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We propose an implicit constitutive relationship for viscoelastic solids with strain rate dependence, where one of the main variables governing the constitution is the density of the body. In the instance of the body being isotropic, an explicit expression is obtained for the constitutive relationship, which is then approximated when the displacement gradient and the velocity gradient are small. The constitutive relationship is further simplified by assuming that it is linear in the stress, strain, and strain rate. Using this simplified constitutive relationship, we solve some boundary value problems. [ABSTRACT FROM AUTHOR]

Many constitutive models have been proposed to describe the mechanical behavior of cemented soil at large strains (above 1%). Less attention has been paid to the highly nonlinear stress–strain behavior at small strains, which are important for accurately analyzing the serviceability of many infrastructures. In this study, a bounding surface model was developed to simulate cemented soil behavior from small to large strains. Some new formulations were proposed to improve the modeling of small-strain behavior, including (1) the elastic shear modulus over a wide range of stress conditions, and (2) the nonlinear degradation of bonding strength (pb) with damage strain (εd) in the lnpb−εd plane. The new model was applied to simulate drained and undrained triaxial tests on cemented soils at different cement contents and confining pressures. Comparisons between the measured and computed results show that the new model can well capture many important aspects of cemented soil behavior, especially the elastic shear modulus at very small strains and stiffness degradation at small strains. Furthermore, the model gives a good simulation of strain softening/hardening and dilatancy/contraction during shearing under various confining pressure and void ratio conditions. [ABSTRACT FROM AUTHOR]

The simultaneously iterative procedure proposed by the authors is applied to elastoplastic problems with damage. From the definition of a coupled problem of the weak form of the equilibrium equation and the constraint conditions for plastic yielding and damage evolution at every material point, the authors develop a numerical procedure based on the block Newton method to solve them with simultaneous linearization. In the proposed block Newton method, the consistent tangent can be derived algebraically, and the internal variables, which consist of the plastic parameter and the damage parameter, can also be updated algebraically without any local iterative calculations. Furthermore, the pseudo-stress for the residuals of both the yield condition and the damage evolution law is incorporated into the linearized weak form of the equilibrium equation. Thus, the proposed approach allows us to simultaneously reduce the residuals in the coupled boundary value problems. Some numerical examples illustrate the validity and effectiveness of the presented procedure for elastoplastic problems with Lemaitre damage model.

A theory for two-dimensional (2D) beams is presented for the case of considering new constitutive equations, wherein the linearized (infinitesimal) strain tensor is assumed to be a nonlinear function of the Cauchy stress tensor. An incremental formulation is developed to solve numerically the resultant equations. Three constitutive equations for elastic bodies are considered: a model wherein we have strain-limiting behavior, a nonlinear model for rock, and a bimodular constitutive equation for rock (which can also be considered as a nonlinear model for rock). Two boundary value problems are studied: the deformation of a cantilever beam with a point load, and a three-point beam with a point load applied on the middle. The numerical results are compared with the predictions of the classical theory for beams for the case of linearized elastic solids. The results for the stresses can be notoriously different, when comparing the predictions of the nonlinear constitutive equations with the results obtained using the linearized theory of elasticity. [ABSTRACT FROM AUTHOR]

The accumulation of waste tires is a global problem related to natural resources and the environment. The storage or burning of tires causes toxic chemicals to seep into the surrounding environment, which poses a serious ecological threat. Many previous studies have shown that waste tires can be used in geotechnical engineering. It was found that rubber reinforcement can increase the plasticity of sandy soil and improve its shear strength. It can control pore water pressure accumulation and improve dynamic properties. For cohesive soils, rubber additives can reduce dry density and improve compressive strength and soil stability. When mixed with soil with optimum content, waste tires can reduce various adverse effects of waste tire accumulation on the environment. The application of rubber has also a good impact on environmental protection and the promotion of “green design”. This paper presents the dynamic properties (shear modulus and damping ratio) of the RCARTW mixture for small, medium, and large ranges of shear strain levels (from about 1.510-4% to 1.310-2%). All specimens are constructed using different percentages of granulated tire rubber and concrete aggregate from curb crushing. A series of laboratory tests, resonant, and damping, are performed in the resonant column apparatus. The maximum shear modulus and minimum damping ratio are presented with the percentage of granulated rubber. The normalization is also applied to the Gmodulus and Dratio data set. Furthermore, a comparison is made between the results obtained for the tested geocomposites and a mixture of pure RCA.

