Relative Deformation Research Articles

DIVERSITY OF STRUCTURAL VARIANTS OF THE m1 ANTEROKONID IN THE VOLE GENERA <i>STENOCRANIUS</i> AND <i>ALEXANDROMYS</i> (ARVICOLINI, RODENTIA): QUALITATIVE AND QUANTITATIVE APPROACHES

75 images of anteroconid morphotypes for five vole species were studied using traditional and GM methods: Stenocranius gregalis, Alexandromys middendorffii, A. mongolicus, A. mujanensis, and A. oeconomus. The morphotypical space is three-dimensional within the framework of the traditional approach, the axes being formed by (1) the complexity of the curve of the lingual and (2) labial sides of the anterior loop, and (3) the number of closed triangles. The total number of morphotypes for four species of Alexandromys is 56, 30 of them having been actualized (the degree of completeness of the morphospace is 53.6%). The thin plate and Procrustean distance analysys were used in the quantitative approach. The distribution of morphotypes in the space of the first two relative deformations, both for individual species and for their complex, corresponds to an arcuate configuration, the first of which is mainly associated with the complication/simplification of the buccal side of the antheroconid, while the second with the bilateral complication/simplification and simultaneous extension/compression of the antheroconid. The part of the potential morphospace that corresponds to a moderately complicated and maximally elongated antheroconid remains unoccupied. The distribution of morphotypes for the complex of species in the space of the first two axes of multidimensional scaling forms a single and almost homogeneous cloud that almost evenly fills the total morphospace. The correlation coefficients between the matrices of morphogenetic and Procrustean distances between morphotypes calculated for each of the species vary from 0.56 to 0.73.

ЩОДО УДОСКОНАЛЕННЯ ДІЮЧИХ НОРМАТИВНИХ ДОКУМЕНТІВ ДЛЯ РОЗРАХУНКУ ЗГИНАЛЬНИХ ДЕРЕВ’ЯНИХ ЕЛЕМЕНТІВ ТА КОНСТРУКЦІЙ

The most common use of wood in construction is for bending elements. The calculation of bending members made of glued laminated timber requires the use of the section modulus of this member and the calculated values of the bending strength of the timber. The design bending strength of wood is determined based on the characteristic values obtained from the laws of elastic material under load. However, this statement completely contradicts the anisotropy of wood in its tensile and compressive behavior. If it is known that wood works 90-95% to failure in longitudinal tension, it is then it can be assumed that it is elastic at all. However, in longitudinal deformation, there is non-linear behavior with increasing elastic and plastic strains. Furthermore, the longitudinal tensile strength of wood is almost twice that of longitudinal compression. Therefore, even if the relative deformations in the wood are the same different compressive and tensile stresses arise in the bending element, i.e. . Many authors who have carried out experimental and theoretical studies on the performance of timber beams have pointed out that the neutral force line in the cross-section of the element in direct transverse bending, with increasing levels of single load, shifts towards the tensile zone. Therefore, using the moment of resistance of the cross section in the wooden element to determine the section modulus is incorrect. The moment of resistance of a section of a timber member is only determined if the centre of gravity of the section coincides with the centre of force line. Usually, the failure of long wooden beams ( ) in transverse bending usually occurs due to the fracture of the most stressed outer layers of wood in the of the tensile area and is brittle in nature. It is on such elements that the the temporary bending strength. It is on such elements that the bending strength is crucial. However, the values of , usually determined in the outermost wood layers of the tensile zone, based on the condition, only reach values of 70-75% of the longitudinal tensile strength of wood . It is not possible to determine the tensile strength of wood at this stress level. Therefore, the results of determining the bending strength of wood using the moment of resistance of the cross-section of a timber element determined in the limiting condition are erroneous due to the impossibility of establishing values

