Material Constitutive Law Research Articles

Coupling 3D geomechanics to classical sedimentary basin modeling: From gravitational compaction to tectonics

Classical sedimentary basin simulators account for simplified geomechanical models that describe material compaction by means of phenomenological laws relating porosity to vertical effective stress. In order to overcome this limitation and to deal with a comprehensive poromechanical framework, an iterative coupling scheme between a basin modeling code and a mechanical finite element code is adopted. This work focuses on the porous material constitutive law specifically devised to couple 3D geomechanics to basin modeling. The sediment material is considered as an isotropic fully saturated poro-elastoplastic medium undergoing large irreversible strains. Special attention is given to the development of a hardening law capable of reproducing the same porosity evolution as provided by the standard basin simulator when the sediment material is submitted to gravitational compaction under oedometric conditions. A synthetic case is used to illustrate the ability of the proposed workflow to integrate horizontal deformations in the basin model as such effects cannot be captured by the simplified geomechanics of the standard basin code. The results obtained by the coupled simulation demonstrate that horizontal compression may significantly contribute to overpressure development and brittle failure of the basin seal rocks, highlighting the importance of a coupled approach to simulate complex tectonic history.

Nonlinear finite element models of reinforced concrete beams strengthened in bending with mechanically fastened aluminum alloy plates

This paper reports 3D nonlinear finite element (FE) models of reinforced concrete (RC) beams externally strengthened with mechanically fastened (MF) and externally bonded (EB) aluminum alloy (AA) plates. The measured and observed parameters of each specimen were obtained from an experiment conducted by the authors of this study. Each FE model adopted accurate material constitutive laws and appropriate element definitions to approximate the mechanical behavior observed during testing. A total of ten models were constructed based on the diameter, embedment depth, and arrangement of the expansion anchor bolt (EAB) as well as the presence or absence of epoxy. Results like the load-carrying capacity of the tested specimens as well as the failure modes like end-plate debonding (ED), local-plate debonding (LD), and plate rupture (PR) were accurately predicted. Additionally, Stress and strain contour plots were generated to investigate the FE models’ mechanical behaviors. Finally, a parametric study was conducted to illustrate the effects of the flexural steel reinforcement ratio and AA plate grades on the models’ structural response. It was concluded that the FE models could serve as a valid predictive platform for simulating the flexural behavior of RC beams strengthened with MF and EB AA plates.

A numerical study of progressive damage in unidirectional composite materials using a 2D lattice model

In this study, we explored the effects of different softening laws on the modelling of progressive damage in unidirectional composites materials using a 2D lattice model. The lattice model was based on axial springs that accounted for nearest-neighbour interactions. We considered linear and exponential softening laws and assessed their influence on the dynamic fracture response of unidirectional composite materials using two numerical examples. In order to overcome one of the drawbacks inherent to lattice models, i.e., the dependence on lattice cell size, we modified the material constitutive law by introducing a characteristic length parameter. The results obtained are also compared with experimental data reported by other researchers.

A simple and robust approach for 2D-simulation of reinforced concrete member

Over the past years, features of the computers aided numerical simulations of reinforced concrete (RC) have been improved with increasing technological developments. However, some difficulties remain such as modelling of snap-back behavior of quasi-brittle materials and convergence issue resulted from shape of the constitutive material law. In this study, a novel approach for the 2D nonlinear numerical modelling of the reinforced concrete member is presented. The proposed method of Linear Degradation Analysis (LDA) is developed integrating the isotropic continuum damage mechanic and the solution algorithm of lattice model. The main distinctive property of LDA is to combine simplicity of homogeneously distributed crack assumption and robustness of using secant stiffness reduction. In order to demonstrate the validity of LDA, several RC member containing beam, slab and frame from the literature are simulated. It can be concluded from the verification that the accuracy of the linear degradation analysis method is approved by remarkable similarity between the simulation and the experiment with regard to damage pattern and load displacement behavior.

