Constitutive Modeling Framework Research Articles

A computational framework for G/XFEM material nonlinear analysis

The Generalized/eXtended Finite Element Method (G/XFEM) has been developed with the purpose of overcoming some limitations inherent to the Finite Element Method (FEM). Different kinds of functions can be used to enrich the original FEM approximation, building a solution specially tailored to problem. Certain obstacles related to the nonlinear analysis can be mitigated with the use of such strategy and the damage and plasticity fronts can be precisely represented. A FEM computational environment has been previously enclosed the G/XFEM formulation to linear analysis with minimum impact in the code structure and with requirements for extensibility and robustness. An expansion of the G/XFEM implementation to physically nonlinear analysis under the approach of an Unified Framework for constitutive models based on elastic degradation is firstly presented here. The flexibility of the proposed framework is illustrated by several examples with different constitutive models, enrichment functions and analysis models.

Peridynamics‐Based Fracture Animation for Elastoplastic Solids

AbstractIn this paper, we exploit the use of peridynamics theory for graphical animation of material deformation and fracture. We present a new meshless framework for elastoplastic constitutive modelling that contrasts with previous approaches in graphics. Our peridynamics‐based elastoplasticity model represents deformation behaviours of materials with high realism. We validate the model by varying the material properties and performing comparisons with finite element method (FEM) simulations. The integral‐based nature of peridynamics makes it trivial to model material discontinuities, which outweighs differential‐based methods in both accuracy and ease of implementation. We propose a simple strategy to model fracture in the setting of peridynamics discretization. We demonstrate that the fracture criterion combined with our elastoplasticity model could realistically produce ductile fracture as well as brittle fracture. Our work is the first application of peridynamics in graphics that could create a wide range of material phenomena including elasticity, plasticity, and fracture. The complete framework provides an attractive alternative to existing methods for producing modern visual effects.

NURBS plasticity: Yield surface evolution and implicit stress integration for isotropic hardening

This paper extends the non-uniform rational basis spline (NURBS) plasticity framework of Coombs et al. (2016) to include isotropic hardening of the yield surfaces. The approach allows any smooth isotropic yield envelope to be represented by a NURBS surface. The key extension provided by this paper is that the yield surface can expand or contract through the movement of control points linked to the level of inelastic straining experienced by the material. The model is integrated using a fully implicit backward Euler algorithm that constrains the return path to the yield surface and allows the derivation of the algorithmic consistent tangent to ensure optimum convergence of the global equilibrium equations. This provides a powerful framework for elasto-plastic constitutive models where, unlike the majority of models presented in the literature, the underlying numerical algorithm (and implemented code) remains unchanged for different yield surfaces. The performance of the algorithm is demonstrated, and validated, using both material point and boundary values simulations including plane stress, plane strain and three-dimensional examples for different yield criteria.

Semi-analytical and semi-numerical method for the single soil layer consolidation problem

PurposeThis paper aims to present a simplified solution method for the elasto-plastic consolidation problem under different stress paths.Design/methodology/approachFirst, a double-yield-surface model is introduced as the constitutive model framework, and a partial derivative coefficient sequence is obtained by using numerical approximation using Gauss nuclear function to construct a discretization constitutive model which can reflect the influence of different stress paths. Then, the model is introduced to Biot’s consolidation theory. Volumetric strain of each step as the right-hand term, the continuity equation is simplified as a Poisson equation and the fundamental solution is derived by the variable separation method. Based on it, a semi-analytical and semi-numerical method is presented and implemented in a finite element program.FindingsThe method is a simplified solution that is more convenient than traditional coupling stiffness matrix method. Moreover, the consolidation of the semi-infinite foundation model is analyzed. It is shown that the numerical method is sufficiently stable and can reflect the influence of stress path, loading distribution width and some other factors on the deformation of soil skeleton and pore water pressure.Originality/valueOriginal features of this research include semi-numerical semi-analytical consolidation method; pore water pressure and settlements of different stress paths are different; maximum surface uplift at 3.5a; and stress path is the main influence factor for settlement when loading width a > 10 m.

