Incremental Formulation Research Articles

A two-dimensional ordinary state-based peridynamic model for plastic deformation based on Drucker-Prager criteria with non-associated flow rule

The plastic behaviors of geomaterials often obey non-associated flow rule. In this paper, a two-dimensional (2D) ordinary state-based peridynamic (OSB-PD) increment model with shear deformation based on Drucker-Prager (D-P) criterion with non-associated flow rule is proposed to study the plastic behavior of geomaterials. An incremental form of peridynamic (PD) strain energy density for plane elastic problems is first established. The material parameters are determined when the incremental PD strain energy density is equal to the incremental strain energy density in classical mechanics. The PD force density for the OSB-PD theory with shear deformation in plane elastic cases is derived accordingly. The relationship between the incremental second invariant of the stress tensor dJ2, the first invariant function of stress tensor dI1 in the classical mechanics and PD are established in this paper, and the Drucker-Prager yield surface is expressed in the framework of peridynamics. To avoid the excessive plastic dilation, the non-associated flow rule is proposed, in which isotropic and deviatoric plastic elongation are employed to describe the plastic behaviors of a bond. Also, the equivalent stress and equivalent plastic strain for the proposed PD model are given. An integration algorithm for the proposed increment model is developed. Numerical examples including circular opening in rocks are performed, and the PD results are compared with that obtained by the finite element method or analytical solution. Those numerical simulations have verified the validity of the proposed PD model to predict the elasto-plastic behavior of geomaterials.

Incremental viscoelasticity at finite strains for the modelling of 3D concrete printing

Within a 3D concrete printing process, the fresh concrete is aging due to hydration. One of the consequences from the purely mechanical point of view is that its constitutive relation must be defined in rate form. This restriction is taken into account in this contribution and, besides on the incremental elasticity, we moreover introduce the relaxation of the internal stresses in order to describe the creep at early age. On another hand, due to the soft nature of the material, the finite strain range is herein a priori assumed. Eventual structural instabilities during the printing process can therefore be predicted as well. On another hand, with regards to the incremental formulation of the boundary value problem, the kinematics must be adapted as well. We use for this the multiplicative decomposition of the actual deformation gradient into its known part at an earlier time and the relative deformation gradient with respect to the configuration at that time. Within a Lagrangian formulation, the incremental constitutive relations and evolution equations can then be ideally defined on the above mentioned intermediate configuration prior to be transported back to the reference configuration. In particular, the early age creep is here described through an internal variable approach the evolution of which is motivated by the generalized Maxwell model. In this work, this latter is adapted for incremental viscoelasticity. Model examples are proposed and the numerical efficiency of the proposed framework is illustrated through a set of representative simulations.

The Relationship Between Intellectual Capital and Performance of Social Enterprises: A Literature Review

There is a need for competition and having a competitive advantage for every enterprise. Moreover, a social enterprise is expected to maintain itself and expand exponentially through innovation and the application of technology. The need to survive implies the need for social innovation within the organizations. When the organization's goal is established, which is the prerequisite for starting a social enterprise, innovation aims to solve the problem. Innovation is a learning outcome that manifests itself into new product features, new products, or production methods. Social innovation is an incremental form of innovation because it emerges from the social needs of a community. The kind of innovation produced is oriented towards the community to provide a solution to their problem. Social enterprises have worked tirelessly to create solutions to the social issues that specific communities are facing. The findings in this research highlight intellectual capital as one of the most fundamental assets in a social enterprise. When discussed in terms of its three branches, intellectual capital's performance of social enterprises is significantly improved. Received: 8 July 2021 / Accepted: 19 August 2021 / Published: 5 September 2021

Incremental Attribute Reduction Based on Knowledge Granularity under Incomplete Data

Traditional attribute reductions can’t be directly applied to miss attribute values and dynamic changes data. Therefore, how to dynamically update attribute reductions efficiently when incomplete data changes dynamically is great research value. For the change of the object, using matrix’s simple and clear characteristics, the paper focus on the incremental attribute reduction algorithm in matrix form of knowledge granularity. Firstly, the knowledge granularity is obtained by matrix which uses to measure the uncertainty of the system, then calculating the attribute importance, and using the attribute importance to devise a static algorithm, and then analyzing incremental matrix form when the object increases. The comparative experiments show that the incremental algorithm can effectively and efficiently update the result of attribute reduction as the object changes.

