Local Strains Theory Research Articles

Piles and lateral loads: comparison of calculation methods

Introduction. Calculation and analysis of pile resistance to loads remains to be a relevant problem in geoengineering. The design of pile foundations is currently performed using diverse analytical, empirical and numerical methods. However, the reliability of these methods remains to be a topic of interest among researchers and designers. This research paper analyses methods used for calculating the lateral-load capacity of piles in comparison with field-test data. Materials and methods. The paper dwells upon the development of reliable analytical expressions based on mathematical models of the pile–soil interaction. Main existing mathematical models of the soil environment, including the Mohr – Coulomb elastic ideal plastic model and the hardening soil model (HSM) were analysed. A particular attention was paid to a variety of factors affecting the pile–soil interaction, such as natural factors, pile types, pile sinking depth and technology, configurations of loads, as well as time-changed processes. A comparison of methods for calculating the lateral-load capacity of piles was conducted. To that end, calculations using the Mohr – Coulomb model and the local elastic strain theory (still required by building codes) were performed. High-level solid elements were used to develop and compute a finite-element pile-in-soil model in a spatial setting. Another model on the basis of parametric pile elements was designed using the MIDAS software. Results. It is established that the use of numerical calculation methods for evaluating the capacity and movements of pile foundations provides results comparable to those of field tests. These methods demonstrate a higher reliability compared to standardized analytical techniques. Conclusions. The reliability of numerical calculations of pile resistance to lateral impact is shown to be sufficiently high, thus being feasible for use in geoengineering. The use of these methods should be based on advanced non-linear soil models, such as HS, CamClay, etc.

Numerical Simulation of Fatigue Performance of Diaphragm of Large-Span Bridge Orthotropic Deck

Under traffic loads, orthotropic steel bridge slabs suffer from an obvious fatigue problem. In particular, fatigue cracking of diaphragms seriously affects application and development of orthotropic bridge slabs. In the paper, based on cracking status quo of an orthotropic deck diaphragm of a large-span bridge, experimental tests were formulated to test stress distribution states of the diaphragm. The finite element software ABAQUS was used to establish a finite element model of the orthotropic deck diaphragm; numerical simulation was conducted on the basis of the experiments. Simulation results were compared with experimental results, so correctness of the finite element model was verified. Finally, Local Strain Approach (LSA) and Theory of Critical Distance (TCD) were used to conduct life assessment of the orthotropic deck diaphragms, and applicability of two methods was discussed. In this way, a fatigue life assessment method with high accuracy and good operability was provided for fatigue life assessment of orthotropic deck diaphragms.

Assessment of brittle fracture for PUR materials using local strain energy density and theory of critical distances

Local strain energy density and theory of critical distances represent two recent approaches in assessing the brittle fracture of cracked and notched components. Experimental validation of these methods was mainly conducted on materials with brittle behaviour (ceramics and PMMA). In this paper the applicability of these methods to another class of plastic materials, i.e. rigid polyurethanes of different densities, was investigated. For this, two types of specimens, single edge U-notched and asymmetric semi-circular bend cracked specimens, were experimentally investigated at room temperature and considered for theoretical predictions. Both criteria provide reasonable predictions for the fracture load.

Yield surfaces of composite media

Yield surfaces with different probabilities of the appearance of plastic strains are obtained for a composite material reinforced in one and two directions. These surfaces (local yield surface density) are obtained using the local strains theory and on the assumption of the inextensibility of the composition material in the directions of reinforcement. The theoretically obtained limit surfaces are shown to be in satisfactory agreement with the experimental data.

Renormalization of the magnon-phonon interaction in HCP ferromagnets

A systematic scheme, based upon Roth linearization of many-body equations of motion (see abstr. A37193 of 1968) is applied to decoupling of the coupled spin-lattice equations of motion of magnetostrictive HCP ferromagnets. Magnetoelastic coupling is characterized by the same microscopic Hamiltonian that gives rise to macroscopic magnetostrictive properties, and magnon-phonon coupling is expressed in terms of macroscopic magnetostriction parameters. Both one- and two-ion magnetoelastic coupling is included through the Evenson and Liu local-strain theory (see abstr. A24313 of 1969). The magnitude of the splitting of magnon and phonon dispersion curves is proportional to appropriate magnetostriction constants divided by the square root of the magnetization, and Jensen's results (see abstr. A13393 of 1972) are recovered in the zero temperature limit.

Investigation of loading surfaces in the local strains theory

Variants of the application of isotropic, kinematic, and combined strain hardening in the local strains theory are analyzed. The subsequent yield surfaces are determined for biaxial tension and combined torsion and tension and the results are compared with experiment. The theory predicts convex yield surfaces and the dependence of the angle (corner point) of the yield surface at the loading point on the loading path. The expediency of employing the concept of a plastic strain probability factor is demonstrated.

Yield surfaces in local strain theory

The initial yield surfaces for biaxial tension and combined tension and torsion are determined on the basis of the local strain theory. The limit surfaces of the resultant stress on a local plane in tension (torsion) are obtained. A plastic strain probability factor is introduced and its values are calculated for various loading paths.

