Biaxial Compressive Loads Research Articles

Mechanism-based strength criterion for 3D needled C/C–SiC composites under in-plane biaxial compression

ABSTRACTBiaxial compressive experiments for 3D needled C/C–SiC composites parallel to the nonwoven cloth were conducted. The failure mechanisms and mechanical properties of the composites were greatly related to the biaxial compressive stress confinement ratio, R. It was found that out-of-plane shear failure controlled the failure of the composites. The failure shear plane was aligned with one of the major loading axes for R (0:1 or 1:3), while the failure shear plane occurred along both loading axes for R (1:2 or 1:1). Compared with uniaxial strength, the biaxial compressive strength increased obviously, which also significantly depended on the value of R. Based on the failure modes, a modified twin-shear strength criterion was established to predict the failure surface of 3D needled C/C–SiC composites under biaxial compressive loading.

A nonlocal continuum model for the biaxial buckling analysis of composite nanoplates with shape memory alloy nanowires

In this study, the buckling behavior of a three-layered composite nanoplate reinforced with shape memory alloy (SMA) nanowires is examined. Whereas the upper and lower layers are reinforced with typical nanowires, SMA nanoscale wires are used to strengthen the middle layer of the system. The composite nanoplate is assumed to be under the action of biaxial compressive loading. A scale-dependent mathematical model is presented with the consideration of size effects within the context of the Eringen’s nonlocal continuum mechanics. Using the one-dimensional Brinson’s theory and the Kirchhoff theory of plates, the governing partial differential equations of SMA nanowire-reinforced hybrid nanoplates are derived. Both lateral and longitudinal deflections are taken into consideration in the theoretical formulation and method of solution. In order to reduce the governing differential equations to their corresponding algebraic equations, a discretization approach based on the differential quadrature method is employed. The critical buckling loads of the hybrid nanosystem with various boundary conditions are obtained with the use of a standard eigenvalue solver. It is found that the stability response of SMA composite nanoplates is strongly sensitive to the small scale effect.

Failure process and mechanism of sandstone under combined equal biaxial static compression and impact loading

AbstractThe process and mechanism of impact fractures in sandstone were investigated under equal biaxial static compression. The cracking process was captured by a high‐speed video camera. The results indicate that the main crack propagates along the circumference and finally forms a crater‐shaped failure zone. The size of the crater‐shaped failure zone increases as the static stress and impact velocity increase. In addition, microscopic features of the fracture surface were observed using a scanning electron microscope. It was found that the microcracks expand after combination loading, making the rock more susceptible to damage. Finally, the influence mechanism of static loading on dynamic failure of the rock was revealed by theoretical analysis and numerical simulation.

A confinement-dependent load-induced thermal strain constitutive model for concrete subjected to temperatures up to 500 °C

This paper proves that, given a Load-Induced Thermal Strain (LITS) curve able to accurately describe the uniaxial LITS development for a specific type of concrete and temperatures up to 500 °C, a more accurate prediction of the 3D LITS state is obtained through a confinement-dependent 3D implementation than through the classic confinement-independent approach. In particular, a new model is presented, obtained by extending to 3D a fourth order polynomial LITS derivative function in a way that allows the effects of the stress confinement to be taken into account. For comparison purposes, the same fourth order polynomial LITS derivative function is also implemented in 3D through the classic confinement-independent modelling approach. These constitutive relationships are adopted to model transient experiments performed on concrete subjected to constant uniaxial and biaxial compressive loads. The results show that the confinement-dependent modelling approach gives a better prediction of the LITS state developing in the case of biaxial compression than the classic confinement-independent approach. Finally, the validated confinement-dependent model is applied to evaluate the LITS-related stress redistribution taking place in a typical Prestressed Concrete Pressure Vessel (PCPV) subjected to heating to 500 °C and cooling back to the normal operating temperature of 50 °C. It is found that including the effects of three dimensional LITS behaviour has significant effects on the predicted stress states.

