Physical Nonlinearity Research Articles

Numerical simulation of the behavior of kinematically unstable slopes under dynamic influences

Introduction. The concept of estimating the dynamic parameters of the “base — weakened layer — block” system is proposed, taking into account the physical nonlinearity of the material and the kinematic method of excitation of vibrations. In accordance with this approach, the physical nonlinearity of the base and block material is considered using the Drucker- Prager model. The weakened layer is modeled by 3D spring finite elements. The verification procedure of the proposed methodology is carried out on the example of the dynamic calculation of the “base — weakened layer — slope” system.Materials and Methods. The computational experiments were performed using the ANSYS Mechanical software package in combination with a nonlinear solver based on the Newton-Raphson procedure. SOLID45 volumetric finite elements were used to discretize the computational domains. Combined elastic-viscous elements COMBIN14 were used to simulate the displacement of the block relative to the fixed base.Results. An engineering technique for the dynamic analysis of the stress-strain state of the “base — weakened layer — block” spatial system with kinematic method of excitation of vibrations is developed. The accuracy and convergence of the proposed method is investigated using specific numerical examples.Discussion and Conclusion. Based on the mathematic simulation performed, it is shown that the developed technique provides assessing the risks of the occurrence of real landslide processes caused by external non-stationary impacts.

ТОЧНОЕ РЕШЕНИЕ ЗАДАЧИ О РЕЛАКСАЦИИ НАПРЯЖЕНИЙ В ТОЛСТОСТЕННОЙ ТРУБЕ ИЗ НЕЛИНЕЙНО ВЯЗКОУПРУГОГО МАТЕРИАЛА, ПОДЧИНЯЮЩЕГОСЯ СООТНОШЕНИЮ РАБОТНОВА

We constructed and studied analytically the exact solution of the quasi-static boundary value problem for a hollow cylinder (a tube) made of physically nonlinear homogeneous isotropic viscoelastic material obeying the Rabotnov constitutive equation with two arbitrary material functions (a creep compliance and a function which governs physical nonlinearity). A time-dependent displacement and zero shear stresses are given on the inside cylinder surface, a pressure (normal stress) is given on outside surface and zero axial displacements and zero shear stresses are preset on the end cross sections of the tube (thus, cylinder stress and plain strain are realized in a tube). We supposed that a material is incompressible and that given boundary displacement and pressure vary slowly enough with time to neglect inertia terms in the equilibrium equations. We obtained explicit expressions for strains and stresses at any point via the ratio of a tube radii, given external pressure and integral operators involving composition of two material functions of the constitutive relation and displacement preset on the internal cylindrical surface. In particular, assuming given boundary displacement and pressure are constant we considered the stress relaxation problem. For arbitrary material functions, we calculated all the hereditary integrals involved in the general representation for the stress field and reduced it to simple algebraic formulas convenient for analysis and use. We studied analytically general properties of the stress relaxation curves at any point of a tube and features of stress distributions along radius. We proved that the first material function (relaxation modulus) of the constitutive equation governs completely stresses dependence on time and the second one (non-linearity function) governs only stresses dependence on radial coordinate and found out that hoop stress and axial stress can change sign and can increase, decrease and be non-monotone with respect to radial coordinate. In case of zero external pressure, we proved that all stress relaxation curves at any point of a tube are proportional to each other (ratio of stresses at different points doesn't depend on time), decrease with time and have no flexure points. We also calculated integral mean values of axial and hoop stresses and discovered that their ratio depends on thickness/radius ratio only and doesn't depend on time and material functions although mean stresses do.

Об учете осадок фундаментов и отклонений опор от вертикали в расчетах сооружений башенного типа

The paper presents the results of field experiments which were carried out by the Department of Metal Structures and the Department of Geodesy of the Leningrad Civil Engineering Institute in 1978-1980 aimed at the study of the 42.0 m high radio towers with displacement of foundations. The results indicate the need to carry out calculations taking into account the physical nonlinearity of soil deformation in the tasks of studying the joint operation of structures and foundations of tower-type structures. There has been carried out an assessment of displacement of power transmission line supports` position from the vertical axis and foundations of supports for the stress-strain state of structures.

