Non-associated Behaviour Research Articles

NTK-3D chaotic map and a non-associative LA-field sequences for image encryption

The imperative protection of digital information and its secure transmission has evolved into a complex challenge. Within this context, non-linear dynamical systems assume a pivotal role in fortifying content security by their unpredictable behavior and susceptibility to initial conditions. This study introduces an innovative 3D-chaotic system. The proposed map is then examined through bifurcation diagrams and randomness tests, revealing an intricate chaotic behavior of the system. Moreover, an advanced method of securing information is introduced, incorporating a non-associative LA-field sequences-oriented affine transformation. The initial procurement of a non-associative LA field through computational approaches is succeeded by utilizing sequences of its components to establish an affine transformation. This transformative process serves as the central aspect of the suggested color image encryption method. In this strategy, the NTK-3D map and the innovative affine transformation collaborate to introduce both confusion and diffusion, thereby fortifying the overall security stance. The non-associative behavior of the involved algebraic structure, combined with a dynamical system, results in highly resilient encryption. The proposed scheme is not only time-efficient but also has an expanded key space. The results of some performance assessments demonstrate that the suggested encryption technique for the digital medium is capable of resisting well-known attacks.

3D Rigid Block Limit Analysis of a Masonry Cross Vault Subjected to Shaking Table Tests

ABSTRACT This paper presents the results of a numerical study on a brick masonry cross vault that was tested on a shaking table, on a scale of 1:1. The study was part of the blind prediction competition organized within the activities of the SERA-AIMS project “Seismic Response of Masonry Cross Vaults: Shaking table tests and numerical validations”. The main objective of the blind prediction competition was to compare various numerical techniques. Among others, the one presented in this paper is based on 3D rigid block limit analysis. In the numerical model, the masonry units of the cross vault are modeled with rigid blocks interacting at no tension-frictional interfaces. A simple iterative procedure is used to take into account the non-associative behavior in sliding failure. Preliminary analyses carried out at the blind prediction competition stage as well as post-diction studies, after the experimental tests, are presented. The paper emphasizes the differences between the pre-diction and post-diction phases to highlight the improvements made during the numerical investigation. The study shows the influence of support and action modeling as well as of friction coefficient on the failure mechanisms and force capacity.

Constitutive model for soil-rock mixtures in the light of an updated skeleton void ratio concept

As a type of special geological body, soil-rock mixtures (SRMs) are widely found in nature and used in civil engineering. Many structures, such as rockfill dams, highways and tunnels, have used SRMs as building materials. Proper modeling of SRMs is of great importance to capture the complex behavior of this heterogeneous material. In this manuscript, a simple constitutive model incorporating the skeleton void ratio concept is proposed for SRMs with varying soil contents (sc). A prominent feature of the model is a unified description of the behavior of SRMs with varying sc such that only model parameters of pure rock and of pure soil are required. After calibration, the model shows a good capacity to predict the stress–strain response of SRMs under a wide range of sc, void ratios, and confining pressures. In particular, it captures well the non-associated behavior of rock-dominated SRMs with different sc. Furthermore, the sc-value is shown to modify the plastic flow direction of the material without influencing its yield surface.

A variationally coupled phase field and interface model for fracture in masonry

This paper presents a computational model for unreinforced masonry structures, where softening plasticity describes the behavior of the mortar joints, while a brittle phase-field model accounts for fracture in the bricks. The governing equations are derived in an energetic framework, ensuring variational and thermodynamic consistency, while taking into account the non-associative behavior of the mortar joints, which allows capturing their experimentally observed low dilatancy. A numerical solution scheme based on an algorithmic decoupling of the governing equations is proposed for the rigorous solution of the quasi-static evolution problem. The presented methodology is applied to four numerical examples, showing that most of the fundamental masonry failure mechanisms are captured and complex crack topologies can be computed. In addition, the results are compared to both experimental data and numerical results reported in the literature.

Correction to: Development and application of state-dependent fractional plasticity in modeling the non-associated behavior of granular aggregates

Correction to: Development and application of state-dependent fractional plasticity in modeling the non-associated behavior of granular aggregates

Fractional Plasticity Model for Coarse Aggregates Incorporating Particle Breakage under Triaxial Loading

Fractional plasticity has been originally proposed for capturing the state-dependent nonassociated behaviour of sand, with no use of state variables and additional plastic potentials. However, for coarse aggregates, significant particle breakage would occur, which could influence the stress-strain behaviour of the material, by shifting the critical state line in the e − ln p ′ plane. In this note, an extension of the fractional plasticity for constitutive modelling of coarse aggregates is made by incorporating particle breakage under triaxial loading. The developed model is validated by simulating a series of laboratory test results of different coarse aggregates under triaxial loading, where a good agreement between the model simulations and test results is observed.