A computational framework for constitutive modelling

The field of computational constitutive modelling for engineering applications is an active research tread in academia. New advanced models and formulations are constantly proposed. However, when dealing with implementation aspects, often the main concern is to provide a minimal environment to show a certain model and its applications, with implementations made from scratch. Though advanced, usually such implementations lack of generality and are well-suited for a certain numerical method while not compatible with other ones, making it difficult to reuse the code in other contexts. The Object-Oriented Paradigm (OOP) to programming have been widely applied in the last years for the realization of numerous academic numerical simulation softwares, due to its fundamental properties of abstraction, inheritance and polymorphism that allow the creation of programs well-suited for an easy collaboration between developers with expertise in different fields of engineering and mechanics. As showed in this paper, the same properties can be effectively extended also to the constitutive aspects of a model. The application of the OOP to the constitutive modelling of a wide range of materials of engineering interest is investigated, aiming to the creation of a computational framework for constitutive models that is fully independent on the other components of a code and easy to expand.

Autotuning of Isotropic Hardening Constitutive Models on Real Steel Buckling Data with Finite Element Based Multistart Global Optimisation on Parallel Computers

An automatic framework for tuning plastic constitutive models is proposed. It is based on multistart global optimisation method, where the objective function is provided by the results of multiple elastoplastic finite element analyses, executed concurrently. Wrapper scripts were developed for fully automatic preprocessing, including model and mesh generation, analysis, and postprocessing. The framework is applied to an isotropic power hardening plasticity using real load/displacement data from multiple steel buckling tests. M. J. D. Powell’s BOBYQA constrained optimisation package was used for local optimisation. It is shown that using the real data presents multiple problems to the optimisation process because (1) the objective function can be discontinuous, yet (2) relatively flat around multiple local minima, with (3) similar values of the objective function for different local minima. As a consequence the estimate of the global minimum is sensitive to the amount of experimental data and experimental noise. The framework includes the verification step, where the estimate of the global minimum is verified on a different geometry and loading. A tensile test was used for verification in this work. The speed of the method critically depends on the ability to effectively parallelise the finite element solver. Three levels of parallelisation were exploited in this work. The ultimate limitation was the availability of the finite element commercial solver license tokens.

A viscoactive constitutive modeling framework with variational updates for the myocardium

We present a constitutive modeling framework for contractile cardiac mechanics by formulating a single variational principle from which incremental stress–strain relations and kinetic rate equations for active contraction and relaxation can all be derived. The variational framework seamlessly incorporates the hyperelastic behavior of the relaxed and contracted tissue along with the rate–and length–dependent generation of contractile force. We describe a three-element, Hill-type model that unifies the active tension and active deformation approaches. As in the latter approach, we multiplicatively decompose the total deformation gradient into active and elastic parts, with the active deformation parametrizing the contractile Hill element. We adopt as internal variables the fiber, cross-fiber, and sheet normal stretch ratios. The kinetics of these internal variables are modeled via definition of a kinetic potential function derived from experimental force–velocity relations. Additionally, we account for dissipation during tissue deformation by adding a Newtonian viscous potential. To model the force activation, the kinetic equations are coupled with the calcium transient obtained from a cardiomyocyte electrophysiology model. We first analyze our model at the material point level using stress and strain versus time curves for different viscosity values. Subsequently, we couple our constitutive framework with the finite element method (FEM) and study the deformation of three-dimensional tissue slabs with varying cardiac myocyte orientation. Finally, we simulate the contraction and relaxation of an ellipsoidal left ventricular model and record common kinematic measures, such as ejection fraction, and myocardial tissue volume changes.

A constitutive modelling framework predicting critical state in sand undergoing crushing and dilation

This paper explains why the critical state of sand is non-unique when expressed in terms of stress and void ratio only. For this purpose, a thermodynamically consistent, micromechanically inspired constitutive modelling framework with competing grain crushing and dilation is developed. While grain crushing is described through the theory of breakage mechanics, dilation is modelled in a novel way by acknowledging its negative contribution to the overall positive rate of dissipation. The competition between dilation and grain crushing underpinned by this framework yields a unique critical state in a space of stress, void ratio and breakage, in agreement with recent experiments. As an example, a simple constitutive model with only five mechanical parameters is proposed, which not only predicts the critical state but also quantitatively connects the full constitutive behaviour to key index properties related to grading- and breakage-dependent minimum and maximum densities.

