. The fracture toughness under pure mode I and mixed mode loading I/II almost has the same increment rate versus strain rate (∼21). While the increment rate of the fracture toughness under pure mode II (∼37) is larger than that under pure mode I and mixed mode loading I/II. S-criterion indicated that by increasing the crack propagation speed, fracture envelope moves up and the fracture resistance for growth under mixed mode loading I/II increases. While for ϭ-criterion, two cases can be distinguished, for crack propagation speed less than 80% the Rayleigh wave speed, fracture envelope moves down by increasing the crack propagation speed, and the vice is versa for crack propagation speed greater than 80% of the Ryleigh wave speed. S-criterion is better than ϭ-criterion to characterize the fracture envelope under low strain rate, and for high strain rates, S-criterion should be developed to better characterize the fracture envelope.

On the validation of mixed-mode I/II crack growth theories for anisotropic rocks

We evaluate the accuracy of three well-known fracture growth theories to predict crack trajectories in anisotropic rocks through comparison with new experimental data. The results of 99 fracture toughness tests on the metamorphic Grimsel Granite under four different ratios of mixed-mode I/II loadings are reported. For each ratio, the influence of the anisotropy orientation on the direction of fracture growth is also analyzed. Our results show that for certain loading configurations, the anisotropy offsets the loading influence in determining the direction of crack growth, whereas in other configurations, these factors reinforce each other. To evaluate the accuracy of the fracture growth theories, we compare the experiment results for the kink angle and the effective fracture toughness with the predictions of the maximum tangential stress (MTS), the maximum energy release rate (MERR), and the maximum strain energy density (MSED) criteria. The criteria are first assessed in their classical forms employed in the literature. It is demonstrated that the energy-based criteria in their classical formulation cannot yield good predictions. We then present modified forms of the ERR and SED functions in which the tensile and shear components are decomposed. These modified forms give significantly better predictions of fracture growth paths. The evaluation of the three criteria illustrates that the modified MSED criterion is the least accurate model even in the modified form, while the results predicted by MTS and modified MERR are well matched with the experimental results.

Study on the Temperature to the Uniaxial Creep Property of the New Similar Soft Rock

In this paper, the standard specimen is made of the new similar soft rock, whose cementing agent is paraffin. The standard specimen are experimental research of creep properties under six temperature ranging from 10°C to 60°C, which can obtain that the raising temperature has a huge impact on creep property law of the similar soft rock. The creep curve of soft rock only shows decay and constant creep law within 2h under 10°C and at 2.5MPa. However under 60°C and at low 0.25MPa, the creep law shows acceleration within 2h and the slope of the stress-strain curve is increasing. While the average creep modulus is decreasing and the capacity of resist deformation. COMSOL is used to numerically calculate the creep characteristics of similar roadway. The maximum elastic strain energy density and the maximum equivalent creep rate of roadway increase with the increasing of temperature. The gradient increasing indicate that similar roadway accelerate into the rheological stage under the action of high temperature, When large deformation, instability and failure are more likely to occur. The maximum strain and energy accumulation of roadway occur at the edge and key points of roadway. Strengthening and supporting key areas is the key to the stability of soft rock engineering.

Accuracy of models of confined concrete in rectangular columns using different proposals for the prediction of failure of the FRP

Confinement with externally applied fiber reinforced polymers (FRP), such as carbon, glass and aramid-based composites, results in notorious improvement of ductility and strength. Several constitutive models, regarding stress–strain relationship, have been proposed. However, few models exist for square and rectangular columns confined with FRP when compared with the number of models for circular concrete columns, and even fewer models satisfactorily predict the failure strain of FRP. In this paper, the accuracy of existing models for the prediction of the failure strain of the FRP is evaluated. Comparison of analytical results with experimental test results of concrete columns reported in the literature is presented, focusing different parameters such as strength, maximum strain and strain energy density.

Accuracy of models of concrete in circular columns using different proposals for the prediction of failure of the confining FRP

Confinement of concrete columns with fiber reinforced polymers results in an increase of strength and ductility. For this reason, the use of aramid, carbon and glass-based composites for confinement of reinforced concrete columns has significantly increased over the last decades. Nevertheless, few models adequately predict the failure strain of the fiber reinforced polymer, which has a determinant influence on the computed results. In this paper the accuracy of existing models of confined concrete using different proposals for the prediction of the failure strain of the confining composite is assessed. This is based on the comparison of analytical results with experimental test results of concrete columns with circular cross-section reported in the literature. The comparison focusses on different parameters such as strength, maximum strain and strain energy density.

Numerical investigation into impacts of major fault on coal burst in longwall mining – A case study

The presence of geological faults is a significant contributing factor to coal burst in underground mining. In this study, a large-scale discontinuum model was established based on geological and geotechnical conditions in a mine site, where a longwall face passed through a major fault. Four model indicators were calculated during the longwall retreat: model seismic energy (energy released by the model system), fault seismic energy (energy released by fault-slip only), peak abutment stress and maximum strain energy density in coal seam. The change pattern of model seismic energy in the discontinuum model was calibrated against the seismic energy recorded in the mine site. It aims to verify that the model seismic energy can properly demonstrate the seismic energy observed in practice. The model results showed that the peak abutment stress and maximum strain energy density in coal seam increased when the longwall face approached the major fault, and then both of them experienced a most significant reduction when the largest fault-slip event occurred. A coal burst risk classification was then developed using multiple model indicators for the case study. A parametric study was conducted based on the calibrated model, which aims to investigate the impacts of various conditions on both fault-slip behaviour and stress and strain energy distributions around longwall excavations. Four factors were studied: the static friction angle of fault, the cover depth of fault, the dip angle of the coal seam and the mining direction. This study and the proposed model indicators can provide an improved understanding of fault-slip burst mechanisms and insights into the associated coal burst proneness assessment.