A numerical and an empirical method for calculating nonlinear load-settlement curves for shallow foundations on sand are examined and used in a new methodology. Both methods have merits and drawbacks. The drawbacks are overcome by the methodology proposed and verified in the paper. This methodology combines the merits of each method. For this purpose, a modification of the empirical method is proposed that accounts for the finite initial soil stiffness at very small strains. Computer programs with sophisticated nonlinear stress-strain relationships, such as Hardening Soil Small in Plaxis 2D, which are versatile in solving complex foundation problems, can cover strains from very small to large. When the foundation soil is layered, it is proposed to fit such a numerical load-settlement curve against the modified empirical relationship for each sand layer separately. This requires cone penetration tests, measurements of the shear wave velocity, and basic laboratory tests. The methodology is described and applied at two locations where load tests on footings were carried out. At one location there was a top layer of clay, which was also taken into account. The results of the application of the proposed methodology are very good.

Experimental data for the strains and stresses is obtained for some classes of rock, for the compression and tension of a cylindrical sample without lateral loads, and for the triaxial load of a bar. A nonlinear constitutive equation is proposed to fit the data, wherein the infinitesimal strain tensor is assumed to be a nonlinear function of the stress tensor. The constitutive equation requires two sets of materials constants, namely the Young’s modulus and Poisson ratio in tension and compression. Some boundary value problems are studied to see the predictions of the above constitutive theory.

In this article, the authors formulate elastoplastic problems as a coupled problem of the equilibrium equation and the yield condition at each material point, and develop a numerical procedure based on the block Newton method to solve the overall structure using the finite element discretization. For the integration of stress, the backward difference scheme is employed. In the conventional return mapping algorithm, the algorithmic tangent moduli are derived analytically so that it is consistent with local iterative calculation to determine internal variables. On the other hand, in the proposed block Newton method, the tangent moduli can be obtained algebraically by eliminating the internal variables, and the internal variables are also updated algebraically without local iterative calculation. The residual of the yield condition is incorporated into the linearized equilibrium equation. The proposed approach enables the errors of the equilibrium equation and the yield condition to decrease simultaneously. Some numerical examples show the validity and effectiveness of the proposed approach by comparing the results of the proposed approach with those of the conventional return mapping algorithm. [ABSTRACT FROM AUTHOR]

In this manuscript two BMO estimates are obtained, one for Linear Elasticity and one for Nonlinear Elasticity. It is first shown that the BMO-seminorm of the gradient of a vector-valued mapping is bounded above by a constant times the BMO-seminorm of the symmetric part of its gradient, that is, a Korn inequality in BMO. The uniqueness of equilibrium for a finite deformation whose principal stresses are everywhere nonnegative is then considered. It is shown that when the second variation of the energy, when considered as a function of the strain, is uniformly positive definite at such an equilibrium solution, then there is a BMO-neighborhood in strain space where there are no other equilibrium solutions. [ABSTRACT FROM AUTHOR]

The problem is a continuation of the research conducted at the University of Warmia and Mazury in Olsztyn, Institute of Building Engineering. It concerns the development of methods for the interpretation of the shear modulus measurements based on the tests conducted on a torsional shear (TS) apparatus. The issue has significant importance in determining the deformation parameters, essential to perform numerical simulations of the interaction between a geotechnical structure and the subsoil. The purpose of this study was to conduct a comparative analysis of the various methods of interpretation of research results based on direct and reverse analysis, as well as automated classification of the first cycle of the relationship between the shear stress and the shear strain components obtained from the TS test. The methodology for verification of the presented interpretative methods consists in carrying out a series of laboratory tests on non-cohesive and cohesive samples of different granulation and state parameters. The course of the research includes the following steps: elaboration of the granulometric composition of several samples of soil, determination of soil index properties and execution of TS tests. Various methods of interpretation of obtained results were taken into account, in addition to conducting a comparative analysis. The study used a non-standard interpretation approach consisting of analysing one-fourth of the hysteresis loop of the first load–unload cycle of the tested samples. The obtained results confirmed the hypothesis that it is possible to estimate the degradation value of the shear modulus based on a part of the TS test results carried out under quasi-monotonic load conditions. The proposed methods of interpreting test results have confirmed their high usefulness, which is devoid of the uncertainty associated with standardised resonant column/TS testing.