МОДЕЛЮВАННЯ РОБОТИ ПІДСИЛЕНОГО ПОПЕРЕДНЬО НАПРУЖЕНОГО ЗГИНАЛЬНОГО ДЕРЕВ’ЯНОГО ЕЛЕМЕНТУ

An undeniable disadvantage of wood when using it in construction is its excessive flexibility. One of the ways to increase the stiffness of wooden elements is to use prestressing and reinforcement with stiffer elements. The manufacturing process of pre-stressed bending elements proposed by us is simple. However, determining the necessary effort, the necessary bending of the beam to ensure reliable operation, preventing the destruction of the element is quite difficult. One of the methods of prestressing is described, namely, the method by which the beam receives internal stresses due to the release of the bending element after the action of the external load by gluing reinforced elements. The principle of such tension can be described in the following sequence: 1. We create a bend in the bending element by applying an external load to the element. 2. We reinforce the lower zone of the bending element. At the same time, we need to know under which stress-strained state the reinforced element was installed, so that its operation can be predicted. 3. We remove the applied force with which we created the bend in the flexible wooden element, while the element wants to acquire its original shape, but this will be prevented by the armature, which will absorb part of the load and leave a small bend. It was established that the level of prestressing, namely the curvature acquired by the bending element after prestressing, depends on the initial curvature of the wooden element, as well as on the area and physical and mechanical characteristics of the materials reinforcing the beam zones. To determine the prestress, it is necessary to establish the stress-deformed states of the bending element, which occur after gluing and release of the external force. At the same time, 3 levels of the stress-strain state can be distinguished. 1. At the first stage, the compressed zone is more than the stretched zone. The relative deformations of the compressed lower zone, where the material is to be attached, is the initial start for the work of the reinforced element. 2. At the second stage, the external bending moment decreases, the internal redistribution of forces takes place, in addition to the moment perceived by the compressed and stretched zone, a moment also occurs in the stretched reinforced element. 3. The third stage is characterized by the absence of an external load, and this causes a balance between the internal forces of the bending prestressed element. The equilibrium equation for three stages was obtained. When using the element as a load-bearing structure, the cross-section in the element can be with both positive and negative curvature. The peculiarities of these two stress-strain states are manifested in the change in the position of the compressed and stretched zones. In the first case, the compressed zone is located in the lower part of the element and the upper part is occupied by the stretched zone. After the curvature changes its sign from negative to positive, the upper part becomes compressed, and the lower part becomes stretched. As a result of the simulation, it is possible to conclude that the cross-section of a bending wooden element undergoes 3 main stress-deformed states during prestressing and two during its operation

Comparative assessment of physical and mechanical parameters of cast plastic material for the manufacture of bases of combined removable orthopedic structures

The urgent task of orthopedic dentistry is the timely and optimal restoration of chewing efficiency, with the creation of new and improvement of existing structural materials, optimization of the use of consumables and improvement of the clinical and technological stages of the manufacture of removable orthopedic structures. The purpose of our study was a comparative assessment of the physical and mechanical properties of cast plastic material for the manufacture of bases of combined removable orthopedic structures using an improved method. We have developed a new domestic material for the manufacture of the bases of removable dentures using foundry compression pressing technology. The following parameters of the study of physical and mechanical properties of plastics were taken into account: material Shore hardness, material consistency, relative deformation during compression, sorption, impact strength, bending stress, tensile strength, abrasion resistance, percentage of residual monomer. The comparative characterization of the physical and mechanical properties of cold polymerization acrylic plastics showed that domestic cold-cured base plastic for casting compression molding is not inferior to the foreign base in terms of its main indicators cold-hardening plastic differs from the analog cold-hardening base plastic by a harder and harder consistency, which makes it possible to more effectively use the material for combined bases of removable dentures. The obtained data indicate that, in general, the domestic material with its physical and mechanical properties meets the requirements for this class of dental materials. Keywords: orthopedic treatment, physical and mechanical properties, cast plastic material, method of compression pressing.