Tilting plane tests for the ultimate shear capacity evaluation of perforated dry joint masonry panels. Part II: Numerical analyses

Within the student competition that took place during the 10th International Masonry Conference (10th IMC, 9–11 July 2018, Technical University of Milan, Milan, Italy), a set of tilting plane tests on dry joint masonry shear panels were carried out. Several tests were conducted by means of a tilting table: in-scale models of different perforated masonry shear walls were inclined until the activation of a global collapse mechanism. The ultimate inclination angle is always representative of the maximum shear force that the structure can bear. A total of 7 wall designs WDs, each one proposed by a student team according to some imposed geometrical criteria (8 bricks length, 27 bricks height, 30% minimum percentage of openings), was tested. In this work, numerical simulations aimed at reproducing experimental results obtained during the competition are presented. The problem is studied both in terms of rigid body structures subjected to a finite base rotational settlement and by means of traditional limit analysis. The finite settlement problem is treated incrementally, i.e. by increasing through a small amount the base rotational settlement at each step. On the other hand, limit analysis is performed assuming both associative and non-associative behavior for the masonry material. Finally, in order to better represent the actual behavior of walls during experiments, some simple strategies aimed at including within the numerical models some geometrical imperfections of the bricks and installation defects are devised and their effects are evaluated by means of sensitivity analyses.

Stress-fractional model with rotational hardening for anisotropic clay

Anisotropic clays are very common in practical engineering, where their constitutive relations were usually developed based on classical plasticity theory with associated flow rule. However, the softening responses of clays under compression following anisotropic consolidation can be non-associated and state-dependent. Fractional derivative is defined based on an integral form that can consider the material state and nonassociativity from the initial mathematical definition. In this study, a new anisotropic constitutive method for clay is developed by enriching the fractional plasticity with combined isotropic and rotational hardening. The developed model can consider the effect of evolving material anisotropy on the state-dependent non-associated behaviour of clay. To validate the approach, undrained and drained test results of different clays, are simulated and discussed, where a good agreement between the model simulations and test results is observed. It is also found that the material anisotropy keeps evolving with shearing, until reaching the final value at critical state.

Plastic Dissipation of the Fractional Plasticity using Modified Cam-Clay Yielding Function

ABSTRACTSoils usually exhibit state-dependent frictional behaviour that undergoes plastic volumetric deformation. To correctly capture such response under the framework of classical plasticity, a non-associated flow rule using additional plastic potential is inevitably needed. Recently, a novel fractional plasticity (FP) without using plastic potential has been developed, and successfully applied in modelling the state-dependent nonassociated behaviour of soils. However, the energy dissipation characteristics of FP has not been probed in depth. This note examines the plastic dissipation behaviour of FP, when modelling the constitutive behaviour of soils. It is found that the plastic dissipation of FP increases continuously with the shear strain. However, the rate of plastic dissipation depends on the initial material state in relation to the critical state line.

Non-associative Behavior of Thiophenols: Trouton’s Rule, Ramsey-Shields- Eötvös Equation and Application of Hammett Equation to the Surface Tension Data

Non-associative behavior of thiophenols is explained on the basis of Trouton’s rule, proton acceptor-donor cites and application of Hammett equation to the surface tension data of thiophenols.

Mixed hardening hyper-viscoplasticity model for soils incorporating non-linear creep rate – H-creep model

This paper focuses on the deformation of soils considering the time-dependent stress-strain evolution. In this paper, a new mixed hardening hyper-viscoplasticity model is proposed for the derivation of the time-dependent constitutive behaviour of soils, with the intention to capture the variation in the shapes of the yield loci by pursuing non-associated flow rules and accounting for kinematic hardening effects. The distinctive departure from the existing viscoplasticity models is the application of thermodynamics, based upon the use of internal variables, to postulate free-energy and dissipation potential functions, from which the corresponding yield locus, isotropic and kinematic hardening laws, flow rules and the elasticity law are deduced in a systematic procedure. The kinematic hardening behaviour of the yield locus is considered using the shift stress, resulting from the additional plastic component of the free-energy function. A non-linear creep formulation is postulated to address the limitation of over-estimating long-term settlement and incorporated into the model for more reliable predictions. The major parameters required for the model are identified, along with the summary of descriptions on how the model parameters can readily be determined. Non-associated behaviour is found to be a natural consequence of this approach, whenever the division between dissipated and stored plastic work is not equal. This study aims to provide a theoretical background and a numerical implementation for those who are interested in the advancement of constitutive modelling of soil behaviour under the framework of hyperplasticity. Validity and versatility of the proposed constitutive model are evaluated against triaxial and oedometer test results available in literature.