A numerical and an empirical method for calculating nonlinear load-settlement curves for shallow foundations on sand are examined and used in a new methodology. Both methods have merits and drawbacks. The drawbacks are overcome by the methodology proposed and verified in the paper. This methodology combines the merits of each method. For this purpose, a modification of the empirical method is proposed that accounts for the finite initial soil stiffness at very small strains. Computer programs with sophisticated nonlinear stress-strain relationships, such as Hardening Soil Small in Plaxis 2D, which are versatile in solving complex foundation problems, can cover strains from very small to large. When the foundation soil is layered, it is proposed to fit such a numerical load-settlement curve against the modified empirical relationship for each sand layer separately. This requires cone penetration tests, measurements of the shear wave velocity, and basic laboratory tests. The methodology is described and applied at two locations where load tests on footings were carried out. At one location there was a top layer of clay, which was also taken into account. The results of the application of the proposed methodology are very good. [ABSTRACT FROM AUTHOR]

A numerical and an empirical method for calculating nonlinear load-settlement curves for shallow foundations on sand are examined and used in a new methodology. Both methods have merits and drawbacks. The drawbacks are overcome by the methodology proposed and verified in the paper. This methodology combines the merits of each method. For this purpose, a modification of the empirical method is proposed that accounts for the finite initial soil stiffness at very small strains. Computer programs with sophisticated nonlinear stress-strain relationships, such as Hardening Soil Small in Plaxis 2D, which are versatile in solving complex foundation problems, can cover strains from very small to large. When the foundation soil is layered, it is proposed to fit such a numerical load-settlement curve against the modified empirical relationship for each sand layer separately. This requires cone penetration tests, measurements of the shear wave velocity, and basic laboratory tests. The methodology is described and applied at two locations where load tests on footings were carried out. At one location there was a top layer of clay, which was also taken into account. The results of the application of the proposed methodology are very good. [ABSTRACT FROM AUTHOR]

In this paper we study the response of bodies that are residually stressed within the context of a new class of constitutive relations, wherein the strains are assumed to be functions of the stresses. Such bodies are said to have residual stresses if there are stresses within the bodies even though the bodies are unstrained in the configuration of interest in the absence of external traction. Problems within the context of the norm of the gradient of the displacement field being small are considered, with regard to the determination of the residual stresses in an anisotropic cylindrical annulus with two preferred directions, and the nature of residual stresses within an anisotropic slab. The residual stresses in a body that is subject to incremental stresses are also studied. [ABSTRACT FROM AUTHOR]

Summary: We present a computational framework for the simulation of J2‐elastic/plastic materials in complex geometries based on simple piecewise linear finite elements on tetrahedral grids. We avoid spurious numerical instabilities by means of a specific stabilization method of the variational multiscale kind. Specifically, we introduce the concept of subgrid‐scale displacements, velocities, and pressures, approximated as functions of the governing equation residuals. The subgrid‐scale displacements/velocities are scaled using an effective (tangent) elastoplastic shear modulus, and we demonstrate the beneficial effects of introducing a subgrid‐scale pressure in the plastic regime. We provide proofs of stability and convergence of the proposed algorithms. These methods are initially presented in the context of static computations and then extended to the case of dynamics, where we demonstrate that, in general, naïve extensions of stabilized methods developed initially for static computations seem not effective. We conclude by proposing a dynamic version of the stabilizing mechanisms, which obviates this problematic issue. In its final form, the proposed approach is simple and efficient, as it requires only minimal additional computational and storage cost with respect to a standard finite element relying on a piecewise linear approximation of the displacement field. [ABSTRACT FROM AUTHOR]

