Formulation Of Constitutive Model Research Articles

Residual mechanical properties of high strength concrete BBR9 subjected to dynamic uniaxial compressive loading

In recent years, enormous efforts have been devoted to accurately quantifying the residual load-bearing capacity of concrete at the material level when exposed to elevated temperatures. However, relatively less attention has been given to investigating the effects of dynamic events such as terrorist attacks, earthquakes, and hurricanes, which can cause complete collapse of concrete structures and have significant public and economic consequences. Hence, in the present study, a modified Kolsky compression bar system integrated with a momentum trapping technique was implemented to develop precisely controlled pre-/post peak high strain-rate loading to introduce distinctive states of damage inside the high strength concrete HSC-BBR9 specimens and to measure the corresponding plastic strain. Thereafter, the partially damaged specimens were tested to quantify the residual mechanical properties (e.g., residual stiffness and residual strength) at different plastic strain levels. Furthermore, a high-resolution laboratory micro-CT scanner was used to visualize the 3D crack network morphology in the partially damaged specimens. The findings demonstrated a remarkable decrease in the residual capacity with increasing levels of damage-induced plastic deformation. Additionally, the results showed a fundamental difference in the influence of internal damage on residual stiffness and strength to be acknowledged in the formulations of future constitutive damage models for concrete materials.

Thermal Conductivity and Temperature Dependency of Magnetorheological Fluids and Application Systems-A Chronological Review.

Many studies on magnetorheological fluid (MRF) have been carried out over the last three decades, highlighting several salient advantages, such as a fast phase change, easy control of the yield stress, and so forth. In particular, several review articles of MRF technology have been reported over the last two decades, summarizing the development of MRFs and their applications. As specific examples, review articles have been published that include the optimization of the particles and carrier liquid to achieve minimum off-state viscosity and maximum yield stress at on-state, the formulation of many constitutive models including the Casson model and the Herschel-Bulkley (H-B) model, sedimentation enhancement using additives and nanosized particles, many types of dampers for automotive suspension and civil structures, medical and rehabilitation devices, MRF polishing technology, the methods of magnetic circuit design, and the synthesis of various controllers. More recently, the effect of the temperature and thermal conductivity on the properties of MRFs and application systems are actively being investigated by several works. However, there is no review article on this issue so far, despite the fact that the thermal problem is one of the most crucial factors to be seriously considered for the development of advanced MRFs and commercial products of application systems. In this work, studies on the thermal conductivity and temperature in MRFs themselves and their temperature-dependent application systems are reviewed, respectively, and principal results are summarized, emphasizing the following: how to reduce the temperature effect on the field-dependent properties of MRFs and how to design an application system that minimizes the thermal effect. It is noted here that the review summary is organized in a chronological format using tables.

A comparative study on different neural network architectures to model inelasticity

AbstractThe mathematical formulation of constitutive models to describe the path‐dependent, that is, inelastic, behavior of materials is a challenging task and has been a focus in mechanics research for several decades. There have been increased efforts to facilitate or automate this task through data‐driven techniques, impelled in particular by the recent revival of neural networks (NNs) in computational mechanics. However, it seems questionable to simply not consider fundamental findings of constitutive modeling originating from the last decades research within NN‐based approaches. Herein, we propose a comparative study on different feedforward and recurrent neural network architectures to model 1D small strain inelasticity. Within this study, we divide the models into three basic classes: black box NNs, NNs enforcing physics in a weak form, and NNs enforcing physics in a strong form. Thereby, the first class of networks can learn constitutive relations from data while the underlying physics are completely ignored, whereas the latter two are constructed such that they can account for fundamental physics, where special attention is paid to the second law of thermodynamics in this work. Conventional linear and nonlinear viscoelastic as well as elastoplastic models are used for training data generation and, later on, as reference. After training with random walk time sequences containing information on stress, strain, and—for some models—internal variables, the NN‐based models are compared to the reference solution, whereby interpolation and extrapolation are considered. Besides the quality of the stress prediction, the related free energy and dissipation rate are analyzed to evaluate the models. Overall, the presented study enables a clear recording of the advantages and disadvantages of different NN architectures to model inelasticity and gives guidance on how to train and apply these models.