Fractional-order modelling of state-dependent non-associated behaviour of soil without using state variable and plastic potential

It was found that the constitutive behaviour of granular soil was dependent on its density and pressure (i.e. material state). To capture such state dependence, a variety of state variables were empirically proposed and introduced into the existing plastic potential functions, which inevitably resulted in the complexity and meaninglessness of some model parameters. The purpose of this study is to theoretically investigate the state-dependent non-associated behaviour of granular soils without using predefined plastic potential and state variable. A novel state-dependent non-associated model for granular soils is mathematically developed by incorporating the stress-fractional operator into the bounding surface plasticity. Unlike previous studies using empirical state variables, the soil state and non-associativity in this study are considered via analytical solution, where a state-dependent plastic flow rule and the corresponding hardening modulus without using additional plastic potentials are obtained. Possible mathematical connection with a well-known empirical state variable is also discussed. The non-associativity between plastic flow and loading directions as well as material hardening is found to be controlled by the fractional-derivative order. To validate the proposed approach, a series of drained and undrained triaxial test results of different granular soils are simulated and compared, where a good agreement between the model predictions and the corresponding test results is observed.

Behavior of Organic Compounds with Different Functional Groups based on Surface Tension, Ramsey-Shields-EÖTVÖS Constants (k), Order of Association (x) and Trouton’s Rule

Hydrocarbons and organic compounds having different functional groups with hetero atoms have shown a discriminative behavior toward surface tension, EÖTVÖS constants (k), order of association (x) and Trouton’s rule. This was explained in terms of associative and non-associative behavior of these compounds.

Development and application of state-dependent fractional plasticity in modeling the non-associated behavior of granular aggregates

To characterize the constitutive behavior of granular aggregates, a non-associated plasticity model with two different yield and plastic potential surfaces was usually used. However, in this paper, a state-dependent fractional elastoplastic model is proposed by only performing the first- and fractional-order differentiations of the yield function. The non-associated plastic flow is obtained without using any plastic potential functions. The state dependence is considered by correlating the fractional order with a state parameter. The model is then validated by simulating a series of test results of different granular aggregates, including sand, ballast and rockfill, under a variety of loading conditions.

3D rigid block micro-modelling of a full-scale unreinforced brick masonry building using mathematical programming

In this paper, we present a three-dimensional limit equilibrium analysis of an unreinforced brick masonry building. The structure under investigation is a one-room one-floor building that has been selected from a full-scale test carried out within the framework of a joint USA-Pakistan research project. The structural model of the building is an assemblage of rigid blocks, which interact through no-tension contact surfaces with Coulomb friction. A micro-modelling approach is adopted where each masonry unit is modelled as a rigid body. The underlying limit analysis formulation is based on the concave contact model, with contact forces located at the vertices of the interfaces. Iterative calculations are carried out to deal with the non-associative friction behaviour. The numerical analysis is carried out with the aid of a computer program that provides as output the failure load and the collapse mechanism. The comparison with experimental outcomes shows that the adopted formulation is capable to predict the actual behaviour of 3D masonry structures with a reasonable computational effort.

A novel paradigm for nonassociative long-term memory in Drosophila: predator-induced changes in oviposition behavior.

Learning processes in Drosophila have been studied through the use of Pavlovian associative memory tests, and these paradigms have been extremely useful in identifying both genetic factors and neuroanatomical structures that are essential to memory formation. Whether these same genes and brain compartments also contribute to memory formed from nonassociative experiences is not well understood. Exposures to environmental stressors such as predators are known to induce innate behavioral responses and can lead to new memory formation that allows a predator response to persist for days after the predator threat has been removed. Here, we utilize a unique form of nonassociative behavior in Drosophila where female flies detect the presence of endoparasitoid predatory wasps and alter their oviposition behavior to lay eggs in food containing high levels of alcohol. The predator-induced change in fly oviposition preference is maintained for days after wasps are removed, and this persistence in behavior requires a minimum continuous exposure time of 14 hr. Maintenance of this behavior is dependent on multiple long-term memory genes, including orb2, dunce, rutabaga, amnesiac, and Fmr1. Maintenance of the behavior also requires intact synaptic transmission of the mushroom body. Surprisingly, synaptic output from the mushroom body (MB) or the functions of any of these learning and memory genes are not required for the change in behavior when female flies are in constant contact with wasps. This suggests that perception of this predator that leads to an acute change in oviposition behavior is not dependent on the MB or dependent on learning and memory gene functions. Because wasp-induced oviposition behavior can last for days and its maintenance requires a functional MB and the wild-type products of several known learning and memory genes, we suggest that this constitutes a paradigm for a bona fide form of nonassociative long-term memory that is not dependent on associated experiences.