The origin of global deformations in granular media stems from various concurrent mechanisms at the microscopic scale. Recent micromechanical studies have pointed out inadequacies of traditional elasto-plastic theories with elastic nucleus to describe such materials. In addition, the fundamentals of additive decomposition of global strain into mechanism-specific contributions have been questioned from a multiscale point of view due to appearance of emergent nonlinearities in the global response. The current study addresses the decomposability of strain and the existence of an elastic zone by systematically scrutinizing the energy aspects of granular deformation under quasi-static loading regime. The results show that the assumption of an exclusively elastic nucleus can potentially introduce non-negligible errors, even at strain ranges below 10 − 4 . By relaxing commonly used assumptions which are often restrictive, a new constitutive model for elastic deformations in granular materials is developed to capture material response as a function of microstructure of the granular assembly. After verification through comparisons with discrete element simulations, the model has been used to investigate the decomposability of strain. The results demonstrate that the elastic strain component can only be extracted through numerical simulations where the dissipative mechanisms are “artificially” prohibited, which relegates the strain decomposition to an abstract concept. [ABSTRACT FROM AUTHOR]

The problem of deformation of a horizontal plane layer of a compressible material is solved in the framework of the theory of small strains. The upper boundary of the layer is under the action of shear and compressing loads, and the no-slip condition is satisfied on the lower boundary of the layer. The loads increase in absolute value with time, then become constant, and then decrease to zero. Various plasticity conditions are consideredwith regard to the material compressibility, namely, the Coulomb-Mohr plasticity condition, the von Mises-Schleicher plasticity condition, and the same conditions with the viscous properties of the material taken into account. To solve the system of partial differential equations for the components of irreversible strains, a finite-difference scheme is developed for a spatial domain increasing with time. The laws of motion of elastoplastic boundaries are presented, the stresses, strains, rates of strain, and displacements are calculated, and the residual stresses and strains are found. [ABSTRACT FROM AUTHOR]

A one-dimensional nonlinear homogeneous isotropic thermoelastic model with an elastic heat flow at low temperatures and small strains is analyzed using the method of weakly nonlinear asymptotics. For such a model, both the free energy and the heat flux vector depend not only on the absolute temperature and strain tensor but also on an elastic heat flow that satisfies an evolution equation. The governing equations are reduced to a matrix partial differential equations, and the associated Cauchy problem with a weakly perturbed initial condition is solved. The solution is given in the form of a power series with respect to a small parameter, the coefficients of which are functions of a slow variable that satisfy a system of nonlinear second-order ordinary differential transport equations. A family of closed-form solutions to the transport equations is obtained. For a particular Cauchy problem in which the initial data are generated by a closed-form solution to the transport equations, the asymptotic solution in the form of a sum of four traveling thermoelastic waves admitting blow-up amplitudes is presented. [ABSTRACT FROM PUBLISHER]

In this paper we generalize the recent implicit models that have been put into place to describe the elastic response of bodies when thermal effects come into play. The implicit constitutive relations for thermoelastic response presented here provide a very natural way to overcome a serious problem associated with the celebrated model due to Fourier, namely infinite speed of the propagation of temperature. We also study some boundary value problems within the context of the implicit equations that we have developed. We carry out a linearization based on the classical assumption that the displacement gradient is small and obtain constitutive relations that allow the linearized strain to be a non-linear function of the stress and temperature. [ABSTRACT FROM AUTHOR]

Microscale mechanisms involving the loss and gain of contacts in granular materials are non-dissipative in nature, but yet irreversible. This is because the creation or disintegration of contacts as an instantaneous event does not pertain to any global deformation of the granular system. Such a contact loss and gain regime is intriguing and has also been shown to play a significant role in altering the internal structure of granular materials, even at the relatively small strain range where irreversibilities can exist within deformation domains often attributed to elasticity. The current study offers a coherent decomposition of mechanisms affecting the microstructure of granular media, and subsequently investigates the contribution of non-dissipative/irreversible mechanisms to global structural rearrangement. An analytical scheme is put forward that relates the directional variations in contact losses and gains to the probability distributions of contact forces and interparticle separating distance, respectively. Thus, microstructural evolution can be statistically computed in terms of two key microvariables, i.e. coordination number and fabric anisotropy, and verified through 2D Discrete Element Method (DEM) simulations. The analytical scheme presented here provides an accurate description of microvariable evolution laws that are needed to formulate micromechanical constitutive models for granular materials. [ABSTRACT FROM AUTHOR]