On a geometrically nonlinear incremental formulation for the modeling of 3D concrete printing

Of interest in this paper is a modeling framework when constitutive relations are given in incremental form. This is particularly true for aging concretes due to hydration. Furthermore, having in mind applications to 3D concrete printing, geometrical nonlinearities must be accounted for due to the soft nature of the fresh material. The kinematics must then be adapted adequately for a theoretically sound formulation. For this, the multiplicative split is chosen here for the deformation gradient into its known part at an earlier time and the relative deformation gradient. From the geometric point of view, this gives rise to an intermediate configuration on which incremental constitutive relations can be ideally defined prior to be transported back to the reference configuration for a Lagrangian formulation. Model examples are given for the purpose of demonstration and a set of simulations illustrate the effectiveness of the proposed framework.

Extension of the unsymmetric 8-node hexahedral solid element US-ATFH8 to geometrically nonlinear analysis

PurposeThe purpose of this paper is to extend a recent unsymmetric 8-node, 24-DOF hexahedral solid element US-ATFH8 with high distortion tolerance, which uses the analytical solutions of linear elasticity governing equations as the trial functions (analytical trial function) to geometrically nonlinear analysis.Design/methodology/approachBased on the assumption that these analytical trial functions can still properly work in each increment step during the nonlinear analysis, the present work concentrates on the construction of incremental nonlinear formulations of the unsymmetric element US-ATFH8 through two different ways: the general updated Lagrangian (UL) approach and the incremental co-rotational (CR) approach. The key innovation is how to update the stresses containing the linear analytical trial functions.FindingsSeveral numerical examples for 3D structures show that both resulting nonlinear elements, US-ATFH8-UL and US-ATFH8-CR, perform very well, no matter whether regular or distorted coarse mesh is used, and exhibit much better performances than those conventional symmetric nonlinear solid elements.Originality/valueThe success of the extension of element US-ATFH8 to geometrically nonlinear analysis again shows the merits of the unsymmetric finite element method with analytical trial functions, although these functions are the analytical solutions of linear elasticity governing equations.

Implementation of visco-pseudo-elastic dampers for vibration reduction of sandwich shells using a large deformation FE technique

This study introduces a numerical method for investigating the appropriate arrangement of visco-pseudo-elastic dampers applicable to shell and plate structures under large deformation. These passive dampers are considered as discrete shape memory alloy (SMA) wires and viscoelastic layers. The SMA constitutive model is adopted and developed based on carried out experimental tests (i.e., calorimetry and tensile tests) on Ni-rich Nitinol alloy samples. Pseudoelastic, pseudoplastic, strain recovery and de-twinning phenomena are perceived experimentally. The presented model characterizes pseudoelastic response of shape memory alloys. The current finite element formulation is based on an incremental updated Lagrangian (UL) approach along with the Newmark's integration technique. The used sandwich element is capable of accurate modeling of the viscoelastic core damping behavior, as a result of independent rotation of element's layers. Also, the creep functions regarding to the viscoelastic constitutive model are estimated using Dirichlet-Prony series. Employing the state variables, the viscoelastic deferred strain is presented in a proper incremental form. A nonlinear FE program is developed to assess the proposed procedure. Obtained results demonstrate that quick vibration mitigation may be possible using visco-pseudo-elastic dampers while overcoming their individual drawbacks.

A model for freeze-thaw-induced plastic volume changes in saturated clays

A new model is proposed for describing freeze-thaw-induced plastic volume changes in saturated clays based on microscopic inhomogeneities inherent in the soil structure and the pore water transfer between them. It is shown through a simple inhomogeneous mesostructure model that the equilibrium state reached after freezing serves as an important reference state for interpreting the volumetric behaviour. The soil state evolution towards this freeze equilibrium state describes many features seen in the experimentally observed freeze-thaw behaviour, such as the existence of a limiting stress level above which no plastic volume change occurs. The process of freezing/thawing is modelled as a rate process approaching the freeze equilibrium line (FEL) and representing the eventual equilibrium states at a particular sub-freezing temperature, exploiting a newly defined state parameter, ψfe. The model offers a mesoscopic three-dimensional yield surface in the specific volume – effective stress – temperature space, expressed by a simple equation. Although the model’s essence is encapsulated in only two simple equations, it can simulate well the experimentally observed volume change accumulation with freeze-thaw cycles under different stress levels and densities (or over-consolidation ratios). As the model is formulated in an incremental rate form, it can be applied to general freeze-thaw problems, even those with irregular temperature and stress history – a feature not seen in existing models.