Determination of the Boundaries of Changes in External Parameters that Complicate the Calculation of the Suspension of Agricultural Machinery

Introduction. The article deals with the problem of calculating the strength of the shaft of the wheel drive of agricultural machinery. The strength conditions of both the maximum torque and the values of relative deformations of the shaft are taken into account. Aim of the Article. Of the research is to determine the limits of external influences on a structural element, caused by the distributed weight of the motor-tractor machinery, at which it is necessary to construct not only the torque and strain diagrams, but also to determine the extreme values at each section, where the strength index of the structure is nonlinear. Materials and Methods. In calculations, the main provisions of continuum mechanics, theory of machines and mechanisms, as well as the basics of design in mechanical engineering are used. Central attention is paid to the influence of external influencing factors on the character of internal force distribution in the shaft. Results. The obtained area of variation of parameters P-q allows us to determine the necessity of more detailed calculation of strength parameters of the considered part. This is due to the emergence of extreme areas outside the boundaries of individual areas of consideration of the shaft work. The results are presented as a two-dimensional graph of the ratio of external influences, at which the specified effect takes place. Discussion and Conclusion. In comparison with typical calculations, regulated by normative documents, the proposed algorithm at the preliminary stage allows to determine the cases when nonlinear regions of bending moment changes require additional investigations. The use of the proposed algorithm allows, without resorting to time-consuming numerical methods of calculating the strength indicators of a wheel drive shaft, such as the finite element method, to obtain a more detailed picture of the nature of distribution of internal forces and deformations in the part under study.

Building foundation settlement in groundwater lowering on sliding territory of Lagerny Garden in Tomsk

Groundwater lowering is a method of stabilizing landslide slopes. To date, the effect of water reduction on the technical condition of buildings has not been sufficiently studied. This may negatively affect the technical condition of buildings due to the development of additional deformation of foundations and foundation soils.Purpose: The aim of this work is to assess the impact of cased hole with filters on the technical condition of buildings in the area of groundwater lowering.Methodology/approach: Long-term field observations of the groundwater level at the water supply site; monitoring of the technical condition of buildings; analysis and generalization of the data obtained.Research findings: Based on annual monitoring of the building height, monitoring of changes in the building state and the engineering and geological analysis are performed in the period from 1987 to 2020. It is found that groundwater lowering leads to building deformation and a decrease in its technical condition due to nonuniform soil compaction in this area.Research implication: Groundwater lowering near buildings can significantly affect their technical condition due to the soil compaction even at a considerable distance from the waterlowering devices. In developing groundwater lowering projects, special attention should be paid to heterogeneity of the ground layer on the building site and its impact on the formation of relative deformation of buildings.

Development of a method for online control of plastic deformations of a tank wall and assessment of its residual life

A method of operational control of the residual resource of the tank is proposed. As a tool, the measurement of deformations of the tank wall, the assessment of plastic deformations are used. To determine the deformation, it is proposed to use a light guide installed on the wall, with the help of which the change in the curvature of the wall is measured. A device prototype containing a light guide and the necessary electronics has been developed, and the dependence of the device readings on the curvature of the light guide has been experimentally determined. The simulation of the tank in the computer simulation program was carried out in order to compare the integral of the relative deformation over the height of the tank with the readings of the device. An algorithm for processing measurements of device readings and estimating the residual life of the tank is proposed.

Changes and mechanisms of apparent resistivity before earthquakes of MS6.0–6.9 on the Chinese mainland

China has been conducting fixed continuous apparent resistivity observations since 1967. Up to June 2022, 45 earthquakes with magnitudes of MS6.0–6.9 have occurred within a range of approximately 250 km from normal operating stations. Through literature investigation and data analysis, monitoring stations counted 61 short-medium-term apparent resistivity anomalous changes (i.e., 44 decrease changes, 15 increase changes, and 2 perturbance changes) appearing before 39 of these earthquakes. In this study, we utilize a fault virtual dislocation model to understand the relative deformations around the epicenters before these earthquakes. The comparison results showed that 36 of the 44 decrease changes were in areas with compression enhancement and that 9 of the 15 increase changes were in areas with relative dilatancy. The results from rock petrophysical experiments and the resistivity model of the cracked medium showed decreased changes in the resistivity of water-bearing geomaterials during the successive loading of compressive stress, while the resistivity showed increased changes during the stress unloading process. Moreover, 45 of the 61 apparent resistivity anomalies were consistent with the mechanism of resistivity change under stress. These apparent resistivity anomalous changes before earthquakes may be related to the seismogenic processes such that the resistivity change is caused by medium deformation.