The dynamic stability of physically nonlinear plate systems under biaxial compression

The article presents the method of dynamic stability analysis of plate systems with nonshifting ribs. A plate system under the biaxial dynamic compression loads is considered. The Kirchhoff - Love hypotheses, the nonlinear-elastic body hypothesis are considered the basis of the calculations. The material of the plate system is assumed to be physically nonlinear, stress-deformation diagram is approximated in the form of a cubic polynomial. The displacement of points in normal direction to middle plane of plates is presented in the form of Vlasov expansion. To derive the basic differential equations of stability, the strainenergy method and Vlasov's variation method are used. The extreme value of total energy of the system is defined using Euler - Lagrange equation, after solving of which the set of basic nonlinear differential equations of buckling of the plate system with non-shifting ribs under dynamic compression loads is given. As an example, the stability calculation of physically nonlinear T-shaped plate system hinge-supported along the contour is carried out. Buckling of the plate system occurs longitudinally on one half-wave of sinusoid. At the solution of a task in the first approximation, a nonlinear differential equation is derived, the numerical integration of which was carried out by the Runge - Kutta method. Based on the results of the calculations, graphs of the relative magnitude of deflection against the dynamic coefficient are plotted. The influence of the degree of physical nonlinearity of the material, the rate of change of the dynamic compressive load on the dynamic criterion of buckling of the plate system was studied.

Domain decomposition technique to simulate crack in nonlinear analysis of initially imperfect laminates

In this research, an effective computational technique is carried out for nonlinear and post-buckling analyses of cracked imperfect composite plates. The laminated plates are assumed to be moderately thick so that the analysis can be carried out based on the first-order shear deformation theory. Geometric non-linearity is introduced in the way of von-Karman assumptions for the strain-displacement equations. The Ritz technique is applied using Legendre polynomials for the primary variable approximations. The crack is modeled by partitioning the entire domain of the plates into several sub-plates and therefore the plate decomposition technique is implemented in this research. The penalty technique is used for imposing the interface continuity between the sub-plates. Different out-of-plane essential boundary conditions such as clamp, simply support or free conditions will be assumed in this research by defining the relevant displacement functions. For in-plane boundary conditions, lateral expansions of the unloaded edges are completely free while the loaded edges are assumed to move straight but restricted to move laterally. With the formulation presented here, the plates can be subjected to biaxial compressive loads, therefore a sensitivity analysis is performed with respect to the applied load direction, along the parallel or perpendicular to the crack axis. The integrals of potential energy are numerically computed using Gauss-Lobatto quadrature formulas to get adequate accuracy. Then, the obtained non-linear system of equations is solved by the Newton-Raphson method. Finally, the results are presented to show the influence of crack length, various locations of crack, load direction, boundary conditions and different values of initial imperfection on nonlinear and post-buckling behavior of laminates.

Buckling analysis of isotropic skew plates under general in-plane loads by the modified differential quadrature method

• Buckling analysis of thin skew plates using modified DQM is presented. • A complete set of differential equations in oblique coordinate system is established. • Accurate buckling loads are presented and verified by the FEM data. • Effects of boundary conditions, loadings, skew angles and aspect ratios are discussed. Perhaps due to the bending moment singularity at the obtuse plate corners, the existing buckling loads vary appreciably even for simply supported rhombic plate under uniaxial loading. In this paper, the buckling analysis of skew plates under various loadings is presented using the modified differential quadrature method (DQM). A complete set of equations of equilibrium, bending and twisting moments, equivalent shear forces and corner force in oblique coordinate system is given. Eight combinations of simply supported, clamped and free boundary conditions, four skew angles, and five aspect ratios are considered. Convergence studies are made for rhombic plates with the largest skew angle subjected to uniaxial and equal biaxial compressive loads. The solution accuracy is further verified by comparing the results with data obtained by the finite element method using very fine meshes. New data are tabulated and plotted for skew plates with different edge conditions, aspect ratios and skew angles, subjected to uniaxial, biaxial, as well as combined shear with uniaxial loads. Most of the data, not available thus far, may be useful for other researches in testing the validity of their numerical techniques for thin plate analysis.