Toward a local maximum‐entropy material point method at finite strain within a B‐free approach

AbstractThe material point method can be regarded as a meshfree extension of the finite element method. This fact has two interesting consequences. On the one hand, this puts a vast literature at our disposal. On the other hand, many of this inheritance has been adopted without questioning it. A clear example of it is the use of the Voigt algebra, which introduces an artificial break point between the formulation of the continuum problem and its discretized counterpart. In the authors' opinion, the use of the Voigt rules leads to a cumbersome formulation where the physical sense of the operations is obscured since the well‐known algebra rules are lost. And with them, the intuition about how stresses and strains are related. To illustrate it, we will describe gently and meticulously the whole process to solve the nonlinear governing equations for isothermal finite strain elastodynamics, concluding with a compact set of expressions ready to be implemented effortless. In addition, the classic Newmark‐ algorithm has been accommodated to the local maximum‐entropy material point method framework by means of an incremental formulation.

Assessment of distributed photovoltaic hosting capacity in integrated electricity and heat systems considering uncertainty

Distributed photovoltaics (DPVs) have been widely integrated into power systems due to their abundance, renewability and low cost, while the stochastic nature of DPVs imposes significant influence on the hosting capacity (HC) of DPVs. Here, the integrated electricity and heat system (IEHS) is explored to increase the deployment of DPVs in comparison to the power system by exploiting the interaction between electric and thermal energy. An MILP-based HC assessment model for DPVs of the IEHS is proposed to efficiently promote the penetration level of DPV generation in distribution networks considering the uncertainty of DPV generation. To reduce the computational burden for HC assessment, the linearisation method combined with the incremental formulations of the big-M method is developed to simplify the complex non-linear model of energy devices and networks in IEHS. A scenario-based uncertainty modelling approach is applied to characterise DPV uncertainty, which improves the accuracy of HC assessment for DPVs. Comprehensive case studies according to a 33-bus electric network and a 6-node heat network validate the superiority of the proposed assessment model.

Numerical integration of an elasto-plastic critical state model for soils under unsaturated conditions

This paper presents the complete set of incremental equations for the numerical integration of the Glasgow Coupled Model (GCM) and a comprehensive algorithm for its numerical integration. The incremental formulation proposed is expressed in terms of strain and suction increments (i.e. strain-driven) and defines an initial value problem (IVP) that can be solved once the initial state and the pair of increments of the driven variables are known. The numerical integration of this IVP is carried out by extending to unsaturated condition, the well-known explicit substepping formulation with automatic error control widely used for saturated soils. A notable feature of the substepping integration scheme presented is that it integrates simultaneously the model equations for both mechanical and water retention responses. Hence, the estimate of the local truncation error to automatically adjust the size of the integration step is not only affected by the local error in stresses and mechanical hardening parameter (as in a saturated soil model) but, additionally, by the local error incurred in the integration of the water retention relations (i.e. degree of saturation and water retention hardening parameter). The correctness of the integration scheme is then verified by comparison of computational outcomes against analytical/reference solutions.

Integral Model Predictive Current Control for Synchronous Motor Drives

Model predictive control (MPC) represents an affirmed optimal control strategy, able to handle multivariable systems and their input-output constraints. However, MPC does not provide an integral control action for reference tracking control problems. Several methods have been proposed to overcome this limitation. Standard MPC methods include a disturbance observer to handle unmodeled uncertainties, such as external unknown disturbances and parameter mismatches. Among these formulations, the authors focus on the velocity form MPC, which considers the incremental formulation of the motor state-space model. This formulation gets rid of the bias errors in reference tracking problems. In this article, the MPC paradigm is applied to the current control of synchronous motor drives. The intent is to compare the velocity form and the MPC with disturbance observer. A theoretical analysis of the MPC coupled with disturbance observers and the equivalence between these formulations and the velocity form is presented. Input constraints are included in the MPC optimization process, thus requiring an online quadratic programming solver. Experimental tests consider a 1 kW anisotropic synchronous motor. Numerical aspects regarding the optimization problem are investigated for both methods.