Effects of tension/compression asymmetry on the buckling and recovery of NiTi tubes under axial compression

We recently demonstrated that pseudoelastic NiTi tubes compressed axially buckle first into an axisymmetric wrinkling mode but subsequently collapse by progressive development of buckle lobes with three circumferential waves. This behavior is governed by the material nonlinearity associated with the austenite to martensite solid-state transformation. On unloading, the material transforms back to austenite, deformation is recovered, and the buckling lobes are erased (Jiang et al., 2016). The problem was simulated numerically using a constitutive model framework for the pseudoelastic behavior of NiTi based on a J2-type nonlinear kinematic hardening model with the back stress represented through a potential. The first generation of the model did not account for the significant tension/compression asymmetry exhibited by the material so the buckling response did not reproduce well the experiments underestimating the dissipated energy. In the present work the constitutive model is extended to include the tension/compression asymmetry. It is introduced through a weighted mix of two potentials that are calibrated to the tensile and compressive stress-strain responses of the material. In addition, the present model allows for plastic deformations at the completion of martensite transformation. Incorporation of the tension/compression asymmetry significantly improves the calculated response of the buckling and recovery of NiTi tubes both qualitatively and quantitatively. The addition of plastic deformations to the model further improves the predictions. The initial axisymmetric wrinkling and the switch to the buckling mode with three circumferential waves are now reproduced correctly, and so are the evolution of localized collapse and the recovery of deformation on unloading. Furthermore, the stress levels during collapse and recovery follow the experimental levels quite closely thus reproducing the energy dissipated.

Image-driven constitutive modeling of myocardial fibrosis

ABSTRACTMyocardial fibrosis is a pathological process that occurs during heart failure (HF). It involves microstructural remodeling of normal myocardial tissue, and consequent changes in both cardiac geometry and function. The role of myocardial structural remodeling in the progression of HF remains poorly understood. We propose a constitutive modeling framework, informed by high-resolution images of cardiac tissue structure, to model the mechanical response of normal and fibrotic myocardium. This image-driven constitutive modeling approach allows us to better reproduce and understand the relationship between structural and functional remodeling of ventricular myocardium during HF.

A size-dependent constitutive modelling framework for localised failure analysis

Localised deformation of materials usually takes place in thin bands during the nonlinear phase of the deformation process. The orientation and size of these localisation bands are important proper...

A constitutive model for mechanical and chemo‐mechanical compaction in sedimentary basins and finite element analysis

SummaryCompaction and associated fluid flow are fundamental processes in sedimentary basin deformation. Purely mechanical compaction originates mainly from pore fluid expulsion and rearrangement of solid particles during burial, while chemo‐mechanical compaction results from Intergranular Pressure‐Solution (IPS) and represents a major mechanism of deformation in sedimentary basins during diagenesis. The aim of the present contribution is to provide a comprehensive 3D framework for constitutive and numerical modeling of purely mechanical and chemo‐mechanical compaction in sedimentary basins. Extending the concepts that have been previously proposed for the modeling of purely mechanical compaction in finite poroplasticity, deformation by IPS is addressed herein by means of additional viscoplastic terms in the state equations of the porous material. The finite element model integrates the poroplastic and poroviscoplastic components of deformation at large strains. The corresponding implementation allows for numerical simulation of sediments accretion/erosion periods by progressive activation/deactivation of the gravity forces within a fictitious closed material system. Validation of the numerical approach is assessed by means of comparison with closed‐form solutions derived in the context of a simplified compaction model. The last part of the paper presents the results of numerical basin simulation performed in one dimensional setting, demonstrating the ability of the modeling to capture the main features in elastoplastic and viscoplastic compaction. Copyright © 2016 John Wiley & Sons, Ltd.

Semi-analytical and semi-numerical method for plane strain consolidation of double-layer foundation considering stress paths

In this work, a simplified solution method is present for the elasto-plastic consolidation of a double-layer foundation under different stress paths. A double-yield surface model is introduced as the constitutive model framework for saturated clay and sand. Using a Gauss kernel function, a partial derivative coefficient sequences is obtained. Then, the model is applied to Biot’s consolidation equations and to establish incremental governing partial differential equations for the plane strain consolidation problem. By simplifying the continuity equation as a Poisson equation, the fundamental solutions are derived for double-layer foundation model. Based on it, a semi-analytical and semi-numerical method is presented which is implemented in our finite element program. Comparisons with different mesh show that the stability of the numerical method is good. Moreover, the consolidation of semi-infinite double-layer foundation models is analysed under two stress paths (conventional loading path under the condition of isotropic consolidation CTC and conventional loading path under the condition of anisotropic consolidation K0 + CTC). It is shown that the model can reflect the influence of stress path, loading distribution width and some other factors on the deformation of the soil skeleton and pore water pressure. This simplified solution appears to be more convenient than the traditional coupling stiffness matrix method.