Load-carrying Capacity of Intermediately Slender Parallel Strand Bamboo Columns with a Rectangular Cross Section under Biaxial Eccentric Compression

Parallel strand bamboo (PSB), a processed bamboo composite, has been used as an alternative to wood products in building and engineering applications. Inelastic analysis of PSB members is important because of the evident nonlinearity of the material. The present work conducted experimental investigations on intermediately slender PSB columns subjected to biaxial eccentric loads. The bending failure, which underwent a pronounced nonlinear process, was the major characteristic of the intermediately slender PSB column that had a biaxial compressive load. The mid-height cross section of the columns can be divided into three parts over its depth: the plastic compressive zone, the elastic compressive zone, and the tensile zone. Both the secondary bending and material nonlinearity were important factors that impacted the nonlinear response of the columns. An analytical method was presented for evaluating the load-carrying capacity of intermediately slender PSB columns with rectangular cross sections under biaxial eccentric compression loads. There was good agreement between the results of the experiments and calculations.

Tuning the electronic and optical properties of XP(X = Al,Ga) monolayer semiconductors using biaxial strain effect: Modified Becke-Johnson calculations

In this paper, based on full potential density functional theory calculations, the electronic and optical properties of aluminium and gallium phosphide (AlP and GaP) graphene-like structures are investigated under different biaxial compressive and tensile strain loads. One of the fascinating properties of these new monolayers is their high stretch-ability and high mechanosensitivity of their electronic and optical features. The electronic calculations display that the energy gap of materials versus the exerted strain can be estimated by a second order polynomial equation. Furthermore, the optical calculations indicate that the electronic and optical gap of AlP and GaP monolayers can be tuned by biaxial strain loads.

Wrinkling of Functionally Graded Sandwich Structures Subject to Biaxial and In-Plane Shear Loads

Benefits of a functionally graded core increasing wrinkling stability of sandwich panels have been demonstrated in a recent paper (Birman, V., and Vo, N., 2017, “Wrinkling in Sandwich Structures With a Functionally Graded Core,” ASME J. Appl. Mech., 84(2), p. 021002), where a several-fold increase in the wrinkling stress was achieved, without a significant weight penalty, using a stiffer core adjacent to the facings. In this paper, wrinkling is analyzed in case where the facings are subject to biaxial compression and/or in-plane shear loading, and the core is arbitrary graded through the thickness. Two issues addressed are the effect of biaxial or in-plane shear loads on wrinkling stability of panels with both graded and ungraded core, and the verification that functional grading of the core remains an effective tool increasing wrinkling stability under such two-dimensional (2D) loads. As follows from the study, biaxial compression and in-plane shear cause a reduction in the wrinkling stress compared to the case of a uniaxial compression in all grading scenarios. Accordingly, even sandwich panels whose mode of failure under uniaxial compression was global buckling, the loss of strength in the facings or core crimpling may become vulnerable to wrinkling under 2D in-plane loading. It is demonstrated that a functionally graded core with the material distributed to increase the local stiffness in the interface region with the facings is effective in preventing wrinkling under arbitrary in-plane loads compared to the equal weight homogeneous core.

Influence of artificial discontinuities in concrete under compression load—A literature review

Research on load‐bearing behavior of textile reinforced concrete (TRC) elements is mostly limited on tension, bending, and shear. Only a few studies address the material behavior under compression, mostly as a side effect while studying shear or other actions. As a basis for an upcoming test program to investigate the behavior of TRC under compression, this paper gives a literature review for concrete behavior under uniaxial and biaxial compression loading on structural discontinuities, which has been observed in prestressing ducts, pipes or other regular, or irregular structural discontinuities. Furthermore, mechanical models from rock mechanics are reviewed, as rock has natural planes of weakness that seem to have a similar impact on load bearing behavior as artificial planes of weakness defined by fabric reinforcement in TRC.

면내 전단하중과 양축압축하중을 받는 선박 판부재의 이중판 설계시스템 개발

A design system for doubler reinforcement of the ship plate members subjected to in-plane shear and biaxial compressive loads was developed. This design system of doubler reinforcement on ship plate members established by design supporting system and this system was based on the buckling evaluation process of ship plate members for these in-plane loads. Each design parameters were suggested by equations as the form of influence coefficients for the doubler reinforcement subjected to the various in-plane loads including shear load. Strength of doubler plate member reinforced on the plate member could be suggested by the equivalent flat plate thickness after the consideration of corelation equations in the design system of doubler reinforcement. Level of strength recovery of ship plate members for these in-plane loads according to the local reinforcement by doubler could be suggested by use of this design system in the initial repair design stage of shipyards.