Performance-based three-level fortification goal and its application in anti-dislocation countermeasures: A case study of Shantou Submarine tunnel

The dislocation momentum is the design basis for anti-dislocation to tunnel when a tunnel crosses an active fault. The influence of different dislocation levels on tunnel performances is not clear. Thus, based on seismic activity parameters at the site of interest and probability of fault dislocation, probability fault displacement hazard analysis (PFDHA) methodology was introduced in this paper to ascertain the fault dislocation level under different exceeding probabilities (63%, 10%, and 2%–3%). Then, based on the definition of different ground motion strength and fortification goals of the tunnel, a three-level fortification goal with different performance requirements of the tunnel was proposed. The first attempt to use the proposed indexes including the maximum dislocation of the tunnel and maximum relative deformation of the tunnel was tried to evaluate deformation and failure states with an experimental approach. Subsequently, the feasibility of the three-level fortification goal was further investigated according to the self-defined qualitative description and quantitative indexes in the segmental design and sectional expansion tunnels comprehensively. The results show that the fault dislocations relying on PFDHA at the site of the Shantou Submarine Tunnel are firstly ascertained as 0.04, 1.8, and 2.4 m respectively. Taking the fault dislocation as model input values into account, the dislocation mechanism of the tunnel under the three levels was revealed. More importantly, judging from the dislocation performance requirements of the three-level fortification goal, the tunnel deformation and failure states are mitigated by adopting the countermeasures. The sectional expansion design can well meet the requirements without the restriction of a strong earthquake, while the effectiveness of the segmental tunnel can be proved under frequently occurred and fortification earthquake. The final research results are expected to provide a new fortification goal for anti-dislocation hazard evaluation on expansion design in high-intensity seismic regions and segmental design in slight and moderate-intensity seismic regions.

Magma reservoir growth and ground deformation preceding the 79 CE Plinian eruption of Vesuvius

The 79 CE eruption of Vesuvius is the first documented Plinian eruption, also famous for the archaeological ruins of Pompeii and Herculaneum. Although much is known regarding the eruption dynamics and magma reservoir, little is known about the reservoir shape and growth, and related ground deformation. Numerical modelling by Finite Element Method was carried out, aimed at simulating the reservoir growth and ground deformation with respect to the reservoir shape (prolate, spherical, oblate) and magma overpressure. The modelling was tuned with volcanological, petrological and paleoenvironmental ground deformation constraints. Results indicate that the highest magma overpressure is achieved considering a prolate reservoir, making it as the most likely shape that led to eruption. Similar deformations but lower overpressures are obtained considering spherical and oblate reservoirs. These results demonstrate that ground deformation may not be indicative of eruption probability, style/size, and this has direct implications on surveillance at active explosive volcanoes.

A beam contact benchmark with analytic solution

AbstractThis paper presents a test case to help validate simulation codes for contact problems involving beams. A closed form solution is derived and the comparison is made with a finite element (FE) implementation that uses the mortar method for enforcing the contact constraints. The test case consists of a semi‐infinite cantilever beam subjected to a constant distributed load and experiencing frictionless contact with a straight rigid substrate. Both an Euler‐Bernoulli and a Timoshenko beam model are considered and the influence of the differing kinematic hypotheses is analyzed. In the case of the Euler‐Bernoulli beam the distributed contact force is equal to the load along the contact region except at the boundary where a point load appears. On the contrary, the rigid substrate exerts a fully distributed load on the Timoshenko beam which decays exponentially from the first contact point and tends towards the applied load. The rate of decay depends on the relative shear deformability. Moreover, whereas in the first case the transverse shear force is discontinuous, it becomes continuous when allowing for shear deformation. An example of benchmarking is given for a particular FE code. The error with respect to the exact solution can be computed and it is shown that the numerical solution converges to the analytic solution when the FE mesh is refined.