Calculation of the strength of objects of water management of the environment

The article discusses the objects of water management of the environment. An algorithm for forming a matrix of the stress-strain state of a prismatic finite element with a triangular cross-section in a mixed formulation is proposed to take into account the physical nonlinearity of water management objects in the form of rotation shells. The basic relations of the flow theory for arbitrary loading are used. The desired displacements and stresses of the inner point of the finite element were approximated by linear functions in terms of their nodal values. The stress-strain state matrix was formed using a functional expressing the equality of the actual work of external and internal work of external and internal forces, in which the actual work of internal forces was represented by the difference between the total and additional work of these forces.

SUBSTANTIATION OF DESIGN DECISIONS OF ELEMENTS OF MILITARY OBJECTS IN CONDITIONS OF CONTACT AND PLASTIC DEFORMATION

New design solutions, technologies and materials are required to improve tactical and technical characteristics of military equipment. Often this implies operation in such conditions as contact interaction and elasto-plastic deformations of materials. New models and research methods are developed for better utilization of modern materials and improved performance of military equipment. They account directly for complex physical and structural nonlinearities. The properties of conventional and novel materials are determined both in bulk and on surfaces at microstructural level. This will enable physically adequate and mathematically correct analysis of stress-strain state. The new advanced design solutions will emerge through the objective-driven search by means of parametric modeling. The project will extend traditional local problem statements with newly developed variational principles that account for structural and physical nonlinearity and are suitable for parameterization. This will create the basis for fundamental analysis of torsion bar suspensions, hydrovolumetric and gear drives and other crucial components of combat vehicles, engineering solutions for domestic manufacturers of military equipment that will bring their tactical and technical characteristics to highest modern standards.
 Keywords: contact interaction; stress-strain state; intermediate layer; contact pressure; contact area; plastic deformation

DEVELOPMENT OF STATISTICALLY AVERAGED MODELS OF DEFORMATION OF MATERIALS WITH RANDOM NETWORK STRUCTURE OF DIFFERENTLY ORIENTED FIBERS

The paper describes the developed statistically averaged models of deformation of materials with a random network structure of differently oriented fibers. New methods of stress-strain analysis and micromacromechanical models of material deformation in the volume of bodies made of material with a network structure taking into account structural and physical nonlinearities have been created. These models are based on the micromechanics of network structures at the level of statistical sets of their chains. The novelty of approaches, models, methods and results is the creation of theoretical foundations for the analysis of the deformation of non-traditional network materials. Nonlinear mathematical models of material deformation in the form of a chaotic network structure of one-dimensional fragments are proposed, which are constructed involving fundamentally new approaches to the description of physical and mechanical properties at the micro level of statistical sets of fiber chains and spatial homogenization of their macroproperties. Compared to traditional models, they more adequately model the features of material deformation in the form of spatial chaotic and ordered network structures, as they do not involve a number of additional non-physical hypotheses. This creates fundamentally new opportunities not only for analyzing the properties of such materials, but also when creating new ones with specified properties. Using the created methods, models and research tools, the basis for solving a number of model and applied problems has been created. The nature of deformation of non-traditional materials with a network structure of one-dimensional elements is determined. The macro-properties of these materials are established on the basis of the developed micromechanical models, variational formulations and averaging methods. Keywords: stress-strain state, network structures, contact interaction, finite element method, contact pressure, machine parts, variational formulation