Effect of Material State and Temperature on Nonlinear Viscoelastic Response: 3D Constitutive Model and Incremental Formulation for Numerical Analysis

Effect of Material State and Temperature on Nonlinear Viscoelastic Response: 3D Constitutive Model and Incremental Formulation for Numerical Analysis

Nonlocal strain regularisation for critical state models with volumetric hardening

The finite element (FE) method may suffer from numerical instability and mesh dependency when modelling the formation of shear bands using strain-softening constitutive models. Nonlocal methods have been shown to be capable of avoiding these numerical issues effectively. This paper proposes a novel generic algorithm for incorporating existing nonlocal methods into the FE formulation of elasto-plastic constitutive models with volumetric hardening laws. Using the example of the modified Cam Clay (MCC) model this paper shows that instabilities are inevitable if the nonlocal plastic volumetric strains are directly used to update the hardening parameter. The paper further proposes a robust regularisation algorithm to overcome this issue. This algorithm has been implemented into a bespoke FE code and its capability in significantly reducing mesh dependency while maintaining numerical stability is verified through a series of numerical analyses of biaxial compression tests for highly overconsolidated clays. The performance of various existing nonlocal methods is also critically assessed.

Formulation and implementation of elastoplastic constitutive model for carbonaceous slate

Formulation and implementation of elastoplastic constitutive model for carbonaceous slate

A theoretical homogenized constitutive model formulation for matrix composite materials reinforced with curved fibers

A theoretical homogenized constitutive formulation to approximate the stiffness of reinforced composite with curved fibers is developed in this work. The theoretical model considers the stiffness contribution of the fibers taking into account their curvatures and spatial orientations. The variation of the geometry of the fibers is taken into account by means of a statistical distribution of their height and angle of orientation. In this way, it is possible to consider various scenarios, including the curvatures introduced by the manufacturing process. Comparisons of the elastic moduli obtained by 3D finite element analysis with the results of the present approach show good agreement. Finally, a parametric study that shows the effect of the main variables included in the proposed model is also presented.

Chemo-mechanical behaviour of non-expansive clays accounting for salinity effects

Changes in the chemistry of the pore fluid are known to have an impact on the hydro-mechanical behaviour of clays. Experimental evidence collected in recent decades has led to the formulation of constitutive chemo-mechanical models for expansive soils used in engineering practice for the containment of pollution, such as bentonite. Less attention has been paid to modelling the chemo-mechanical behaviour of non-expansive clays, which are less frequently used for geoenvironmental applications, but equally exposed to chemical changes. Key differences between the impact of salinity on the fabric of expansive and non-expansive clays are pointed out. At the macroscopic scale, an increase in salinity causes a translation of the normal compression line of non-expansive clays to higher void ratios, which in some cases is also accompanied by an increase in compressibility. The opposite occurs for expansive clays. Such experimental evidence provides the basis for a chemo-mechanical model formulated in the frame of elasto-plasticity with generalised hardening, whose yield surface expands with pore fluid concentration. The model is validated against experimental results, both original and from the literature. Simulation results compare very well with those of tests performed on reconstituted, compacted and intact samples.

Rate-dependent constitutive model of high-strength reinforcing steel HTRB600E in tension

High-strength reinforcing steel HTRB600E has significant potential application in reinforced concrete (RC) structures because of its high strength and ductility. Under the risk that structures with HTRB600E are subjected to severe dynamic loadings, the rate-dependent behavior and constitutive model of HTRB600E need to be investigated to provide a basis for the structural analysis. A series of tension tests were carried out to acquire the engineering stress–strain curves of HTRB600E in the strain rate range from 0.00025 to 590 s−1. Moreover, a hybrid experimental–numerical converse method was used to obtain the true stress–strain curves beyond the necking of HTRB600E at different strain rates. The test results indicate that the strain rate significantly affects the mechanical properties of HTRB600E. The effect of strain rate on yield and ultimate tensile strength, uniform elongation, and yield to tensile ratio of HTRB600E was discussed. Three commonly-used models were calibrated or modified to predict the dynamic increase factors (DIFs) for yield and ultimate tensile strength of HTRB600E. A rate-dependent constitutive model for the engineering stress–strain curves modified from the Mander model was presented for the structure's analytical model based on the section analysis technique. A new rate-dependent constitutive model for the true stress-plastic strain relationship with necking behavior was proposed for the structure's nonlinear finite element analysis model. The formulations of DIFs and constitutive models agree with the test results well.