A thermodynamic framework for constitutive modeling of coupled moisture-mechanical induced damage in partially saturated viscous porous media

A general thermodynamic-based framework is proposed to derive coupled moisture-mechanical induced damage constitutive relationships for multi-phase viscoelastic porous media. The well-known (Kachanov, 1958) effective (undamaged) configuration and the concept of effective stress space are extended to moisture-susceptible materials to couple the detrimental effects of moisture to the mechanical response of materials. A physically-based moisture-induced damage internal state variable is introduced within the proposed framework to account for the moisture aggravation effect, and to couple moisture-induced damage with mechanical responses. The principle of virtual power, Clausius–Duhem inequality and maximum rate of energy dissipation are constructed for multi-phase porous media. These principles are used to obtain the main macroscopic and microscopic balance laws, the general framework, and the constitutive relationships. The thermodynamic conjugate forces are decomposed into energetic and dissipative components, obtained from Helmholtz free energy and the rate of energy dissipation, to accurately estimate the rate of energy dissipation. The proposed thermodynamic framework is used to develop a comprehensive viscoelastic model, which takes into account the effect of pore water pressure, a constitutive relationship to model the detrimental effect of moisture diffusion inside the solid phase, Darcy’s law, Fick’s second law and, the Fourier heat conduction equation. The resulting constitutive relationships describe the coupled effects of mechanical loading and moisture-induced damage and accurately predict the response of partially saturated viscous porous media under various mechanical loading and environmental conditions.

A solution strategy for non-linear implicit BEM formulation using a unified constitutive modelling framework

A new solution strategy for the non-linear Implicit Formulation of the Boundary Element Method is presented. Such strategy is based on a decomposition of the strain increment variation vector in two parts: one associated to the cumulative external loads and another associated to the current unbalanced vector, obtained from the difference of the first part and the calculated internal strain field distribution, during the iterative process. This approach makes the algorithm generic enough to deal with different control methods that governs the progression of the non-linear analysis. Also, a unified constitutive modelling framework for a single loading function is used to provide the material constitutive informations required by the solution strategy, which permits the implementation of a very comprehensive series of models in an independent way. However, only local models were treated. To demonstrate the efficiency and versatility of the methodology, some numerical examples are presented.

Thermodynamic-based cohesive zone healing model for self-healing materials

This work presents a thermodynamic-based cohesive zone framework to model healing in materials that tend to self-heal. The nominal, healing and effective configurations of continuum damage-healing mechanics are extended to represent cohesive zone configurations. To incorporate healing in a cohesive zone model, the principle of virtual power is used to derive the local static/dynamic macroforce balance and the boundary traction as well as the damage and healing microforce balances. A thermodynamic framework for constitutive modeling of damage and healing mechanisms of cracks is used to derive the evolution equations for the damage and healing internal state variables. The effects of temperature, resting time, crack closure, history of healing and damage, and level of damage on the healing behavior of the cohesive zone are incorporated. The proposed model promises solid basis for understanding the self-healing phenomena in self-healing materials.

On the thermomechanical coupling in dissipative materials: A variational approach for generalized standard materials

This paper deals with the thermomechanical coupling in dissipative materials. The focus lies on finite strain plasticity theory and the temperature increase resulting from plastic deformation. For this type of problem, two fundamentally different modeling approaches can be found in the literature: (a) models based on thermodynamical considerations and (b) models based on the so-called Taylor–Quinney factor. While a naive straightforward implementation of thermodynamically consistent approaches usually leads to an over-prediction of the temperature increase due to plastic deformation, models relying on the Taylor–Quinney factor often violate fundamental physical principles such as the first and the second law of thermodynamics. In this paper, a thermodynamically consistent framework is elaborated which indeed allows the realistic prediction of the temperature evolution. In contrast to previously proposed frameworks, it is based on a fully three-dimensional, finite strain setting and it naturally covers coupled isotropic and kinematic hardening — also based on non-associative evolution equations. Considering a variationally consistent description based on incremental energy minimization, it is shown that the aforementioned problem (thermodynamical consistency and a realistic temperature prediction) is essentially equivalent to correctly defining the decomposition of the total energy into stored and dissipative parts. Interestingly, this decomposition shows strong analogies to the Taylor–Quinney factor. In this respect, the Taylor–Quinney factor can be well motivated from a physical point of view. Furthermore, certain intervals for this factor can be derived in order to guarantee that fundamental physically principles are fulfilled a priori. Representative examples demonstrate the predictive capabilities of the final constitutive modeling framework.

