An X–FEM Technique for Modeling the FRP Strengthening of Concrete Arches with a Plastic–Damage Model; Numerical and Experimental Investigations

In this paper, an enriched–FEM method is presented based on the X-FEM technique by applying a damage–plasticity model to investigate the effect of FRP strengthening on the concrete arch. In this manner, the damage strain is lumped into the crack interface while the elastic and plastic strains are employed within the bulk volume of element. The damage stress–strain relation is converted to the traction separation law using an acoustic tensor. The interface between the FRP and concrete is modeled using a cohesive fracture model. The X-FEM technique is applied where the FE mesh is not necessary to be conformed to the fracture geometry, so the regular mesh is utilized independent of the position of the fracture. The accuracy of the proposed plastic-damage model is investigated under the monotonic tension, compression, and cyclic tension loading. Furthermore, the accuracy of the cohesive fracture model is investigated using the experimental data reported for the debonding test. In order to verify the accuracy of the proposed computational algorithm, the numerical results are compared with those of experimental data obtained from two tests conducted on reinforced concrete arches strengthened with FRP. Finally, a parametric study is performed by evaluating the effects of high to span ratio, longitudinal reinforcement ratio, and strengthening method.

On hyperbolicity of the dynamic equations for plastic fluid-saturated solids

The paper deals with the analysis of hyperbolicity of the dynamic equations for plastic solids, including one-phase solids and porous fluid-saturated solids with zero and nonzero permeability. Hyperbolicity defined as diagonalizability of the matrix of the system is necessary for the boundary value problems to be well posed. The difference between the system of equations for a plastic solid and the system for an elastic solid is that the former contains additional evolution equations for the dependent variables involved in the plasticity model. It is shown that the two systems agree with each other from the viewpoint of hyperbolicity: they are either both hyperbolic or both non-hyperbolic. Another issue addressed in the paper is the relation between hyperbolicity and the properties of the acoustic tensor (matrix). It remained unproved whether the condition for the eigenvalues of the acoustic matrix to be real and positive is not only necessary but also sufficient for hyperbolicity. It is proved in the paper that the equations are hyperbolic if and only if the eigenvalues of the acoustic matrix are real and positive with a complete set of eigenvectors. The analysis of the whole system of equations for a plastic solid can thus be reduced to the analysis of the acoustic matrix. The results are not restricted to a particular plasticity model but applicable to a wide class of models.

Bifurcation analysis of shear band in sand under true triaxial conditions with hypoplasticity

Predicting the onset of shear band is of significance in understanding the failureof geomaterials. The prediction accuracy is dictated by the constitutive modelused for the description of the pre-bifurcation behaviour. In this study, we firstmodify a recently proposed hypoplastic constitutive model by incorporating ageneral strength criterion and a stiffness function. We proceed to consider theonset of shear band in sand under true triaxial conditions. We demonstrate thatour analyses capture the pre-bifurcation stress–strain relationship at differentvalues of intermediate principal stress and predict fairly well the onset ofshear band. The acoustic tensor criterion generally adopted in elastoplasticapproaches is inadequate for hypoplastic approaches. No special non-coaxialtreatment is required for the present approach to yield a reasonable variationtrend of bifurcation strain with intermediate principal stress ratio 𝑏.

Sufficient conditions for hyperbolicity and consistency of the dynamic equations for fluid-saturated solids

Previous studies showed that the dynamic equations for a porous fluid-saturated solid may lose hyperbolicity and thus render the boundary-value problem ill-posed while the equations for the same but dry solid remain hyperbolic. This paper presents sufficient conditions for hyperbolicity in both dry and saturated states. Fluid-saturated solids are described by two different systems of equations depending on whether the permeability is zero or nonzero (locally undrained and drained conditions, respectively). The paper also introduces a notion of wave speed consistency between the two systems as a necessary condition which must be satisfied in order for the solution in the locally drained case to tend to the undrained solution as the permeability tends to zero. It is shown that the symmetry and positive definiteness of the acoustic tensor of the skeleton guarantee both hyperbolicity and the wave speed consistency of the equations.

The purpose of this work is the development and application of an RVE-based multiscale modelling framework for the transition from micro-discrete to macro- continuum by means of the Method of Multi-scale Virtual Power (MMVP). In con- tinua, the homogenisation operators (micro-to-macro) are successfully developed and implemented purely within the context of applied and computational solid mechanics. In order to predict mechanical properties and design new composite materials with complex microscopic structures, it is essential to use the discrete microscopic models based on Representative Volume Elements (RVE).In the first part of this thesis, a methodology is developed for the micro-discrete to macro-continuum transition by means of the MMVP. A discrete model of atomic structure is proposed which incorporates interatomic potential energies using well- known potential functions and molecular force field constants. At the micro-scale level, a Finite Element-type procedure is used to describe interatomic forces and a Newton-Raphson/arc-length method is used to solve the corresponding equilibriumproblem.The second part of this work investigates the macroscopic continuum elastic prop- erties and strength of atomic lattices. Macroscopic strength is determined as the onset of material instability at the macroscale. This is predicted by means of the analysis of the acoustic tensor associated with the homogenised constitutive tangent operators that results from the proposed micro-to-macro transition procedure.Numerical examples are presented including the modelling of two common atomic structures: graphene and boron nitride. In addition, the atomic RVE models are considered as a single layer and multiple layers, with and without defects. The ob- tained results are in good agreement with numerical and experimental data reported in the literature. The results demonstrate the capability of the proposed framework to predict the behaviour of macro-continuum with discrete structure at microscalelevel.