A thermo-viscoelastic model of anisotropic polyamide short glass fiber composites

This study presents experimental investigation and formulation of a new anisotropic nonlinear thermo-viscoelastic constitutive model to understand the time-dependent multi-axial responses of polyamide composites subjected to various histories of mechanical loading at several isothermal temperatures: 20 °C-100 °C. The composites were tested under uniaxial tension along 0° and 90° injection molding directions and the axial and lateral responses of the specimens were recorded. Experimental results indicate that composites exhibit pronounced time-dependent responses, even at low temperatures, and mechanical loadings, even at relatively low strain levels, cause permanent deformations and hysteretic responses. A new constitutive model that accounts for continuous microstructural changes under thermo-mechanical stimuli was formulated to describe the macroscopic anisotropic responses of the composites. The model was derived based on a multi-network approach and the microstructural changes are governed by the deformations of the composites. Elevated temperatures soften the polymers, making it easier to deform the composites, and thus accelerate the microstructural changes. The model is shown capable of describing mechanical responses of polyamide composites under various loading conditions, loading histories, and temperatures.

Incorporating Rheological Nonlinearity into Fractional Calculus Descriptions of Fractal Matter and Multi-Scale Complex Fluids

In this paper, we use ideas from fractional calculus to study the rheological response of soft materials under steady-shearing flow conditions. The linear viscoelastic properties of many multi-scale complex fluids exhibit a power-law behavior that spans over many orders of magnitude in time or frequency, and we can accurately describe this linear viscoelastic rheology using fractional constitutive models. By measuring the non-linear response during large step strain deformations, we also demonstrate that this class of soft materials often follows a time-strain separability principle, which enables us to characterize their nonlinear response through an experimentally determined damping function. To model the nonlinear response of these materials, we incorporate the damping function with the integral formulation of a fractional viscoelastic constitutive model and develop an analytical framework that enables the calculation of material properties such as the rate-dependent shear viscosity measured in steady-state shearing flows. We focus on a general subclass of fractional constitutive equations, known as the Fractional Maxwell Model, and consider several different analytical forms for the damping function. Through analytical and computational evaluations of the shear viscosity, we show that for sufficiently strong damping functions, for example, an exponential decay of fluid memory with strain, the observed shear-thinning behavior follows a power-law response with exponents that are set by the power-law indices of the linear fractional model. For weak damping functions, however, the power-law index of the high shear rate viscosity is set by the terminal behavior of the damping function itself at large strains. In the limit of a very weak damping function, the theoretical formulation predicts an unbounded growth of the shear stress with time and a continuously growing transient viscosity function that does not converge to a meaningful steady-state value. By determining the leading terms in our analytical solution for the viscosity at both low and high shear rates, we construct an approximate analytic expression for the rate-dependent viscosity. An error analysis shows that, for each of the damping functions considered, this closed-form expression is accurate over a wide range of shear rates.

Micromechanical thermo-hydro-mechanical coupled model for fractured rocks considering multi-scale structures and its engineering application

Most existing studies on the coupled thermal-hydro-mechanical models for fractured rock mass are formulated using the macroscopic phenomenology method. As a result, the micromechanical behaviors of discontinuities, which essentially control the macroscopic response of the material, are not well considered in modeling the thermal-hydro-mechanical coupling processes for disturbed rock mass. In this study, the fractured rock mass is characterized by an anisotropic medium containing arbitrarily distributed penny-shaped microcracks in rock blocks separated by multiple sets of critically orientated fractures of large scales. This is an anisotropic coupled thermal-hydro-mechanical model for deformed saturated rock masses, which is capable of considering the alteration of macro-meso discontinuities. A multiscale damage constitutive model for fractured rock mass with the thermal-hydro-mechanical coupling is presented based on the Mori-Tanaka homogenization method and the thermodynamics theory. The influences of anisotropic damage growth, sliding dilatancy and normal compression of small-scale microcracks, and shear sliding and mobilized degradation of large-scale fractures are commendably accounted for. To reflect the anisotropic strength, the interaction between large-scale fractures and small-scale microcracks is also considered by practically relating the microcracks damage resistance to the orientation of fractures. By capturing the deformation of fractures and the opening and connectivity variations of microcracks with the constitutive model, the multi-scale structural change-induced permeability variation is modeled by the volumetric averaging method. The constitutive model and permeability tensor formulation have been implemented in a FEM code, which is then coupled with the well-established non-isothermal fluid flow simulator TOUGHREACT by an interlaced algorithm to establish a coupled thermal-hydro-mechanical numerical simulation platform. A numerical example is finally performed to investigate the effects of multi-scale structures and thermal-hydro-mechanical couplings on the water injection-induced temperature, pressure, and deformation responses of a deeply buried geothermal reservoir. The research may provide a useful reference for deepening the study of the thermal-hydro-mechanical couplings in deep rocks.