Modeling of anisotropic hardening of sheet metals including description of the Bauschinger effect

The present paper proposes a framework for constitutive modeling of plasticity to describe the evolution of anisotropy and the Bauschinger effect in sheet metals. An anisotropic yield function, which varies continuously with increasing plastic strain, is defined as an interpolation between two yield functions at two discrete levels of plastic strain. Several types of nonlinear functions of the effective plastic strain are proposed for the interpolation. A framework for a combined anisotropic-kinematic hardening model of large-strain cyclic plasticity with small elastic strain is presented, and the details of modeling which is based on the Yoshida–Uemori model (Yoshida et al., 2002, Yoshida and Uemori, 2002, 2003) are described. The shape of the yield surface and that of the bounding surface are assumed in the model to change simultaneously. The model was validated by comparing the calculated results of stress–strain responses with experimental data on r-value and stress-directionality changes in an aluminum sheet (Hu, 2007) and a stainless steel sheet (Stoughton and Yoon, 2009), as well as the variation of the yield surface of an aluminum sheet (Yanaga et al., 2014). Furthermore, anisotropic cyclic behavior was examined by performing experiments of uniaxial tension and cyclic straining in three sheet directions on a 780-MPa advanced high-strength steel sheet.

An enriched constitutive modelling framework for localised failure of geomaterials

Fallas localizadas en geomateriales estan precedidas y se dan en conjunto con deformaciones intensas y cambios micro estructurales irreversibles del material en una region de tamano finito, pero pequena. Corte, compactacion y bandas de dilatacion observables en suelos y rocas porosas son ejemplos tipicos de fenomenos que conducen a fallas localizadas. Ha sido experimentalmente demostrado que el ancho h de la banda de localizacion es una cantidad fisica relacionada con la micro estructura del material. Por otro lado, metodos numericos para la resolucion de problemas de valor en la frontera usualmente introducen otra longitud de escala H como un resultado de la discretizacion espacial del dominio considerado en partes mas pequenas sobre el cual la respuesta constitutiva del material esta definida en terminos de relaciones incrementales de tension-deformacion. Mientras h como cantidad fisica esta fija, H varia con la resolucion de la discretizacion numerica. Dado que h escala con la micro estructura del material y por lo tanto es usualmente mucho mas pequeno que la resolucion de la discretizacion numerica, el caso H > h es considerado en este estudio, por ejemplo el comportamiento en falla gobernado por una banda de localizacion de ancho h inserta en una masa elastica de lado nominal H. Se presenta un marco de modelamiento constitutivo general para conectar estas dos escalas, y las respuestas correspondientes del material dentro y fuera de la zona de localizacion. Se demuestra como esta estrategia puede ayudar a obtener soluciones con significado fisico que son independientes de la discretizacion espacial en analisis numericos. Analisis numericos de falla localizada en materiales cuasi fragiles son ademas usados para destacar las caracteristicas y aplicabilidad de la estrategia propuesta.

A constitutive modelling framework featuring two scales of behaviour: Fundamentals and applications to quasi-brittle failure

We propose a constitutive modelling framework with enhanced kinematics to capture localised mode of deformation. The total strain is decomposed into two components to reflect an inelastic localisation band embedded in an elastic bulk. This is the usual case in numerical analysis of localised failure in geomaterials, when the size of the localisation band is very small compared to an element of the discretised domain under consideration. The proposed framework takes into account the sizes and corresponding behaviours of the two inelastic and elastic zones and hence gives derived constitutive models a length scale. This is an essential feature in dealing with size effect issues as a consequence of localised failure in geomaterials. The proposed framework is applied to a constitutive model for the failure analysis of quasi-brittle materials. The implementation algorithms are developed and novel features are illustrated through numerical examples.