Modeling and modal analysis of suspension bridge based on continual formula method

A continnum model is developed for the dynamic analysis of a suspension bridge with inclined main cables and hangers, based on incremental Lagrangian formulation and kinematics theories. The static equilibrium equations are derived from a shape-finding method followed by the equations of motion. Comparison of modal analysis results of the proposed model and the finite element method demonstrates the accuracy of the proposed modelling technique.Modal analysis is further conducted with variations of the following system parameters, i.e. inclination angle of main cable, the ratio of flexural stiffness of deck in the vertical and lateral directions, the ratio of vertical flexural stiffness of deck and tensile stiffness of cable, and torsional moment of inertia of cross-section of deck. Results show that the difference of eigenfrequencies within the eigenfrequency cluster is smaller for a suspension bridge with vertical cables than that with inclined cables. Phenomena of crossover and veering of eigenfrequency loci of the bridge system are observed. The mechanism of such phenomena is further studied with the help of a sectional bridge model. The effect of variation of stiffness matrix of bridge system on the eigenfunction is studied. The condition for crossover and veering of the eigenfrequency loci of this bridge model is identified. It is noted that veering can affect the modal property of the system by coupling two involved modes. This effect should be carefully examined during the design of the suspension bridge.

Incremental variational formulation of time evolution of cure-degree along with viscoelasticity for thermosetting resins

Incremental variational formulation of time evolution of cure-degree along with viscoelasticity for thermosetting resins

A fresh look at the dynamics of a flexible body application to substructuring for flexible multibody dynamics

AbstractThe general formulation of the dynamics of an elastic body undergoing arbitrary motion is revisited with emphasis on the orthogonality between rigid body motion and elastic deformation on the one hand, and on the appropriate definition of the relative velocities induced by elastic deformation on the other hand. A mixed displacement–velocity approach is adopted, thus allowing a local frame definition of velocities which results in simplification of the discretization and solution steps. The proposed formulation is applied to model reduction starting from a set of free‐free elastic modes and attachment modes. The Herting–Martinez component mode synthesis method is used to replace the modal intensities by a body‐frame nodal set of elastic degrees of freedom. A body‐to‐global frame transformation is then applied to the system equations in incremental form to avoid the use of Lagrange multipliers for expressing node‐to‐node connections. Examples are presented to assess the methodology proposed and its numerical implementation.

System analysis and controller design for the electric pump of a deep-throttling rocket engine

This paper proposes a controller design for the electric pump of a deep-throttling rocket engine. The nonlinearity of the system is taken into consideration by analyzing the gap metric. Then, proportional-integral-derivative controller and gain-scheduling linear quadratic regulator are designed. Analyzing the amplitude- and phase-frequency characteristics as well as the pole-zero distribution of the system, the results show that the designed controllers can stabilize the linearized equations in incremental form at different operating points. This indicates that these two controllers are available for the original system in the whole range of working conditions and this is verified in the simulation. Meanwhile, the comparison between proportional-integral-derivative controller and gain-scheduling linear quadratic regulator is presented. It demonstrates that the proportional-integral-derivative controller is better at tracking both step and ramp signals but with worse control signals. It means that the proportional-integral-derivative controller seems less suitable for real use due to severe oscillations. Meanwhile, the parameter tuning of a proportional-integral-derivative controller depends on more extensive manual tuning. Therefore, the gain-scheduling linear quadratic regulator is preferred.