Problems of the theory of deformation of polymeric materials under complex loading

Research on problems of the theory of deformation of polymeric materials under complex loading based on a synthesis of creep theories and the local strains theory is reviewed.

Variants of the local strains theory

By means of the proposed new variants of the local strains theory it is possible to solve a broad class of complex loading problems for initially isotropic materials. The basic equations for a series of variants of incompressible and compressible materials are derived. The author investigates the possibility of using the relations obtained to solve complex loading problems for materials with irreversible plastic strains or with different physical reversible or irreversible creep relations depending on the loading path.

Effect of loading history on changes in the characteristic Angles and the length of the retardation trace

The local strains theory and the theory of small elastoplastic strains are used to determine the values of the components of the plastic strain vector e{e1, e2} for nonlinearity n=3 in five-dimensional Euclidean space in the case of complex loading along a two-segment broken line, when both tensile and compressive stresses are present in each loading stage. The relation between the vectors e, and S and the tangents to the deformation and loading trajectories are examined. Values of the retardation trace are obtained in terms of the loading history. Numerical results have been derived with the aid of a BESM-3M computer.

Relation between the vectors ? and S for a plastic material with a sequence of ray-like loading paths

Two different complex loading paths are investigated in stress space — longitudinal tension with subsequent total unloading and reloading in transverse tension or compression. For these loading paths the local strains theory [4] is used to determine the values of the components of the strain vector Э{Э1, Э2} in five-dimensional space for nonlinearities n=3 and n=5 together with the components of the stress vector S{S1, S2}. A relation between the vectors Э and S is established in terms of the given loading parameter k.

Model of viscoplasticity in the local strains theory

A model of viscoplasticity is proposed within the framework of the local strains theory. The proposed model, which applies to a small local area, takes into account the interaction of rheonomic and plastic strains, the Bauschinger effect, and recovery of the material after unloading.

Physical relations for an orthotropic material in the local strains theory

Compressible and incompressible orthotropic materials are investigated. A method of constructing variants of the local strains theory describing the deformation properties of an orthotropic material is developed on the basis of the concept of an elastic potential.

Retardation trace in tension with subsequent compression in the transverse direction

The local strains theory is employed to determine the strain components e1 and e2 in five-dimensional space in the case of tension with subsequent compression at nonlinearities n=3 and n=5. The relations between the vectors e and S and the tangents to the loading and deformation trajectories and between the moduli e of the strain for complex and simple loading are considered.

Development of the local strain function and the slip function in statistical theories of plasticity

The development of the concept of a local strain function is examined. The principal forms and methods of approximation of the local strain function are described and compared. A generalization of the local strains theory in differential form is proposed. Yosimura's criticism of the slip theory is shown to be invalid. Certain aspects of the local strains and slip theories are compared.

Relation between the vectors E and S for a plastic material in succesive biaxial tension

The local strains theory is used to determine the values of the components of the vector E{E1, E2} in five-dimensional space for a material subjected to successive biaxial tension at degrees of nonlinearity n=3 and n=5. The relation between the vectors E and S and the tangents to the loading and strain trajectories is considered together with the relation between the moduli E of the strains for simple and complex loading.

Effect of initial imperfections on the equilibrium states of elastoplastic sheets

The local strains theory provides the basis for an analysis of the equilibrium states of initially imperfect compressed sheets of elastoplastic strain-hardening material. In the presence of initial imperfections of the sheet geometry there is no clearly expressed limit at which the deflection increases sharply. Such a limit, corresponding to the critical stress in the linear theory of plates and shells, emerges as the initial imperfection parameter tends to zero. The difference between the total transverse deflections of the initially imperfect and ideal sheets reaches a maximum at the stress level corresponding to this limit. Beyond this limit the initial imperfection effect is important at leastic and weakly developed plastic strains but diminishes considerably as the plastic strain level develops.

Analysis of possible combinations of local stresses in local strain theory

In determining the strain tensor eij instead of all the components of the local stress deviator, it is possible to use only the shear stress σxz acting on a small local area. This fact makes it easy to establish the incremental loading conditions in solving complex loading problems for a plastic material. It is shown that in the local strain theory, distinct from the deformation theory, at degrees of nonlinearity n>3 the effect of the third, as well as the second, invariant of the stress deviator is taken into account.

Complex loading of a polymer material with nonlinear creep

The nonlinear tensor stress, strain, and time relations for a memory-type medium under complex loading are examined using degenerate kernels. The basic expressions for simple loading and the material parameters were determined in [5]. The local strains theory is used to find expressions for the strain components in the presence of stepwise complex variation of the stress components, and these expressions are shown to be in satisfactory agreement with the experimental data for high-density polyethylene.

Torsional mode of buckling in nonlinear creep with allowance for the difference in loading and unloading laws

The torsional mode of creep buckling of a thin-walled element of material with nonlinear creep is investigated. The local strains theory is used for the physical relations.