The purpose of this work is the development and application of an RVE-based multiscale modelling framework for the transition from micro-discrete to macro- continuum by means of the Method of Multi-scale Virtual Power (MMVP). In continua, the homogenisation operators (micro-to-macro) are successfully developed and implemented purely within the context of applied and computational solid mechanics. In order to predict mechanical properties and design new composite materials with complex microscopic structures, it is essential to use the discrete microscopic models based on Representative Volume Elements (RVE).In the first part of this thesis, a methodology is developed for the micro-discrete to macro-continuum transition by means of the MMVP. A discrete model of atomic structure is proposed which incorporates interatomic potential energies using well- known potential functions and molecular force field constants. At the micro-scale level, a Finite Element-type procedure is used to describe interatomic forces and a Newton-Raphson /arc-length method is used to solve the corresponding equilibrium problem.The second part of this work investigates the macroscopic continuum elastic properties and strength of atomic lattices. Macroscopic strength is determined as the onset of material instability at the macroscale. This is predicted by means of the analysis of the acoustic tensor associated with the homogenised constitutive tangent operators that results from the proposed micro-to-macro transition procedure.Numerical examples are presented including the modelling of two common atomic structures: graphene and boron nitride. In addition, the atomic RVE models are considered as a single layer and multiple layers, with and without defects. The obtained results are in good agreement with numerical and experimental data reported in the literature. The results demonstrate the capability of the proposed framework to predict the behaviour of macro-continuum with discrete structure at microscale level.

Failure in granular materials based on acoustic tensor: a numerical analysis

We investigate localization in granular material with the support of numerical simulations based upon DEM (Distinct Element Method). Localization is associated with a discontinuity in a component of the incremental strain over a plane surface through the condition of the determinant of the acoustic tensor to be zero. DEM simulations are carried out on an aggregate of elastic frictional spheres, initially isotropically compressed and then sheared at constant pressure p0. The components of the stiffness tensor are evaluated numerically in stressed states along the triaxial test and employed to evaluate the acoustic tensor in order to predict localization. This occurs in the pre-peak region, where the aggregate hardens under the circumstance to be incrementally frictionless: it is a regime in which the tangential force does not change as the deformation proceedes and, consequently, the deviatoric stress varies only with the normal component of the contact force.

ANALYSIS OF ACOUSTIC ANISOTROPY PARAMETERS OF PYROXENE-MAGNETITE ROCKS OF THE PISCHANKA STRUCTURE

The analysis of the results of acoustic properties of rocks study of Pischans`ka iron-ore structure is presented. The aim of the work is to establish the features of the distribution of acoustic properties and parameters of acoustic anisotropy in samples of core rocks selected from the well No. 3 of the Pischans`ka structure to determine the nature of its occurrence. A sample of 35 samples from the depth range 144-273 m is divided into 3 groups of rocks, namely: magnetite-pyroxene, quartz-magnetitepyroxene and biotite-amphibole crystalline shales. Based on an invariant polarization method, a number of acoustic laboratory measurements have been carried out. The values of the measured phase velocities "quasi-longitudinal" and two "quasi-transverse" waves at the stage of measurements showed significant acoustic anisotropy of the rocks. The ranges of the measured speeds of the collection samples are 7661 ÷ 5046 m / s for longitudinal waves and 4232 ÷ 2648 m/s for transverse ones. The difference in values measured for each of the sides of the cubic rhombic dodecahedron is from 100 to 800 m / s and from 0 to 500 m/s for Vp and Vs, respectively. The parameters of an acoustic ellipsoid were calculated, on the basis of which the division of samples into 3 main groups has been performed, according to the acoustic texture: acoustically linear, shale and rhombic. Separately, a group of samples with a more complex texture was discovered. The analysis of coefficients of anisotropy by different methods is carried out: longitudinal, transverse and relative acoustic anisotropy. Most of the samples are characterized by low or average acoustic anisotropy (from 2 to 7 %). A group of highly anisotropic rocks (11–14 %), represented by samples of biotite-amphibole crystalline silicates, is singled out. According to the parameters of the acoustic tensor of most samples, the transverse isotropic type of symmetry inherent to samples from the depth intervals 174–220 m and 222–232 m, while the smaller part is rhombic, is inherent. Differences in the parameters of anisotropy of samples can be explained by the significant heterogeneity of their textures, namely: micro cracks, minerals of various sizes, shapes and orientations. The results of the research show that the acoustic properties of the samples are quite heterogeneously distributed along the investigated depth range. This indicates the difficult conditions for the formation of rocks at different depths and the presence of different types of deformations, which accompanied the formation of the Pischans`ka structure.

A Two-Scale Numerical Approach to Granular Systems / Wybrane Problemy Szacowania Prawdopodobienstwa Zawodu W Sytuacji Pozaru

A two-scale numerical homogenization approach was used for granular materials. At small-scale level, granular micro-structure was simulated using the discrete element method. At macroscopic level, the finite element method was applied. An up-scaling technique took into account a discrete model at each Gauss integration point of the FEM mesh to derive numerically an overall constitutive response of the material. In this process, a tangent operator was generated with the stress increment corresponding to the given strain increment at the Gauss point. In order to detect a loss of the solution uniqueness, a determinant of the acoustic tensor associated with the tangent operator was calculated. Some elementary geotechnical tests were numerically calculated using a combined DEM-FEM technique

A NEW LAGRANGIAN FORMULATION OF IDEAL MAGNETOHYDRODYNAMICS

We propose a reformulation of ideal magnetohydrodynamics written in the Lagrangian variable as an enlarged system of hyperelastic type, with a specific potential. We study the hyperbolicity of the model and prove that the acoustic tensor is positive for all directions which are non orthogonal to the magnetic field. The consequences for Eulerian ideal magnetohydrodynamics and for numerical discretization are briefly discussed.