FE analysis of RC structures using DSC model with yield surfaces for tension and compression

The nonlinear finite element method with eight noded isoparametric quadrilateral element for concrete and two noded element for reinforcement is used for the prediction of the behavior of reinforcement concrete structures. The disturbed state concept (DSC) including the hierarchical single surface (HISS) plasticity model with associated flow rule with modifications is used to characterize the constitutive behavior of concrete both in compression and in tension which is named DSC/HISS-CT. The HISS model is applied to shows the plastic behavior of concrete, and DSC for microcracking, fracture and softening simulations of concrete. It should be noted that the DSC expresses the behavior of a material element as a mixture of two interacting components and can include both softening and stiffening, while the classical damage approach assumes that cracks (damage) induced in a material treated acts as a void, with no strength. The DSC/HISS-CT is a unified model with different mechanism, which expresses the observed behavior in terms of interacting behavior of components; thus the mechanism in the DSC is much different than that of the damage model, which is based on physical cracks which has no strength and interaction with the undamaged part. This is the first time the DSC/HISS-CT model, with the capacity to account for both compression and tension yields, is applied for concrete materials. The DSC model allows also for the characterization of non-associative behavior through the use of disturbance. Elastic perfectly plastic behavior is assumed for modeling of steel reinforcement. The DSC model is validated at two levels: (1) specimen and (2) practical boundary value problem. For the specimen level, the predictions are obtained by the integration of the incremental constitutive relations. The FE procedure with DSC/HISS-CT model is used to obtain predictions for practical boundary value problems. Based on the comparisons between DSC/HISS-CT predictions, test data and ANSYS software predictions, it is found that the model provides highly satisfactory predictions. The model allows computation of microcracking during deformation leading to the fracture and failure; in the model, the critical disturbance, Dc, identifies fracture and failure.

Pushover analysis of large scale unreinforced masonry structures by means of a fully 2D non-linear model

A simple 2D model for the evaluation of the seismic performance of large scale unreinforced masonry structures in-plane loaded is presented. The approach is fully two dimensional and allows performing pushover analyses on large scale structures without the reduction of the walls to an equivalent frame, competing with 1D codes. In the model, a macroscopic approach is used, where the so called disturbed state concept (DSC) with modified hierarchical single yield surface (HISS) plasticity are used to characterize the constitutive behavior of masonry in both compression and tension. Two HISS yield surfaces for compressive and tensile behavior are utilized. The DSC model allows for the characterization of non-associative behavior through the use of disturbance, and it computes micro-cracking during deformation, which eventually leads to fracture and failure. The DSC model is validated at both (1) specimen and (2) structural level. At a structural level, three large scale masonry walls subjected to incremental horizontal loads are analyzed and pushover curves obtained with the model proposed are compared to those obtained by means of standard equivalent frames and existing literature models.

The DSC Model for the Nonlinear Analysis of In-plane Loaded Masonry Structures

A nonlinear finite element method with eight-noded isoparametric quadrilateral elements is used to predict the behavior of unreinforced masonry structures. The disturbed state concept (DSC) with modified hierarchical single yield surface (HISS) plasticity which is called DSC/HISS-CT is used to characterize the constitutive behavior of masonry in both compression and tension. The model uses two HISS yield surfaces for compressive and tensile behavior. The DSC model allows for the characterization of non-associative behavior through the use of disturbance. It computes microcrack-ing during deformation, which eventually leads to fracture and failure. the critical disturbance, Dc, identifies fracture and failure. In the DSC model the DSC model was validated at two levels: (1) specimen and (2) practical boundary value problem. At the specimen level, predictions are obtained by integrating the incremental constitutive relations. The pro-posed constitutive model is verified by comparing numerical predictions with results obtained from test data; the compari-sons are found to be highly satisfactory. A new explicit formula is also presented to estimate the strength of unreinforced masonry structures.

Application of the DSC model for nonlinear analysis of reinforced concrete frames

A nonlinear finite element method with eight-noded isoparametric quadrilateral elements for concrete and two-noded elements for reinforcement was used to predict the behavior of reinforced concrete frame structures. The disturbed state concept (DSC) and the hierarchical single surface (HISS) plasticity model with the associated modified flow rule were used to characterize the constitutive behavior of concrete in both compression and tension. The DSC model allows for the characterization of non-associative behavior through the use of disturbance, and it computes microcracking during deformation, which eventually leads to fracture and failure. In the DSC model, the critical disturbance, D c , identifies fracture and failure. Elastic perfectly plastic behavior is assumed in models of steel reinforcement. The DSC model was validated at two levels: (1) specimen and (2) practical boundary value problem. At the specimen level, predictions are obtained by integrating the incremental constitutive relations. The finite element procedure and the DSC model are used to obtain predictions for practical boundary value problems. Based on comparisons between DSC predictions and test data, the model is capable of providing highly satisfactory predictions.