Modeling of rubber-cord layers under quasi-static loading

Modeling a pneumatic tire with a strong change in shape causes the problem of choosing an adequate model for rubber-cord plies. Generally, the classical method of asymptotic homogenization is not suitable due to physical and geometrical nonlinearity for the strain up to 15 %. The known models used for simulation the entire tire as well as rubber-cord plies are analyzed. A choice is made in favor of modeling the plies using the stress anisotropic potential, which is an anisotropic function of the strain tensor invariants. The relationship of such a constitutive law with a quasi-linear constitutive equation in terms of stress and strain differentials is indicated. A convenience of these two types of constitutive equations in terms of numerical implementation is also given. A modification of the effective properties definition for an inhomogeneous layer is explained. The difference from the standard effective moduli definition is clarified. The arrangement of the cords is supposed to be approximately periodic and all cords to be equivalent to the effective fiber. Two models of a rubber-cord plies are described under such assumption. These are a model of an orthotropic material and a model of a transversely isotropic material. Computational experiments, which make it possible to determine the material parameters of anisotropic potentials, are pointed out. Real tests with a sample of rubber ply under slow quasi-static loading were conducted. Significant hysteresis was detected. It is shown that an additive model combining a hyper elastic material with Maxwell viscoelastic model provides good accuracy in stress dependence on the strain rate. The numerical procedure developed to calculate solution to the quasi-static problem of tire deformation is described. It is implemented in home-made computer code. A numerical example on the tire simulation is given. That is so-called breaking test, in which strong deformation is achieved and the developed model is applied to.

Smart stiffness computation of one-dimensional Finite Elements

In the present study, three sophisticated methods are introduced to compute tangent stiffness matrices in Finite Element Analysis by Artificial Neural Networks (ANNs). We propose a modified training procedure by adding a loss term corresponding to the element tangent stiffness matrix in the optimization criteria. This training procedure is referred to as Sobolev training and it ensures that the ANN learns the functional relationship to approximate the converged internal force and its corresponding first derivative to compute the converged tangent stiffness matrix. This new development eliminates the need to perform iterations in the nonlinear solver and leads to a significant acceleration of the Finite Element simulation. We then propose a simple scaling strategy that uses the trained network to predict the stiffness information of elements with different geometrical properties. Thus, the focus of this work is to establish a neural network-based FEM framework (independent of NN topology) to introduce an enhanced stiffness replacement for truss and beam elements taking physical non-linearities into account. The performance of the proposed methods is demonstrated on academic examples showing a maximum of 41% boost in simulation speed.

Визначення силової характеристики взаємодії системи пасивної безпеки головного вагона з великим транспортним засобом при зіткненні

One of the priorities of the National Economic Strategy of Ukraine for the Period up to 2030 is the development of the transport sector, in particular railway vehicle renewal, the introduction of high-speed railway passenger transport, and railway traffic safety improvement. The home motor-car trains must be renewed in compliance with new home standards harmonized with European ones, among which one should mention the Ukrainian State Standard DSTU EN 15227, which specifies the passive safety of a passenger train in its emergency collisions with different obstacles. New car designs must provide not only effective up-to-date braking systems to prevent emergency collisions, but also passive safety systems with energy-absorbing devices. The main purpose of these devices is to reduce the longitudinal forces in the intercar connections and the car accelerations to an acceptable level for the three collision scenarios specified in the DSTU EN 15227. The Department of Statistical Dynamics and Multidimensional Mechanical Systems Dynamics, Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine, developed a passive protection concept for home high-speed passenger trains in emergency collisions by the DSTU EN 15227 scenarios, proposals on the passive protection of a motor-car train head car, and honeycomb designs of lower- and upper-level energy-absorbing devices (EAD 1 and UL EAD, respectively), which are integrated into the head car front part and serve to damp the major part of the impact energy in front collisions with obstacles. This paper considers DSTU EN 15227 Scenario 3: a collision of a reference motor-car train at a speed of 110 km/h at a railway crossing with a large 15 t road vehicle, which is simulated as a large-size deformable obstacle (LSDO). The aim of the paper is to determine the force characteristic of the interaction of energy-absorbing devices mounted on the head car front part with a large road vehicle in a collision to assess the compliance of the proposed passive protection with the normative requirements. Finite-element models were constructed to analyze the plastic deformation of the elements of the EAD 1 – LSDO, UL EAD – LSDO, and EAD 1 – UL EAD –LSDO systems in a collision with account for geometric and physical nonlinearities, steel dynamic hardening as a function of the impact speed, and varying contact interaction between the elements of the systems considered. The studies conducted made it possible to determine the force characteristics of energy-absorbing device – obstacle interaction and the total characteristic of the contact force between two lower-level devices and two upper-level ones as a function of the obstacle center of mass displacement in a collision. The proposed mathematical models and the calculated force characteristics may be used in the study of the dynamics of a reference motor-car train – large road vehicle collision with the aim to assess the compliance of the passive protection of the home head car under design with the DSTU EN 15227 requirements.