Research on the close-range photogrammetry accuracy of 3D digital interactive platform of Hunan intangible cultural heritage

Abstract This paper designed a three-dimensional digital interactive platform, which takes power supply module, image data acquisition module, control module, data transmission module and ESAM module as the main hardware and makes it feasible to realize power supply transmission, multiple data acquisition, platform process control, data transmission, data encryption and decryption, and identity authentication. Then, through relative orientation element calculation, model point coordinate calculation, relative orientation model proportion coefficient calculation, relative orientation model deformation accuracy calculation, and relative orientation accuracy calculation, this paper realized the relative control of close-range photogrammetry, improving the accuracy of close-range photogrammetry. The results show that the relative control method of close-range photogrammetry studied in this paper can increase the relative accuracy from 319 to 769 and improve the average value of the relative orientation model deformation accuracy from 0.4282 to 0.5938. In addition, in performance analysis, the response time of the platform is 0.32s, the accuracy of close-range photogrammetry is 96.3%, and the comprehensiveness of data detection is 94.37%. Therefore, it is concluded that using the method proposed in this paper, the relative orientation model deformation accuracy is increased, the accuracy of close-range photogrammetry is the highest, and the data detection is more comprehensive.

Computational analysis of yield stress buildup and stability of deposited layers in material extrusion additive manufacturing

This paper investigates the stability of deformable layers produced by material extrusion additive manufacturing. A Computational Fluid Dynamics (CFD) model is developed to predict the deposition flow of viscoplastic materials such as ceramic pastes, thermosets, and concrete. The viscoplastic materials are modelled with the Bingham rheological equations and implemented with a generalized Newtonian fluid model. The developed CFD model applies a scalar approach to differentiate the rheology of two layers in order to capture the deposition of a wet layer onto a semi solidified printed layer (i.e., wet-on-semisolid printing). The semi solidification is modelled by a yield stress buildup. The cross-sectional shapes of the deposited layers are predicted, and the relative deformation of the first layer is studied for different yield stress buildups and processing conditions such as printing- and extrusion-speed, layer height, and nozzle diameter. The results of the CFD model illustrate that the relative deformation of the first layer decreases non-linearly with an increase in yield stress, and that stable prints can be obtained when taking into account the semi solidification. Furthermore, it is found that the deformation is dependent on a non-trivial interplay between the extrusion pressure, the shape of the cross-section, and the contact area between the layers. Finally, the results highlight which process conditions can be changed with benefit in order to limit the requirement on the yield stress buildup and still provide stable prints.

Mechanics of isolated individual collagen fibrils.

Collagen fibrils are the fundamental structural elements in vertebrate animals and compose a structural framework that provides mechanical support to load-bearing tissues. Understanding how these fibrils initially form and mechanically function has been the focus of a myriad of detailed investigations over the last few decades. From these studies a great amount of knowledge has been acquired as well as a number of new questions to consider. In this review, we examine the current state of our knowledge of the mechanical properties of extant fibrils. We emphasize on the mechanical response and related deformation of collagen fibrils upon tension, which is the predominant load imposed in most collagen-rich tissues. We also illuminate the gaps in knowledge originating from the intriguing results that the field is still trying to interpret. STATEMENT OF SIGNIFICANCE: Collagen is the result of millions of years of biological evolution and is a unique family of proteins, the majority of which provide mechanical support to biological tissues. Cells produce collagen molecules that self-assemble into larger structures, known as collagen fibrils. As simple as they appear under an optical microscope, collagen fibrils display a complex ultrastructural architecture tuned to the external forces that are imposed upon them. Even more complex is the way collagen fibrils deform under loading, and the nature of the mechanisms that drive their formation in the first place. Here, we present a cogent synthesis of the state-of-knowledge of collagen fibril mechanics. We focus on the information we have from in vitro experiments on individual, isolated from tissues, collagen fibrils and the knowledge available from in silico tests.