Formulation and calibration of two-dimensional constitutive models for composite structures based on panel tests

Steel Plate Concrete (SC) composite members have been widely adopted because of its cost-efficiency and enhanced structural behavior. While researchers have attempted to study its in-plane shear behavior in the past twenty years, very limited number of large-scale pure shear tests were performed due to the challenge of experimental set-up and the availability of facilities. In this paper, a series of uniaxial loading tests and two full-scale pure shear panel tests of SC members were reported, on which the “mechanics-based Membrane Model of SC elements (MM-SC)” is developed. The MM-SC model is based on the fixed-angle crack formulation and the smeared-crack formulation, in which the experimental-based uniaxial constitutive models are implemented, considering the local buckling of faceplate, the tension stiffening of steel plate, the strength degradation of cracked concrete and the confinement effect of concrete. The proposed MM-SC model is subsequently incorporated into the object-oriented software OpenSEES. The simulation results of proposed model well predict the SC test observations in terms of critical branch points and structural behaviors, including initial stiffness, cracking strength, post-crack stiffness, yield strength, maximum strength, and failure modes.

Localised failure of geomaterials: how to extract localisation band behaviour from macro test data

The formulation and calibration of constitutive models for geomaterials require material behaviour from experiments under a wide range of triaxial loading conditions. However, failure of geomaterials usually involves localisation of deformation that leads to very strong inhomogeneous behaviour. Therefore, the experimentally measured macro (specimen) behaviour is a mix between very different responses inside and outside the localisation zone and thus should not be used as a true representation of the material responses. This paper proposes a theoretical framework that provides links between mechanical responses inside and outside the localisation band, alongside their contributions toward the overall behaviour of a specimen undergoing localised deformation. This meso–macro connection allows the quantification of behaviour inside the localisation band, which is the main source of material inelasticity, from experimentally measured specimen behaviour. Correlation between the thickness of the localisation band and its behaviour is shown, bounded by a unique stress–deformation relationship describing the behaviour of an idealised zero-thickness localisation band.

Low velocity impact on pre-loaded composite plates: A novel standard-based experimental apparatus

Despite composite materials presenting a viable design solution for structural weight savings, their low resistance to impact damage portraits a potential drawback. This work presents a study on the compressive pre-loading effects on Low Velocity Impact, LVI, for composite laminated plates. Despite the absence of a standard testing procedure accounting for pre-load effects, a test rig was designed specifically for LVI on pre-loaded plates while preserving ASTM D7136M-15 guidelines for the stress-free specimens. Woven fabric composite laminated plates were manufactured using the Resin Transfer Moulding (RTM) process and subjected to impact on pre-loaded conditions. Three pre-load levels were prescribed, representing conditions ranging from low strain levels until post buckling regime. FE numerical models were implemented in ABAQUS FE code, comparing different Continuum Damage Mechanics (CDM) constitutive model formulations with experimental results. Analytical and numerical predictions showed good correlation with experimental results, allowing for further application of the test apparatus and methodology.

Systematic Review on the Creep of Fiber-Reinforced Concrete.

Fiber-reinforced concrete (FRC) is increasingly used in structural applications owing to its benefits in terms of toughness, durability, ductility, construction cost and time. However, research on the creep behavior of FRC has not kept pace with other areas such as short-term properties. Therefore, this study aims to present a comprehensive and critical review of literature on the creep properties and behavior of FRC with recommendations for future research. A transparent literature search and filtering methodology were used to identify studies regarding creep on the single fiber level, FRC material level, and level of structural behavior of FRC members. Both experimental and theoretical research are analyzed. The results of the review show that, at the single fiber level, pull-out creep should be considered for steel fiber-reinforced concrete, whereas fiber creep can be a governing design parameter in the case of polymeric fiber reinforced concrete subjected to permanent tensile stresses incompatible with the mechanical time-dependent performance of the fiber. On the material level of FRC, a wide variety of test parameters still hinders the formulation of comprehensive constitutive models that allow proper consideration of the creep in the design of FRC elements. Although significant research remains to be carried out, the experience gained so far confirms that both steel and polymeric fibers can be used as concrete reinforcement provided certain limitations in terms of structural applications are imposed. Finally, by providing recommendations for future research, this study aims to contribute to code development and industry uptake of structural FRC applications.