Coupled poro‐mechanical tangent formulation applied to sedimentary basin modeling

AbstractSedimentary basin modeling involves large space domains and time periods. Reproducing the compaction processes of the sediment material requires the constitutive model to be formulated in the framework of large irreversible strains, taking both geometric and physical nonlinearities into account. This work presents a tangent formulation for the coupled poro‐mechanical system of equations resulting from the weak form of the momentum and fluid mass balance equations. The proposed workflow is integrated in a thermo‐poro‐mechanical finite element basin simulator. At material level, purely mechanical and chemo‐mechanical deformations are respectively addressed by means of plastic and viscoplastic components in the macroscopic state equations. The accuracy and efficiency of the proposed tangent formulation are assessed through the simulation of a basin geological scenario involving gravitational compaction and tectonic shortening. Both drained and undrained behaviors of the basin rocks are simulated. The procedure has significantly improved the convergence rate and reduced the computational cost with comparison to the original formulation based on the standard poro‐elastic coefficients. In order to illustrate the potential of the basin simulator to deal with real case applications, a well model from the Neuquén basin in Argentina is also presented. The results are validated against available numerical and field data for porosity, pore‐pressure and temperature.

РАСЧЕТ ЦЕНТРАЛЬНО СЖАТЫХТРУБОБЕТОННХ КОЛОНН КОЛЬЦЕВОГО СЕЧЕНИЯ С УЧЕТОМ ФИЗИЧЕСКОЙ НЕЛИНЕЙНОСТИ

In the article, the resolving equations are obtained for the calculation taking into account the physical nonlinearity and creep of centrally compressed concrete filled steel tubular columns of annular cross-section. The examples of the calculation of the bearing capacity with a short-term load are given. The solution was carried out numerically in the Matlab environment using the finite difference method. The deformation theory of plasticity by G.A. Geniev was used.

Roll-over stability as a problem of high-rise buildings’ designing

Roll-over stability of tall buildings under wind loads is considered. The nonlinear nature of the problem is taken into account, including geometric, physical, and structural non-linearity. The problem is solved on the base of a system of linearized incremental equations of structural mechanics that describes the behavior of a system tall building - foundation soil. Several methods are examined for solving nonlinear problems of roll-over stability, specifically: 1) deformation method of systems equilibrium states tracing; 2) method of linearization of nonlinear equations and systems equilibrium states tracing; 3) method of linearization of nonlinear physical relations of a systems with constructive, static, geometric nonlinearity; 4) method of linearization of nonlinear physical relations of a system with constructive nonlinearity based on nonlinear incremental structural mechanics; 5) method of the deformation process tracing for a physically nonlinear soil base, given the increase of discharge zones and constructive nonlinearity. Each of these methods is used to solve a model task. These tasks take into account roll-over stability of high structures under action of wind loads. In general, the problem of roll-over stability of a high object can be represented as repeatedly nonlinear one with various types of non-linearity. In this regard, in the practice of high-rise buildings designing, it is necessary to develop scientifically and methodically substantiated methods of assessing roll-over stability, considering non-linear factors. Taking these factors into account will make it possible to assess the roll-over stability of a high-rise object more accurate.