Two different methods, power spinning and annealing (PSA), quenching and power spinning followed by annealing (QPSA), for manufacturing the cylindrical parts with ultrafine-grained (UFG) structure were reviewed, the dislocation density and microstructural evolution during the two different processes of PSA and QPSA were further studied. The results show that the required strains for obtaining the UFG structure by power spinning is only 0.92 when the initial microstructure of the material is in the phase of lath martensite. The dislocation density and storage energy are increased to 10 times that of the blank after quenching and power spinning and decreased to the level of the blank after recrystallization annealing. Microstructures with fine grain size after quenching, storage energy of 1.8 × 105 kJ/m3 obtained after power spinning and second phase particle with nano-scale precipitated during annealing are the necessary formation conditions for manufacturing the cylindrical parts with UFG structure based on small strains. Compared with the original tubular blank, the mechanical properties of the spun parts with UFG structure improves significantly. The tensile strength and hardness of the spun parts manufactured by QPSA method is 815 MPa and 305 HV, respectively, and the elongation is 17.5%.

In this work, a recently proposed quadratic NURBS-based solid-shell element based on the Assumed Natural Strain (ANS) method is applied in the analysis of shell-like structures in the geometrical nonlinear regime, together with small strain plasticity. The proposed formulation is based on the additive split of the Green–Lagrange strain tensor, leading to a straightforward implementation of the nonlinear kinematics and to the introduction of a corotational coordinate system, used to integrate the constitutive law, ensuring incremental objectivity. Since the proposed approach is based on Updated Lagrangian formulation combined with a corotational coordinate system, the extension of the ANS methodology is straightforward. Well-known benchmark tests are employed to assess the performance of the proposed formulation and to establish a detailed comparison with the formulations available in the literature. The results indicate that the proposed solid-shell approach based on the NURBS ANS methodology presents good predictability characteristics in the analysis of elasto-plastic thin-shell structures subjected to large deformations. [ABSTRACT FROM AUTHOR]

Highlights: [•] Existence of spurious modes in finite elements with incompatible modes. [•] Geometrically nonlinear displacements with small displacements and strains are considered. [•] An analytical derivation is presented. [•] Numerical examples give further insights. [Copyright &y& Elsevier]

The compatibility equation for the Cauchy-Green tensor field (squared tensor of pure extensionwith respect to the reference configuration) is directly derived from the well-known relation expressing this tensor via the vector field determining the mapping (transformation) of the reference configuration into the actual one. The derivation is based on the use of the apparatus of coordinatefree tensor calculus and does not apply any notions and relations of Riemannian geometry at all. The method is illustrated by deriving the well-known compatibility equation for small strains. It is shown that when the obtained compatibility equation for finite strains is linearized, it becomes the compatibility equation for small strains which indirectly confirms its correctness. [ABSTRACT FROM AUTHOR]

Abstract: Tensile test curves of an austenitic stainless steel (AISI 316L) are described through the Voce equation in combination with the kinetic approach to strain hardening analysis proposed by Kocks and Mecking (KM) at temperatures ranging from 700 to 1000°C with strain rates between 10−2 and 10−5 s−1. The KM approach to strain hardening analysis is used to find the Voce parameters (saturation stress σ V , relaxation strain ε C , back-extrapolated flow stress to zero strain σ o ) from the strain hardening rate dσ/dε vs. the flow stress σ. The obtained Voce equations can well describe the flow curves only at large strains in Stage III of strain hardening, while a significant discrepancy occurs at small strains. In order to reduce this discrepancy an improved KM approach is here proposed. The original KM approach assumes that in Stage III of strain hardening the mean free path of mobile dislocations Λ is defined as with β constant and ρ the total dislocation density. Λ, and in turn β, are linked to the dislocation cell-pattern typical of Stage III. The proposed improvement of the KM approach consists of assuming that β is not constant at small strains, where dislocations are not organised in cell-pattern, but homogeneously distributed in the material. Based on TEM observations reporting dislocation distributions at small and at high strains, it is proposed that β varies from an initial value at small strains to achieve at high strains the equilibrium value predicted by the original KM approach in Stage III of strain hardening. This assumption provides very good modelling flow curves also at small strains. [Copyright &y& Elsevier]