Capacity Assessment of Existing RC Columns

Existing reinforced concrete (RC) members, designed in accordance with obsolete codes, are often characterized by high stirrup spacing. The collapse mechanisms generated by high stirrup spacing are typically related to the buckling of longitudinal reinforcement and can be accentuated when corrosion takes place. In this paper, new refined material constitutive laws for steel, including inelastic buckling and corrosion of reinforcement, are implemented in a fixed crack model suitable for RC elements subjected to cyclic loadings called the PARC_CL 2.1 crack model. The effectiveness of the proposed model is validated through comparison with available experimental data and analytical predictions. Finally, the proposed model is used to calibrate correction coefficients to be applied to current codes formulation for the ultimate rotational capacity prediction of non-conforming elements subjected to buckling phenomena and characterized by corrosion of reinforcing bars.

Analytical and numerical simplified modeling of a single-lap joint

This paper is devoted to the theoretical modeling of the mechanical response of bonded structures and particularly focuses on the single-lap joint which corresponds to the simplest and most fundamental bonding configuration. Such a geometry brings into play all the features of any bonded assembly in terms of mechanical response (stress/strain heterogeneities, singularities, adhesion at the interfaces,...). It can especially be used to characterize the mechanical behavior of new adhesives within an assembly. In all cases, an accurate description of the stress/strain distribution (specifically in the adhesive layer) is required both for the calibration of an adhesive behavior and for dimensioning purposes. Accordingly, the present study aims at developing a specific 1D enriched finite element devoted to the numerical modeling of single-lap joints, especially of the overlap region. First, analytical solutions for a single-lap joint under tensile forces are investigated in the framework of elasticity. They are particularly based on the choice of a 2D representation of the adhesive layer with polynomial displacement fields in terms of the thickness coordinate. Such a preliminary study allows one to identify optimally the appropriate kinematics for each layer (adhesive but also substrates) and highlights the importance of non-linear terms in the polynomial expressions of both longitudinal and transverse displacements within the adhesive. A three-layer finite element model is then formulated for the overlap region, based on the retained kinematics, and involving an elastoplastic constitutive law for the adhesive material. The numerical integration through the adhesive thickness and the assembly of the three layers lead to the definition of a very low-cost 1D finite element, which provides nevertheless a complete and accurate description of the stress fields, especially within the adhesive layer. This new finite element (used simultaneously with a more classical beam finite element for the unbonded parts of the adherends) is finally validated by comparison with 2D reference results computed using Abaqus software.

Thermoelastoviscoplastic Bilinear Compressive Constitutive Law of an AlSi-PE Abradable Material Based on Experimental Investigations

Abradable coatings are part of dynamic seals used in aircraft engines to reduce inter-stage leakages. However, during running, severe interactions may occur between the rotating blades and the coating of the casing leading to these parts getting damaged. Numerical approaches simulating these interactions could be a way to prevent these contact risks but they require both a characterization of the thermomechanical behavior of the abradable material and of the blade. This paper presents a quasi-static compression behavior study of a heterogeneous and porous AlSi-PE abradable used in the low-pressure compressor of aircraft engines. Combined with the results obtained for tests conducted at high compression strain-rates and extreme temperatures recently published in a previous paper (Skiba et al., in Dyn Behav Mater 6:213–223, 2020. 10.1007/s40870-020-00242-y), a thermoelastoviscoplastic bilinear constitutive law is proposed. This formulation allows the prediction of the macroscopic behavior of a heterogeneous and porous AlSi-PE abradable material from room temperature to 360 °C and with strain-rates ranging from 10–3 to 103 s−1.

The Ether Made Explicit Through Light, A Possible Universal Informational Matrix

Abstract Supossing that the ether is an infinite elastic medium, the constitutive material law that describes such a behaviour is determined. In a totally particular case, corresponding both to the stress tensor, and also to the strain tensor, it is shown that this constitutive material equation can be identified with an electromagnetic field, and, by extension, the Universe is of a informational type (universal informational matrix).