Physics-inspired pseudo-transient method and its application in modelling focused fluid flow with geological complexity

SUMMARY Two-phase flow equations that couple solid deformation and fluid migration have opened new research trends in geodynamic simulations and modelling of subsurface engineering. Physical non-linearity of fluid-rock systems and strong coupling between flow and deformation in such equations lead to interesting predictions such as spontaneous formation of focused fluid flow in ductile/plastic rocks. However, numerical implementation of two-phase flow equations and their application to realistic geological environments with complex geometries and multiple stratigraphic layers is challenging. This study documents an efficient pseudo-transient solver for two-phase flow equations and describes the numerical theory and physical rationale. We provide a simple explanation for all steps involved in the development of a pseudo-transient numerical scheme for various types of equations. Two different constitutive models are used in our formulations: a bilinear viscous model with decompaction weakening and a viscoplastic model that allows decompaction weakening at positive effective pressures. The resulting numerical models are used to study fluid leakage from high porosity reservoirs into less porous overlying rocks. The interplay between time-dependent rock deformation and the buoyancy of ascending fluids leads to the formation of localized channels. The role of material parameters, reservoir topology, geological heterogeneity and porosity is investigated. Our results show that material parameters control the propagation speed of channels while the geometry of the reservoir controls their locations. Geological layers present in the overburden do not stop the propagation of the localized channels but rather modify their width, permeability, and growth speed.

Matrix Description of Non-Linear Properties of Materials or Structural Components-Idea and Application Examples.

Numerical methods are widely used in structural analysis problems. In the cases of the most complex and practical problems, they are often the only way to obtain solutions, as analytical methods prove ineffective. The motivation for this paper was the desire to extend the scope of numerical methods to cover the problems of creating constitutive models of structural materials. The aim of this research was to develop a matrix or numerical discrete constitutive model of materials. It presents the general assumptions of the developed method for modeling the physical properties of materials. The matrix model is only useful with an appropriate numerical algorithm. Such an algorithm was created and described in this paper. Based on its findings, computer software was developed to perform numerical simulations. Presented calculation examples confirmed the effectiveness of the developed method to create constitutive matrix models of various typical materials, such as steel, but also, e.g., hyper-elastic materials. It also presents the usefulness of constitutive matrix models for simulations of simple stress states and analyses of structural elements such as reinforced concrete. All presented examples involved the physical nonlinearity of the materials. It is proved that the developed matrix constitutive model of materials is efficient and quite versatile. In complex analyses of structures made of nonlinear materials, it can be used as an effective alternative to classical constitutive or analytical models based on elementary mathematical functions.

Influence of Retardation Time on Viscoelastic Behavior of Plane Beams Modeled by the Nonlinear Positional Formulation of the Finite Element Method

A numerical procedure is presented to avoid the divergence problem during the iterative process in viscoelastic analyses. This problem is observed when the positional formulation of the finite element method is adopted in association with the finite difference method. To do this, the nonlinear positional formulation is presented considering plane frame elements with Bernoulli–Euler kinematics and viscoelastic behavior. The considered geometrical nonlinearity refers to the structural equilibrium analysis in the deformed position using the Newton–Raphson iterative method. However, the considered physical nonlinearity refers to the description of the viscoelastic behavior through the adoption of the stress-strain relation based on the Kelvin–Voigt rheological model. After the presentation of the formulation, a detailed analysis of the divergence problem in the iterative process is performed. Then, an original numerical procedure is presented to avoid the divergence problem based on the retardation time of the adopted rheological model and the penalization of the nodal position correction vector. Based on the developments and the obtained results, it is possible to conclude that the presented formulation is consistent and that the proposed procedure allows for obtaining the equilibrium positions for any time step value adopted without presenting divergence problems during the iterative process and without changing the analysis of the final results.

Algorithm of finite elemental SSS analysis of thin-walled technosphere objects based on a triangular discretion element with elastic-plastic deformation

The article describes an algorithm for the strength calculation of thin-walled objects of the technosphere, taking into account the plastic stage of the work of the material used, which is quite relevant with the increased requirements for material saving of designed and reconstructed objects. The finite element method is used as a tool for studying the stress-strain state of technosphere objects, taking into account the physical nonlinearity of the applied structural material. As a sampling element, a fragment of the middle surface of a thin-walled triangular technosphere object with main nodes at the vertices of the triangular element and additional nodes at the midpoints of the sides is used. The sought unknowns at the main nodes at the loading step are the increments of the displacement vector components and their first derivatives with respect to the curvilinear coordinates of the middle surface. At additional nodes, Lagrange multipliers act as unknowns, introduced to improve the consistency of the bin along the boundaries with adjacent elements. When deriving the plasticity matrix at the loading step, we used the hypothesis that the components of the stress increment tensor are proportional to the components of the strain increment tensor. The developed algorithm was implemented as a package of applied programs and verified by the example of calculating a rigidly restrained cylinder loaded with internal pressure.