This paper describes the results of triaxial compression tests carried out at effective cell pressures ranging from 12.5 to 100 kPa to investigate the influence of fabric structure on the yield and failure of intact Reigate silver sand. In some of the tests, a digital image-based technique was used to determine the instant of onset of strain localisation, and the distribution of strain localisations within the specimen as overall deformation progressed. Comparative tests on intact and reconstituted specimens showed that fabric structure in the intact material allows the mobilisation of stress ratios close to peak before the onset of dilation, and increases the shear modulus at a given effective cell pressure and strain. Localisation was found to start at or after the onset of dilation, with a tendency to delay at increasing effective cell pressure. More localised deformation was observed at low effective cell pressures. Consistency between the critical state strengths of intact and reconstituted specimens is demonstrated, provided that the effect of shear band geometry is taken into account in stress analysis. [ABSTRACT FROM AUTHOR]

The d-dimensional thermo-visco-elasticity system for Kelvin-Voigt-type materials at small strains with a general nonlinear coupling is considered. Thermodynamical consistency leads to a heat capacity dependent both on temperature and on the strain. Using higher-gradient theory, namely the concept of so-called second-grade non-simple materials (or of hyper-stresses), existence of a weak solution to a system arising after an enthalpy-type transformation is proved by a suitably regularized Rothe method, fine a-priori estimates for the temperature gradient performed for the coupled system, and a subsequent limit passage. [ABSTRACT FROM AUTHOR]

A geometrically nonlinear formulation to analyze structures in the hypotheses of large displacements and rotations and small strains is presented. In this formulation, applied to low-order elements and based on the total Lagrangian kinematics, the use of the rotation matrices is bypassed. A selectively based definition of the strain tensor, used in order to avoid shear-locking problems, is effected by the linear definition of deformations because it is element reference system independent. In addition, complex manipulations required to obtain conservative descriptions and well-posed transformation matrices are avoided. Numerical tests have been carried out to validate the developed technique both in the statical and in the quasi-statical context. [ABSTRACT FROM AUTHOR]

Viscoelastic solids in Kelvin-Voigt rheology at small strains exhibiting also stress-driven Prandtl-Reuss perfect plasticity are considered quasistatic (i.e. inertia neglected) and coupled with heat-transfer equation through dissipative heat production by viscoplastic effects and through thermal expansion and corresponding adiabatic effects. Enthalpy transformation is used and existence of a weak solution is proved by an implicit suitably regularized time discretisation. [ABSTRACT FROM AUTHOR]

A technique for pore pressure measurement in triaxial tests of clay soils under small strains is considered. The essential role of the following methodic aspects of the measurements is shown, namely, the effect of temperature on the pore pressure under measurement, its difference in the central part and on the ends, and the dependence of pore pressure on strain rate. [ABSTRACT FROM AUTHOR]

Abstract: Some simple boundary value problems are studied, for a new class of elastic materials, wherein deformations are expressed as non-linear functions of the stresses. Problems involving ‘homogeneous’ stress distributions and one-dimensional stress distributions are considered. For such problems, deformations are calculated corresponding to the assumed stress distributions. In some of the situations, it is found that non-unique solutions are possible. Interestingly, non-monotonic response of the deformation is possible corresponding to monotonic increase in loading. For a subclass of models, the strain–stress relationship leads to a pronounced strain-gradient concentration domain in the body in that the strains increase tremendously with the stress for small range of the stress (or put differently, the gradient of the strain with respect to the stress is very large in a narrow domain), and they remain practically constant as the stress increases further. Most importantly, we find that for a large subclass of the models considered, the strain remains bounded as the stresses become arbitrarily large, an impossibility in the case of the classical linearized elastic model. This last result has relevance to important problems in which singularities in stresses develop, such as fracture mechanics and other problems involving the application of concentrated loads. [ABSTRACT FROM AUTHOR]