Sensitivity of friction coefficients, material constitutive laws and yield functions on the accuracy of springback prediction for an automotive part

High Strength Steel is more used in automotive industry to combine safety improvements and weight reductions of the vehicles. However, these steels raise new challenges for manufacturer, especially for springback and its prediction. Finite Element Analysis is widely used for the prediction of springback but accuracy is strongly depending on numerical as well as physical parameters. Such parameters affecting prediction are for example frictional behavior, constitutive model, loci function. In this paper the sensitivity of friction coefficients and the influence of some material laws on the springback prediction were studied and analyzed in details. Several numerical models are investigated in this work in order to allow the different aspects of materials mechanical behavior to be better described: isotropic work-hardening (Swift, Hockett-Sherby, SHS), isotropic-kinematic hardening, yield loci (Hill 48, Hill 90 and Barlat 91). In this study, we use an industrial example of the deep drawing process: the side sill closing with the material steel TRIP800. All the simulations are carried out with the commercial code Pam-Stamp 2G and comparison with the experimental results are presented.

Behaviors of steel-plate and concrete in steel-concrete-steel panels subjected to biaxial tension-compression

With the increasing application of steel–concrete-steel (SCS) composite structures in engineering constructions, the mechanical behaviors of steel plates and concrete in SCS structures are becoming increasingly important. This study aimed to evaluate the individual smeared behaviors of the steel plate and concrete from some tested SCS panels and analyze the main characteristics of the plates and concrete. An incremental step analysis method was used to analyze prior experimental research, in which seven SCS panels were subjected to proportional biaxial tension–compression loading. This method is based on Navier’s three principles (stress equilibrium, strain compatibility, and the constitutive laws of materials). Using this method, the smeared behaviors of the steel plates and concrete were evaluated. Through analysis, it was found that these smeared behaviors exhibit the following characteristics: When plastic flow occurs, the smeared stress state of steel plates flows on the yield surface after yielding, which results in an increasing principal tensile stress and a decreasing principal compressive stress. For the concrete in the principal compressive direction of the SCS panels, confinement and softening effects may coexist. The concrete in the principal tensile direction of the SCS panels exhibits two different behaviors, and an unexpected compressive stress may be generated. These findings will provide a clearer understanding of the mechanical behaviors of concrete and steel plates in SCS panels in future research.

Identification methodology of a rate-sensitive constitutive law with mean field and full field modeling approaches for polycrystalline materials

The present paper deals with the consideration of the rate-sensitivity mechanical behavior of metallic materials, in the framework of mean field and full field homogenization approaches. We re-examine the possibility of describing properly this rate sensitivity with a simple and widely used power law expressed at the level of the slip system, and we propose a methodology to accelerate the identification of the global material constitutive law for Finite Element (FE) simulations. For such an aim, simulations of a tensile test are conducted, using a simple homogenization model (the Taylor one, used in a relaxed constraint form) and an FE code (Abaqus), both using the same single-crystal rate-dependent constitutive law. It is shown that, provided that the identification of this law is performed with care and well adapted to the examined case (rate-sensitive or insensitive materials, static and/or dynamic ranges), the simple power law can be used to simulate the macroscopic behavior of polycrystalline aggregates in a wide range of strain rate (including both static and dynamic regimes) and strain-rate sensitivity values (up the rate-insensitive limit).

Numerical simulation of multi-hit impact on Ceramic/Composite armor

The numerical simulation of ballistic multi-hit impact on ceramic/composite armors is very challenging. The damage introduced by the previous hit affects the performance of the armor. In composite backings the damage is often more diffused than for metallic backings. Moreover, different sources of damage can intervene within the composite material. The present work proposes a mesoscopic scale approach to assess these issues. The 2D woven material is modelled with beams elements embedded in volume elements. Each component has its own material constitutive law and its damaging law. This approach allows to better model the damaging of the material, but also to better identify the material parameters from a set of basic experiments.