Heated slabs under biaxial compressive loading: a test set-up for the assessment of concrete sensitivity to spalling

Explosive spalling of concrete members in fire is the violent expulsion of shards from the exposed face caused by the combined effect of pressure build-up in the pores due to water vaporization and of in-plane stress induced by both external loads and thermal gradients. Spalling progression leads to the reduction of bearing cross-section and often to the direct exposure of rebars to the flames. Since established predictive models are not available yet, experimental studies appear to be the most effective means of investigation on this phenomenon. To this purpose an experimental setup has been developed for the assessment of concrete sensitivity to spalling. The specimen is a concrete slab (800 × 800 mm) with a thickness comprised between 100 and 200 mm. The bottom face is heated via a horizontal furnace, in which a propane burner is actively controlled in order to follow the prescribed fire curve. During heating, a biaxial compressive load can be applied thanks to hydraulic jacks restrained by a steel frame. Load and slab thickness can be adjusted in order to represent the mechanical conditions achieved in the hottest region of thicker concrete members such as tunnel lining segments. The setup proved to be very effective in comparing spalling sensitivity among different concrete mixes, as is often required in initial material testing for strategic infrastructures such as tunnels.

Buckling of moderately thick arbitrarily shaped plates with intermediate point supports using a simple hp-cloud method

This paper presents the simple hp-cloud meshless method for the stability analysis of moderately thick plates with various shapes subjected to uniaxial and biaxial in-plane compressive and pure shear loads. To allow the effect of transverse shear deformation on the critical buckling load of the plate, the Mindlin's plate theory is employed. Simple hp-cloud method is applied for constructing the cloud shape functions and for discretization of the domain. Shepard functions are also used for the partition of unity and complete polynomials are utilized for the enrichment functions part. The simple hp-cloud method has Kronecker delta property, so contrary to most of meshless methods the essential boundary conditions can be imposed directly. Constructing the stiffness and geometry matrices leads to an eigenvalue problem that should be solved to determine the critical buckling load of the plate. Numerical results are verified against the results reported elsewhere to illustrate the accuracy and effectiveness of the present method. To show the applications of simple hp-cloud method in the buckling analysis of moderately thick plates, local buckling coefficients of various shapes of plates, rectangular, skew, trapezoidal, triangular, circular, semi-circular, hexagonal and general shape with different boundary conditions are determined. Also, local buckling coefficients of plates with point supports and intermediate support are calculated.

Hyper-elastic modeling and mechanical behavior investigation of porous poly-D-L-lactide/nano-hydroxyapatite scaffold material

Poly-D-L-lactide/nano-hydroxyapatite (PDLLA/nano-HA) can be used as the biological scaffold material in bone tissue engineering as it can be readily made into a porous composite material with excellent performance. However, constitutive modeling for the mechanical response of porous PDLLA/nano-HA under various stress conditions has been very limited so far. In this work, four types of fundamental compressible hyper-elastic constitutive models were introduced for constitutive modeling and investigation of mechanical behaviors of porous PDLLA/nano-HA. Moreover, the unitary expressions of Cauchy stress tensor have been derived for the PDLLA/nano-HA under uniaxial compression (or stretch), biaxial compression (or stretch), pure shear and simple shear load by using the theory of continuum mechanics. The theoretical results determined from the approach based on the Ogden compressible hyper-elastic constitutive model were in good agreement with the experimental data from the uniaxial compression tests. Furthermore, this approach can also be used to predict the mechanical behaviors of the porous PDLLA/nano-HA material under the biaxial compression (or stretch), pure shear and simple shear.

Asymptotic nonlocal elasticity theory for the buckling analysis of embedded single-layered nanoplates/graphene sheets under biaxial compression

A three-dimensional (3D) asymptotic formulation is developed for the buckling analysis of simply-supported, single-layered nanoplates/graphene sheets (SLNP and SLGS) embedded in an elastic medium and under biaxial compressive loads. In the formulation, the Eringen nonlocal elasticity theory is used to capture the small length scale effect, and the interaction between the SLNP/SLGS and its surrounding medium is simulated using a Pasternak-type foundation. After performing the mathematical processes of nondimensionalization, asymptotic expansion and successive integration, we finally obtain recursive sets of governing equations for various order problems. The nonlocal classical plate theory (CPT) is derived as a first-order approximation of the 3D nonlocal elasticity theory, and the governing equations for higher-order problems retain the same differential operators as those of nonlocal CPT, although with different nonhomogeneous terms. Some accurate nonlocal elasticity solutions of the critical load parameters of simply-supported, biaxially-loaded SLNP/SLGS with and without being embedded in the elastic medium are given to demonstrate the performance of the 3D asymptotic nonlocal elasticity theory.