Abstract: A geometrically nonlinear formulation to analyse structures in the hypotheses of large displacements and rotations and small strains is presented. In this formulation, applied to low-order elements and based on the total Lagrangian kinematics, the use of the rotation matrices is bypassed. A selective based definition of the strain tensor, used in order to avoid shear-locking problems, is effected by the linear definition of deformations because it is element reference system independent. In addition, complex manipulations required to obtain conservative descriptions and well-posed transformation matrices are avoided. Numerical tests have been carried out to validate the developed technique both in the statical and in the dynamical context. [ABSTRACT FROM AUTHOR]

The one-dimensional equations that describe the geometrically nonlinear deformation with arbitrary displacements and small strains are constructed for the planar laminated curved beams based on the Timoshenko model taking into account transverse compression. The equations are based on the relations of the classical nonlinear theory of elasticity for the case of realizing plane stressed state in a beam and also on the similar relations previously proposed in the consistent variant. Based on the equations constructed, we form the linearized equations of the neutral equilibrium of beams that enables investigating all possible buckling modes under the action of conservative forces and a stationary temperature field. [ABSTRACT FROM AUTHOR]

The intensive use of urban subsoil and the evolution of technical regulations require to develop new tools to calculate the displacements caused by the construction of new structures. The performance of usual calculation methods is often inadequate, because they have been developed mainly for the analysis of the failure behaviour of structures; thus in these models, the soil behaviour for small strains is not represented in a realistic manner. The soil shear modulus exhibits significant variations between the field of very small strains and the field of usual deformations next to geotechnical structures during their construction. Experience shows that the displacements of a structure can not be correctly evaluated without taking into account these variations. In this context, a Mohr-Coulomb model has been implemented in Flac2D code in explicit finite difference method to calculate real structure for which soil data as well as displacements and efforts measurements were available. The study of this case confirms the interest of using a Mohr-Coulomb constitutive law to produce calculation results similar to the strain and displacement patterns of real structures. [ABSTRACT FROM AUTHOR]

In this paper, we consider the unilateral frictional contact problem of a hyperelastic body in the case of large displacements and small strains. In order to retain the linear elasticity framework, we decompose the deformation into a large global rotation and a small elastic displacement. This corotational approach is combined with a primal-dual active set strategy to tackle the contact problem. The resulting algorithm preserves both energy and angular momentum. [ABSTRACT FROM AUTHOR]

Standard nonlinear schemes for the the simulation of elastodynamic problems have several shortcomings when considering high-speed rotations. To tackle these problems, we use a corotational framework and a corresponding specific linearization to design new energy-conserving numerical schemes. In the two-dimensional case, an algorithm preserving also angular momentum is presented. The existence of a solution for the fully discrete setting of this algorithm is established. Numerical results illustrate the flexibility and efficiency of the proposed algorithms. [ABSTRACT FROM AUTHOR]

The surface-buckling problem for elastic transversely isotropic laminates is solved using the three-dimensional linearized theory of stability with the assumption of small prebuckling strains. The influence of the orientation of the isotropy axis on the critical parameters of the problem and the equilibrium state of the material is studied analytically and numerically [ABSTRACT FROM AUTHOR]

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The elongation of a ferroelastic material sample (whose initial shape is a sphere or an ellipsoid of revolution) under the action of an external magnetic field is studied in an in approximation of small strains. For a sphere, there is a classical estimate obtained under the assumption that elongating in the direction of the field, it becomes a spheroid and the stress and strain fields remain uniform. In the present calculation, it is assumed that the body is an ellipsoid (a sphere in a particular case) only in the absence of an external field; the shape of the sample in the presence of a field is not specified in advance but is found from the condition of balance of surface forces (elastic and magnetic). For the spherical case, the problem is solved exactly: it is shown, that the contour of the deformed body is described by a third-order algebraic equation. The case where the initial configuration is an ellipsoid of revolution is studied numerically. It is shown that in all versions, the refined solution leads to an appreciable increase in the elongation of the sample compared to the classical estimate. [ABSTRACT FROM AUTHOR]