Mathematical modeling of the acetabulum fracture (type 62-B1.3 by AO/ASIF) deformities and hip endoprosthetics in combination with osteosynthesis

Secondary degenerative disabling changes in the hip joint often develop in the long term after surgical treatment of hip fractures. A well-founded differential approach to the selection of endoprosthesis components and additional means of stabilizing bone fragments is necessary. Objective. To investigate changes in relative deformation values in a hip joint model with a acetabulum fractures 62–B1.3 type by AO/ASIF classification under the conditions of its endoprosthesis using various osteosynthesis options. Methods. A basic finite-element model of the pelvic girdle of a person with a fracture of the bottom of the cruciate ligament type 62-B1.3 (АО/ASIF) was developed, on which 7 variants of endoprosthesis of the left hip joint were modeled: without fracture (1); without osteosynthesis of fragments (2); fixation of a fragment of the acetabulum back wall with two screws (3), two screws and a bone plate (4), two screws and a bone plate with a Jumbo cup implantation (5); 5 case, long screw in the front column (6); option 5, long screws in the front and rear columns (7). Results. When using a large-sized Jumbo cup, the relative deformations of the bone regenerate in the center of the bottom of the KZ were reduced to 1.0 %, regardless of the osteosynthesis option. Around the free fragment of the short circuit, the largest relative deformations (3.0 %) were found in version 5 of the model. The use of long rods in the columns led to decrease in the relative deformations of the bone regenerate around the free fragment of the KZ to 2.0 %. Conclusions. Mathematical models proved that an increase in the number of osteosynthesis tools under the conditions of the total hip endoprosthesis replacement, 62-B1.3 (АО/ASIF) type KZ fracture leads to a decrease in the relative deformations of the bone regenerate along the entire fracture line. The use of a large-sized Jumbo cup makes it possible to reduce the level of relative deformations of the bone regenerate in the cent­ral part of the KZ.

Management of temporomandibular joint arthritis in children and adolescents: An introduction for orthodontists.

Juvenile idiopathic arthritis (JIA) is the most common inflammatory rheumatic disease of childhood. JIA can affect any joint and the temporomandibular joint (TMJ) is one of the joints most frequently involved. TMJ arthritis impacts mandibular growth and development and can result in skeletal deformity (convex profile and facial asymmetry), and malocclusion. Furthermore, when TMJs are affected, patients may present with pain at joint and masticatory muscles and dysfunction with crepitus and limited jaw movement. This review aims to describe the role of orthodontists in the management of patients with JIA and TMJ involvement. This article is an overview of evidence for the diagnosis and treatment of patients with JIA and TMJ involvement. Screening for the orofacial manifestation of JIA is important for orthodontists to identify TMJ involvement and related dentofacial deformity. The treatment protocol of JIA with TMJ involvement requires an interdisciplinary collaboration including orthopaedic/orthodontic treatment and surgical interventions for the management of growth disturbances. Orthodontists are also involved in the management of orofacial signs and symptoms; behavioural therapy, physiotherapy and occlusal splints are the suggested treatments. Patients with TMJ arthritis require specific expertise from an interdisciplinary team with members knowledgeable in JIA care. Since disorders of mandibular growth often appear during childhood, the orthodontist could be the first clinician to see the patient and can play a crucial role in the diagnosis and management of JIA patients with TMJ involvement.

Mechanical properties analysis of joints for prefabricated metro station structure based on Whole-process in-situ monitoring

Changchun Metro Line 2 implemented the whole-process monitoring and measurement of prefabricated metro station for the first time. This paper analyzes the mechanical behavior and deformation of the joints of vault and arch springing, which bear high bending moments, in order to study the mechanical properties of these joints, which play a key role in the bearing capacity of prefabricated structure. In addition, it also discusses the trend of the joint stress, relative deformation and relative rotation angle as it changes with the construction process and after opening for traffic. Furthermore, it analyzes the performance of the joints in different construction stages, and compares it with the numerical calculation results based on the long-term in-situ monitoring and survey data carried out at the prefabricated station of Changchun Metro during the whole construction period. As indicated by the result, at the beginning of the assembly and arching into a ring of the components at the top, the structure undergoes a self-adaptation period, where the joints are subject to heavy stress and deformation. After backfilling and water level recovery, the joints are subject to increased axial force and reduced stress and deformation, resulting in a positive effect on the bearing capacity of the joints. The overall change range in joint stress is rather small. During the construction period, the two tenons of double-tenon joint of vault bear external force by mutual engagement, which are subject to two types of stresses, namely, tensile stress and compressive stress. The concave-convex tenon of single-tenon joint at the arch springing is markedly engaged with each other, with the tenon subject to a bending effect. The test results are relatively stable, and the overall deformation at the joint of vault and arch springing is relatively small, with sufficient safety margin from the end of construction disturbance through the operation stage till today. The research results demonstrate great practical guiding significance for the joint and structure design of prefabricated metro station.