The Interphase Influences on the Particle-Reinforced Composites with Periodic Particle Configuration

This work improved upon an effective micromechanical method to analyze the mechanical properties of three-dimensional particle-reinforced composites (PRC) with consideration of the interfacial debonding. By incorporating the interfacial debonding model, Mises yield criterion, and failure theory, the effects of particle shape, particle volume fraction, and loading condition on the mechanical properties are studied. A comparison of simulation results obtained from the established method and published experimental data is presented. Good consistency can be found in this study. On this basis, the interfacial cohesive strength and particle shape effects on the biaxial failure strength of particle-reinforced composites with interfacial debonding were also studied. The results revealed that both interfacial strength and particle shape have significant effects on biaxial tensile failure strength. However, the different interfacial strength influence on failure envelope can hardly be discerned in biaxial compressive loading.

Shape optimization of the hole in an orthotropic plate

ABSTRACTThe exploration in this work is how to minimize the stress concentration around the edge of the hole in an orthotropic plate. The study first presents the analytical solution of the stress distribution around arbitrary holes using the complex variable method and then carries out the shape optimization using the mixed penalty function method. In the optimization process, optimal holes and stress distributions under the different factors are investigated, i.e., the loading, the Young’s modulus, and the fiber direction. Finally, we come to the conclusion that in the biaxial compressive load state, the shape and the stress are mainly affected by the loading, followed by the fiber direction and the Young’s modulus. In the pure shear condition, all three factors determine the optimum results.

Concrete under biaxial dynamic compressive loading

Abstract A concrete type C20/25 was examined under biaxial dynamic compressive loading with several stress ratios and two different loading rates (75 and 150 1/s). The question to be answered is, if the two strength enhancing effects of biaxial compressive loading and elevated strain rate overlay under this combined loading condition. For these experiments a unique biaxial Split-Hopkinson-Pressure-Bar, developed at TechnischeUniversitat Dresden, was used to load the cubic specimen with two compression pulses from two perpendicular directions, simultaneously. That means the pulses have to reach the specimen within a time span of maximum 25 μs to achieve a rising stress level in both spatial directions in the specimen. For comparison, further static uni- and biaxial trials, static-dynamic biaxial trials and dynamic uniaxial trials were conducted. After the trials, the particles of the fragmented specimens were analysed in size and shape. The results show clearly that the two examined strength increasing effects superimpose in case of a combined biaxial dynamic compressive loading, but not completely. Therefore the influence factor of each single effect was analysed, depending on the stress ratio and the strain rate. For the considered range of high loading velocities, the strain rate effect has the main influence on the strength enhancement. This effect is decreasing with a growing stress ratio, here the biaxiality gains more influence but still remains behind the strain rate effect.

Buckling characteristics and static studies of multilayered magneto-electro-elastic plate

This article deals with the buckling behaviour of multilayered magneto-electro-elastic (MEE) plate subjected to uniaxial and biaxial compressive (in-plane) loads. The constitutive equations of MEE material are used to derive a finite element (FE) formulation involving the coupling between electric, magnetic and elastic fields. The displacement field corresponding to first order shear deformation theory (FSDT) has been employed. The in-plane stress distribution within the MEE plate existing due to the enacted force is considered to be equivalent to the applied in-plane compressive load in the pre-buckling range. The same stress distribution is used to derive the potential energy functional. The non-dimensional critical buckling load is accomplished from the solution of allied linear eigenvalue problem. Influence of stacking sequence, span to thickness ratio, aspect ratio, load factor and boundary condition on critical buckling load and their corresponding mode shape is investigated. In addition, static deflection of MEE plate under the sinusoidal and the uniformly distributed load has been studied for different stacking sequences and boundary conditions.