Large deflection analysis of functionally graded saturated porous rectangular plates on nonlinear elastic foundation via GDQM

In the current study, large deflection analysis of a functionally graded saturated porous (FGSP) rectangular plate subjected to transverse loading which is located on a nonlinear three-parameter elastic foundation is provided. The constitutive law for the porous materials is written based on Biot's model which considers the effect of fluids within the pores. The mechanical properties of the plate are changed through its thickness according to different functions which are called porosity distributions. The shear deformation effects are taken into account, accordingly, the first-order shear deformation theory (FSDT) is used to describe the displacement components of the plate. Employing the Minimum total potential energy principle and calculus of variation, the governing equations, and associated boundary conditions are extracted. A generalized differential quadrature method (GDQM) is used to solve them for various boundary conditions. The results for the simpler state are validated with the previously published works and then the effects of different parameters on the deflection of the plate are investigated. It is seen increasing the porosity and Skempton coefficient, enhances and reduces the deflection of the structure, respectively. The results of this study may help to design and manufacture more reliable engineering structures that are exposed to loads.

Blind competition on the numerical simulation of steel‐fiber‐reinforced concrete beams failing in shear

AbstractExperimental research has shown the extraordinary potential of the addition of short fibers to cement‐based materials by improving significantly the behavior of concrete structures for serviceability and ultimate limit states. Software based on the finite element method has been used for the simulation of the material nonlinear behavior of fiber‐reinforced concrete (FRC) structures. The applicability of the existing approaches has often been assessed by simulating experimental tests with structural elements, in general of a small scale, where the parameter values of the material constitutive laws are adjusted for the aimed predicting level, which constitutes an inverse technique of arguable utility for structural design practice. For assessing the predictive performance of these approaches, a blind simulation competition was organized. Two twin T‐cross section steel FRC beams, flexurally reinforced with steel bars and without conventional shear reinforcement in the critical shear span, were experimentally tested up to failure. Despite the experimental data provided for the definition of the relevant model parameters, inaccuracies on the load capacity, deflection, and strain at peak load attained 40, 113, and 600%, respectively. Inadequate failure modes and highly different results were estimated with the same commercial software, indicating the need for deeper analysis and understanding of the models and influence of their parameters on their predictive performance.

Dimensionally reduced nonlinear solids with general loads and constitutive laws: Theory and finite element formulation for rod-like bodies

Dimensionally reduced solids are formulated by linking the kinematics of a slender, rod-like body and a true, geometrically exact, rod. This link is enforced in such a way that the solid, where volumetric and surface loads can be applied, becomes slave of the rod, where the mechanical equilibrium is enforced. The model poses no limitations on the size of the deformations and displacements in either body and it can be used for quasistatic or dynamic analyses. A general finite-element approximation of the ensemble is described in detail, and shown to require only modifications at the assembly level for its implementation, resulting in large computational savings. These dimensionally reduced models are especially useful for problems such as fluid/solid interaction and contact where the surface forces among neighboring bodies need to be calculated accurately. By accounting for the internal energy in the slave solid instead of the rod, the proposed formulation allows also to model — without any additional ingredients — the mechanics of rods with complex material constitutive laws. Numerical examples illustrate the use of the new models in situations with complex loading and constitutive behavior.

Variational upscaling for modeling state of strain-dependent behavior and stress-induced crystallization in rubber-like materials

The purpose of this paper is to present a general upscaling strategy for deriving macroscopic constitutive laws for rubber-like materials from the knowledge of the network distribution and a mechanical description of the individual chains and of their free energy. The microscopic configuration is described by the position of the cross-links and is not obtained by an affine assumption but by minimizing the corresponding free energy on stochastic large representative volume elements with adequate boundary conditions. This general framework is then approximated by using a microsphere (directional) description of the network. It is presented in a global setting and is extended in order to handle situations with tube-like constraints and stress-induced crystallization.