Artificial neural network model of the mechanical behaviour of shape memory alloy Schwartz primitive lattice architectures

This work proposes a novel artificial neural network (ANN)-based framework to explore the mechanical behaviour of shape memory alloy (SMA) Schwartz primitive triply periodic minimal surfaces (TPMSs) architectures where a loop with multiple conditions (LMCs) is introduced into the framework to improve its accuracy. Remarkably, it is found that the introduced ANN-based framework comprehends extremely well the example data and then provides a highly accurate prediction for the topology-driven mechanical behaviour of the SMA TPMS lattice architectures, which do not belong to the example. Indeed, the mechanical responses obtained from ANN-based approach excellently agree with that from numerical homogenization, with the maximum percent difference below 2.7% attained when the TPMS is subjected to tension or shear during the loading and unloading processes. More interestingly, the ANN-based approach can perform well with the increment of relative density or temperature 1000 times smaller than that in the homogenization, only requiring a little simulation time or thousands of times faster than that in the homogenization at the same computer setup. Hence, the mechanical behaviour of SMA TPMSs can be accurately characterized by the proposed framework at almost any value of the relative density or the temperature after the training. Subsequently, the ANN-based framework is used to map two-dimensionally the impact of varying relative density, temperature, and deformation on the effective hardness and superelasticity of the SMA TPMS architectures. The results show that the superelasticity of SMA TPMS scaffolds increases with decreased temperature and relative density and with increased deformation, in a nonlinear pattern. This work lays the foundation for further research on using ANN to explore the mechanical response and advanced applications of the complex SMA-based structures, such as smart composite systems, helical springs, and metamaterials at considerably reduced computational and financial costs.

Microstructural evolution and high-temperature deformation mechanism of 4Cr5MoSiV1Ti steel

Hot-working die steel usually withstands complex loading conditions and higher service temperatures, and its mechanical properties will inevitably deteriorate because of dynamic recovery, recrystallization, and plastic deformation of tempered martensite during service. A systematic study was carried out on a newly developed 4Cr5MoSiV1Ti hot working die steel to clarify the related microstructure evolution and deformation mechanism by stretching deformation at different temperatures ranging from room temperature to 640 °C. Results obtained show that the ultimate and yield tensile strength values at room temperature are about 1904 MPa and 1691 MPa, respectively. With increasing testing temperature, the strength decreases, the plasticity increases, and the fracture mode changes from brittle to ductile. All of these are closely related to a combined effect of tempered martensitic dynamic recovery, recrystallization, and secondary phase re-dissolution. Deformation mechanisms change from dislocation slip to rotation or sliding of ferrite with increasing stretching temperature.

Lie n-algebras and cohomologies of relative Rota-Baxter operators on n-Lie algebras

Based on the differential graded Lie algebra controlling deformations of an n-Lie algebra with a representation (called an n-LieRep pair), we construct a Lie n-algebra, whose Maurer-Cartan elements characterize relative Rota-Baxter operators on n-LieRep pairs. The notion of an n-pre-Lie algebra is introduced, which is the underlying algebraic structure of the relative Rota-Baxter operator. We give the cohomology of relative Rota-Baxter operators and study infinitesimal deformations and extensions of order m deformations to order m+1 deformations of relative Rota-Baxter operators through the cohomology groups of relative Rota-Baxter operators. Moreover, we build the relation between the cohomology groups of relative Rota-Baxter operators on n-LieRep pairs and those on (n+1)-LieRep pairs by certain linear functions.