Using finite element analysis to predict the damage in FGM-3D notched plate under tensile load; Different geometric concept

FGM (functionally graded materials) have experienced rapid expansion in recent years in several industrial fields. The analysis of their mechanical behavior by the finite element method requires the use of subroutines established under a FORTRAN compiler given the difficulty in implementing the type of behavior of the materials constituting the FGM. Our work aims to establish a program in MATLAB (UMM) making possible to introduce the behavior of the FGM by element in the mesh model of the structure, hence the advantage and reliability of graded the material in three dimensions for two or even three constituents of FGM and secondly, for different geometric designs. This technique is more sensitive to the mesh, hence the adaptation strategy of a driven mesh in order to improve the precision and the convergence of results under minimal computation time. The constitutive law of our model follows the von Mises equivalent stress flow theory with a hardening variable in incremental form. Moreover, to describe the elastic–plastic behavior of FGM, the model of TTO (Tamura-Tomota-Ozawa) was used for both methods that of UMAT in the form of a numerical algorithm and for our new method in the form of calculated values by the MATLAB code. The parameters used in the two calculation methods are taken from the results of stress–strain tests of the two materials; ceramic (TiB; Titanium mono biorde) and metal (Ti; Titanium). A comparison between the two methods has taken place in the form of load–displacement curves in order to present the capacities of our technique with respect to the usual UMAT technique. However, for damage, the use of the XFEM technique in our UMM method has shown its advantage in the separation of the structure after crack initiation. The crack path as well as its propagation speed under the effect of the volume fraction exponent of the FGM has been highlighted. The two models used in this study (UMM and UMAT) were validated on the one hand with analytics through the TTO model and on the other hand by the experimentation of a tensile test.

A Viscoelastic Constitutive Model of Propellant with Pressure Cure

AbstractThe application of pressure cure molding technology can effectively reduce the structural integrity problems of casting solid rocket motors. In order to describe the curing and cooling process under this new technology more realistically, it is decomposed into two processes, pressurization curing, and pressure relief cooling and a time‐varying segmented solid propellant intrinsic equation applicable to the pressure cure molding technology is proposed. The constitutive equation takes into account the change in material properties caused by the change in the state of the propellant during the curing process. In order to accurately model the changes in mechanical properties of the propellant during curing, the present constitutive equations for this process are rewritten in incremental form and implemented in the user subroutine UMAT of the finite element analysis platform ABAQUS. The detailed derivation steps of the constitutive equation are introduced in this paper, and the subsequent application analysis is carried out with reference to the star‐shaped grain. The final stress and strain state of the propellant after cooling is used as the main analytical index. The results show that the pressure cure molding technology can effectively reduce the residual stress and the residual strain on the inner surface of the propellant grain. The pressure cure effect on the outer surface of the grain is relatively small compared to the overall reduction. The time‐varying constitutive model provides technical support for a more accurate description of the pressure cure process.

Optimal operation of integrated energy system considering virtual heating energy storage

The integrated energy system (IES) is the physical carrier of the Energy Internet, whose optimal operation has become a hot topic because of its effectiveness in improving energy utilization efficiency. This paper proposes an optimal operation model of integrated energy system, where the internal energy flow transmission characteristic of the heating network is modeled as virtual heating energy storage by the node method to enhance the operating flexibility of IES. The second-order cone relaxation method and the incremental formulation for the piecewise linearization method are utilized to transform the proposed nonlinear model into mixed integer quadratic constraint programming model, which can be effectively solved by the commercial solver. Case studies show that the proposed model effectively reduces the operating costs and improves the renewable energy penetration level of IES.

Analysis of cylindrical cavity expansion in anisotropic overconsolidated clays using the Extended UH model

Anisotropy and overconsolidation are two important features of depositional clay and are not comprehensively addressed in current cavity expansion solutions. Aiming at better modeling the cavity expansion responses in the natural soils, this paper develops a novel and rigorous elastoplastic semi-analytical solution by implementing the advanced anisotropic unified hardening (UH) model in conjunction with incorporating the anisotropic SMP criterion. The novel incorporation of the anisotropic SMP criterion and the proper consideration of overconsolidated properties are the major contributions of the present solution. By utilizing the anisotropic stress transformation method, the initial stress-induced anisotropy, anisotropic yielding and anisotropic failure of soil are also incorporated into the proposed solution. Following the derived constitutive equations in incremental form and large strain theory, both undrained and the drained cases are reduced to boundary-value problems consisting of several first-order ordinary differential equations formed in the Lagrangian scheme. Detailed parametric analyses are presented and compared with other existing solutions to investigate the effects of anisotropy and initial overconsolidation on the cavity responses. The present solution could properly capture the cross-anisotropy and 3D strength of overconsolidated soil and hence provides a more advanced and generic approach for modeling the cavity expansion responses in wide ranges of soils.