The presented method to identify material parameters for inelastic deformation laws is based on the numerical analysis of inhomogeneous stress and strain fields received from suitable experiments. Tensile and bending tests were carried out to obtain elastic and hardening parameters. The deformation law for small elasto-plastic strains is presented as a system of nonlinear differential and algebraic equations (DAE) consisting of the stress–strain relation, evolution equations for the internal variables and the yield condition. Different rules for the evolution equations of isotropic, kinematic and distorsional hardening are proposed. The DAE are discretized using an implicit Euler method, and the resulting system of nonlinear algebraic equations is solved using the Newton method. Deterministic optimization procedures are preferred to identify material parameters from a least-squares functional of numerical and measured comparative quantities. The gradient of the objective function was calculated using a semianalytical sensitivity analysis. Due to measurement errors, the optimal sets of material parameters are non unique. The approximate estimation of confidence regions and the calculation of correlation coefficients is presented. The results of several optimization processes for material parameters of elasto-plastic deformation laws show a good agreement between measured and calculated values, but they show also problems which may occur if systematic errors will not be recognized and deleted. [ABSTRACT FROM AUTHOR]

• The valorization of local material satisfies the design standards of Saharan roads. • Significant increase in stiffness according to suction. • The elastic modulus increases by a factor of 10 between wet and dry states. • Capillary cohesion is strongly influenced by the variation in water content. In the context of valorizing local materials at Saharan region for road constructions, a mixture composed of 65% tuff and 35% dune sand (named 65T35DS) was previously studied. The 65T35DS was shown to have the optimum geotechnical and mechanical properties. As an extension, this study consists in investigating the behavior of the 65T35DS mixture under coupled hydro-mechanical loadings. Suction-controlled drying-wetting tests were performed on the 65T35DS statically compacted at the modified Proctor optimum (MPO) state. A series of small-strain cyclic triaxial tests under constant water content condition was then followed. Key findings of this paper include i) the 65T35DS prepared at MPO state is able to resist severe drought condition without inducing significant shrinkage. However, it swells during wetting and the swelling indices are quantified by correlations; ii) the elastic modulus under small-strains is governed by suction and the applied confining stress. The effect of confining stress becomes dominant at lower suction level and negligible when suction increases; iii) at failure, the apparent cohesion drops quickly on the dry side of the MPO, on wet side, it decreases a little. The apparent friction angle decreases for the specimens with water content larger than 5.5%, i.e. w MPO – 5. The studied mixture satisfies the design standards of Saharan pavements and seems to be a good compromise for the valorization of local materials. [ABSTRACT FROM AUTHOR]

• Development of a new pressuremeter apparatus equipped with a Hall Effect sensor. • The new pressuremeter helps to have richer information concerning small strains. • The device is different from the conventional by a deformation measurement system. • Interpretation of results indicates mainly the degree of accuracy of the device. Soil characterization plays a key role in the construction of various civil engineering infrastructures. For the purpose of developing a geotechnical design model, it is essential first to describe the behavior of natural soil masses before proceeding to the calculation of a structure. The use of numerical modeling for solving soil-structure interaction problems is a crucial prerequisite; these problems can be solved properly just by measurement of small-strain stiffness and the stiffness degradation curve of soils. To meet these needs, the present paper starts by introducing the concept of a new pressuremeter probe equipped with a Hall Effect sensor that provides reliable small strain measurements of the mechanical properties of soils. The main steps that allowed validating of the new pressuremeter probe and the results obtained from previous tests in a physical model are presented in the second part. This approach allows drawing a degradation curve of the shear modulus; this would be useful in the practice of geotechnical engineering, and particularly for a better understanding of the nonlinear behavior of soils subjected to dynamic or seismic loads. [ABSTRACT FROM AUTHOR]