Effect of prior deformation on the subsequent creep and anelastic recovery behaviour of an advanced martensitic steel: Unified constitutive modelling

This paper presents an elastic-viscoplastic constitutive model formulation for the representation of different aspects of high-temperature deformation behaviour of an advanced martensitic steel under various loading conditions. The model is a variant of the well-known Chaboche constitutive model and uses a bi-term power-law equation for describing the stress dependency of the viscoplastic strain rate. Isotropic and kinematic hardening/softening considerations have been incorporated through the employment of drag-stress and back-stress concepts. The evolution equations for drag-stress and back-stress consider contributions from strain hardening, dynamic strain softening, and static recovery. The effectiveness of the model formulation has been examined for the representation of the deformation behaviour of a 10%Cr martensitic steel at 600 °C. It has been demonstrated that the developed model could provide a fairly accurate description for i) constant-load creep, ii) constant-strain stress-relaxation, iii) anelastic recovery, and iv) negative creep behaviour of the alloy. More importantly, evidence on the capability of the model for taking into consideration the effect of prior-loading on the subsequent viscoplastic response has been presented.

Elastoplastic constitutive modeling for concrete: a theoretical and computational approach

Abstract This article presents a study of the plasticity model applicability to concrete in a theoretical framework that generalizes the formulation of constitutive models for physically nonlinear analysis of structures. In this sense, the theoretical framework for the computational implementation of the plasticity mathematical theory is described, detailing the models formulations capable to describe the inelastic behavior of concrete. The loading surfaces associated to Drucker Prager and Ottosen criterion are highlighted. Furthermore, the Cutting Plane return mapping algorithm, necessary to the integration of constitutive relations that govern the behavior of the material in the context of computational plasticity, is described. Finally, numerical simulations are presented, such as the direct tension loading and three-point bending tests. The results of these simulations are compared with those from the literature to verify the model stability and accuracy.

A new approach for physically nonlinear analysis of continuum damage mechanics problems using the generalized/extended finite element method with global-local enrichment

The Generalized/Extended Finite Element Method (G/XFEM) is a numerical technique suitable to solve a wide range of continuum mechanics problems. It applies hierarchical nodal enrichment strategies within the Finite Element Method framework, allowing more flexibility in the numerical solution of boundary value problems (BVP) and being a powerful mesh-reduced method that takes advantage of the state-of-art of the standard FEM. One of the enrichment mechanisms is the so-called global-local enrichment (G/XFEMGL), in which the solution of a refined local BVP generates enrichment functions for the global domain. In this context, this work presents a new two-scale nonlinear strategy, associated with the G/XFEMGL, able to solve the material nonlinear analysis of continuum damage mechanics problems, in which quasi-brittle media degrade and soften, using a versatile mesh refinement strategy. A comprehensive description of the proposed strategy is registered and the aforementioned computational technique is validated throughout a set of plane stress numerical experiments that employ smeared crack constitutive model formulations, with well-known stress-strain laws. The results indicate that the implemented methodology could be used to solve a reasonable range of problems with considerable flexibility.

The fixed-strut-angle finite element (FSAFE) model for reinforced concrete structural walls

This paper evaluates the capabilities and limitations of a relatively simple mesoscopic finite element modeling approach, referred to as the Fixed Strut Angle Finite Element (FSAFE) Model, in simulating the hysteretic lateral load behavior of reinforced concrete structural walls designed to yield in flexure. The behavioral characteristics of the constitutive panel (membrane) elements incorporated in the model are based on a simple fixed-crack-angle formulation, where normal stresses in concrete are calculated along fixed crack directions using a uniaxial stress–strain relationship, with modifications to represent biaxial softening effects. The constitutive panel model formulation also incorporates behavioral models for the shear-aggregate-interlock effects in concrete and dowel action on reinforcing bars, constituting the shear stress transfer mechanisms across cracks. Model predictions are compared with experimentally-measured responses of benchmark wall specimens with a variety of configurations and response characteristics. Accurate predictions are obtained for important global response attributes of the walls prior to failure, including their lateral load capacity, stiffness, ductility, and hysteretic response characteristics; although instability failures related to buckling of reinforcement and/or out-of-plane instability of the wall boundary region are not captured. The model provides accurate estimates of the relative contribution of nonlinear flexural and shear deformations to wall lateral displacements, as well as local response characteristics including the distribution of curvatures, strains, and shear deformations on the walls, prior to failure. Based on the response comparisons presented, model capabilities are assessed and possible model improvements are identified. Overall, the FSAFE model is shown to be a practical yet reliable modeling approach for simulating nonlinear wall behavior, which can be used within the framework of performance-based seismic design and assessment of building structures.