Dynamic Analysis of Functionally Graded Porous Beams Using Complementary Functions Method in the Laplace Domain

In this study, an efficient numerical procedure is introduced to the solution of the dynamic response of functionally graded porous (FGP) beams. The elastic modulus and mass density of the porous materials are considered to have non-uniform distributions along the thickness direction. The typical open-cell metal foam is assumed to govern the material constitutive law. Within the framework of the first-order shear deformation theory (FSDT) the influence of shear strain is included in the formulations. The impact of damping is also considered. By using the canonically conjugate momentums and their derivatives, the governing canonical equations of motion of FGP beams are derived for the first time. These equations are then transformed into the Laplace space and solved numerically with the aid of the Complementary Functions Method (CFM). Obtained results are retransformed to the time domain by using an efficient inverse transform method. The dynamic response of FGP beams is studied for several boundary and loading conditions. The suggested procedure is verified with the available published literature and the finite element method. Detailed parametric studies are conducted to show the influence of porosity constants, symmetric and asymmetric porosity distributions and damping ratios on the dynamic response of FG porous beams.

Stable Generalized/eXtended Finite Element Method with global–local enrichment for material nonlinear analysis

This paper presents a novel methodology for the solution of nonlinear problems using the Stable Generalized/eXtended Finite Element Method (SGFEM) in two-scale approach. The nonlinear analysis is performed in a coarse mesh and the solution of a local problem, represented by a fine mesh, is used to enrich the partition of unity of the coarse mesh in the so-called global–local strategy. The SGFEM is adopted to deal with the problem of ill-conditioning of the stiffness matrix triggered by the enrichment strategy. Here, this problem is investigated for the first time for global–local analysis of physically nonlinear problem. In addition to the use of SGFEM, it is noteworthy that the relationship between the incremental-iterative process and changes in the constitutive variables are simultaneously updated on both scales. Differently from original GFEM global–local strategies, the evolution of the state variables is conduced only in the global scale. The local problem heritages the material degradation of the global scale, by using a mapping technique, and provides the numerically obtained functions that enriches the global approximation. Different constitutive models and material laws are adopted to incorporate the material degradation. Numerical examples are presented for validating this approach and to show its generality and efficiency.

Modeling and simulation of anisotropic linear viscoelasticity

A constitutive material law for linear viscoelasticity in the time domain is presented. It does not only allow for anisotropic elastic behavior but also for anisotropic (i.e. direction dependent) relaxation response. Under the assumption of thermo–rheological simple material behavior, the model is capable to account for direction dependent time–temperature-shift functions.The application is demonstrated for a linear viscoelastic matrix material reinforced by linear viscoelastic continuous fibers. The effective orthotropic linear viscoelastic response of the composite is computed by means of a periodic unit cell approach. These data, evaluated at different temperatures, are used to calibrate the input for the developed material law. Predictions from the latter are compared to the results from the unit cell simulations.

Numerical simulation of double-sided concrete corbels internally-reinforced with GFRP bars

Three-dimensional (3D) finite element (FE) models were developed in this study to simulate the nonlinear structural behavior of double-sided concrete corbels internally-reinforced with glass-fiber reinforced polymer (GFRP) bars. The accuracy of the numerical models was demonstrated by comparing their results with published experimental data of twelve specimens tested previously by the authors. Two sets of models were first developed. In one set, a perfect bond assumption was adopted between the GFRP bars and the concrete. In the other set, a bond stress-slip law was adopted at the GFRP-concrete interface. Numerical results were in good agreement with those recorded experimentally, except for the specimens with a high concrete strength and high GFRP reinforcement ratio, which failed prematurely in a diagonal splitting mode of failure. In an effort to capture such a mode of failure numerically, additional four models were developed without considering the tension-softening curve in the concrete material constitutive law. Results of the models with the bond-slip law were insignificantly lower than those with perfect bond assumption at GFRP-concrete interface. Eliminating the tension-softening curve from the concrete material constitutive law used in modeling specimens with a high concrete strength and high GFRP reinforcement ratio yielded numerical results closer to those obtained from the tests.