EVALUATION OF THE RELIABILITY OF BUILDING STRUCTURES IN SIMULIA ABAQUS: MODELING OF STOCHASTIC MATERIAL PROPERTIES

This article describes a software module component integrated with the SIMULIA Abaqus engineering analysis software package and designed to simulate random values of material parameters in a finiteelement model based on specifiedstatistical characteristics, with the possibility of taking into account the physical nonlinearity of material behavior under various combinations of loads and influences.The target group of materials under study is materials of load-bearing elements of building structures, such as concrete, stone, steel. This software module can be recommended for use by specialists, engineers and scientists engaged in probabilistic analysis of the reliability of structures of buildings and structures, apparatus, machines, devices, with the combined use of complexes of computer modeling and engineering analysis. Has a certificateof state registration of the computer program "AS for modeling stochastic properties of materials" No. 2019667439 dated 12.24.2019.

MODELING OF THE SUBWAY DYNAMIC INFLUANCE ON THE GROUND STRUCTURE

The article discusses a new approach to modeling the behavior of structures under the influence of dynamic loads, including loads from ground and underground transport. The approach is to apply the direct integration method, as well as the SBFEM method to calculate the forces in load-bearing building structures under dynamic influences, taking into account a number of factors - the damping properties of the subgrade, physical nonlinearity of soils and the passage of waves in the soil space. The article presents the main theoretical premises, the results of a numerical experiment of a real monolithic building, built in the zone of influence of the subway.

Comparison of Different Procedures for Progressive Collapse Analysis of RC Flat Slab Structures under Corner Column Loss Scenario

Progressive collapse is the failure of the whole structure caused by local damage, which leads to significant economic and human losses. Therefore, structures should be designed to sustain local failures and resist subsequent nonproportional damage. This paper compared four procedures for a progressive collapse analysis of two RC structures subjected to a corner column loss scenario. The study is mainly based on the methods outlined in the current Russian standard (linear static (LS) pulldown, nonlinear static (ND) pulldown, and nonlinear dynamic), but also includes LS and NS pushdown procedures suggested by the American guidelines and linear dynamic procedure. We developed detailed finite element models for ANSYS Mechanical and ANSYS/LS-DYNA simulations, explicitly including concrete and reinforcement elements. We applied the Continuous Surface Cap Model (MAT_CSCM) to account for the physical nonlinearity of concrete. We also validated results obtained following these procedures against known experimental data. Simulations using linear static pulldown and linear dynamic procedures lead to 50–70% lower results than the experimental because they do not account for the nonlinear behavior of concrete and reinforcement. Displacements obtained from the NS pulldown method exceed the test data by 10–400%. It is found that correct results for both RC structures can only be found using a nonlinear dynamic procedure, and the mismatch with the test data do not exceed 7%. Compared to static pulldown methods, LS and NS pushdown methods are more accurate and differ from the experiment by 28% and 14%, respectively. This relative accuracy is provided by more correct load multipliers depending on the structure type.

Stress-strain state of reinforced thin-walled structural elements

The most common structures designed for the installation of technological equipment in workshops are beam platforms mounted from rolled steel and sheet elements. The values of strains and stresses of ribbed plates obtained in accordance with the linear theory, significantly differ from the values obtained in terms of physical and geometrical nonlinearities. A joint consideration of the double nonlinearity significantly clarifies the mathematical model of the reinforced flexible plates and shells, which provides a complete idea of the stress-strain state of the structure. The paper presents a calculation algorithm for the flexible plates reinforced by a stiffening plates and hollow shells based on the Lagrange function method. The stress-strain state of a plate symmetrically reinforced by a stiffening plate is investigated under the uniform loading conditions.