Elasto-plastic Phases Research Articles

Effective quasistatic evolution models for perfectly plastic plates with periodic microstructure: The limiting regimes

Abstract We identify effective models for thin, linearly elastic and perfectly plastic plates exhibiting a microstructure resulting from the periodic alternation of two elastoplastic phases. We study here both the case in which the thickness of the plate converges to zero on a much faster scale than the periodicity parameter and the opposite scenario in which homogenization occurs on a much finer scale than dimension reduction. After performing a static analysis of the problem, we show convergence of the corresponding quasistatic evolutions. The methodology relies on two-scale convergence and periodic unfolding, combined with suitable measure-disintegration results and evolutionary Γ-convergence.

On the Macroscopic Response and Field Statistics in Particulate Composites With Elasto-Plastic Phases and Random Microstructures

Abstract In this article, we carry out a theoretical investigation of the macroscopic response and field statistics in two-phase particulate composites with elasto-plastic constituents and random microstructures under cyclic loading conditions. To this end, we make use of the “incremental variational homogenization” (IVH) procedure of Agoras et al. (2016, “Incremental Variational Procedure for Elasto-Viscoplastic Composites and Application to Polymer- and Metal-Matrix Composites Reinforced by Spheroidal Elastic Particles,” Int. J. Solid Struct., 97–98, pp. 668–686) and corresponding unit cell finite element simulations. Results are obtained for statistically isotropic distributions of spherical particles and for “spheroidal distributions” of spheroidal particles. It is shown analytically that the IVH estimate of Agoras et al. and that of Lahellec and Suquet (2013, “Effective Response and Field Statistics in Elasto-Plastic and Elasto-Visco-Plastic Composites Under Radial and Non-Radial Loadings,” Int. J. Plasticity, 42, pp. 1–30) are equivalent. In addition, it is illustrated by means of specific numeral comparisons that the IVH estimate is also equivalent (to within numerical accuracy) to the corresponding estimates of Idiart and Lahellec (2016, “Estimates for the Overall Linear Properties of Pointwise Heterogeneous Solids With Application to Elasto-Viscoplasticity,” J. Mech. Phys. Solids, 97, pp. 317–332) and Lucchetta et al. (2019, “A Double Incremental Variational Procedure for Elastoplastic Composites With Combined Isotropic and Linear Kinematic Hardening,” Int. J. Solid Struct., 158, pp. 243–267). Furthermore, it is shown in the context of specific exact results for composite materials with lamellar microstructures that the elastic–plastic coupling and the Bauschinger effect are the macroscopic manifestations of the incompatibility of the local elastic strains. Local strain hardening is incorporate in the IVH model. The predictions of the IVH model for the macroscopic response of particulate composites are found to be in good agreement with the corresponding numerical results, in general. For the extreme cases of rigidly reinforced composites and porous materials, however, the IVH model fails to capture the elastic–plastic coupling and the Bauschinger effect. The underlying reasons for this shortcoming are discussed and a strategy toward the improvement of the IVH model is proposed.

Uniaxial tensile behavior of ultra-high performance fiber-reinforced concrete (uhpfrc): Experiments and modeling

Ultra-High Performance Fiber-Reinforced Concrete (UHPFRC) is considered a promising material for many structural applications where high strength and high energy absorption capacity are required.The purpose of this work is to study the uniaxial tensile behavior of soft cast (flowable at casting time) UHPFRC by varying the amount of hooked steel fibers (30-mm long) from 0% up to 2.55% by volume. Direct tensile tests have been performed on dog-bone shaped specimens and Digital Image Correlation (DIC) has been used to measure displacements and deformations and to monitor the evolution of cracks. Then, a phase-field model has been implemented in a FE code and numerical simulations have been performed to better understand the effects of different fiber dosages on the mechanical behavior of UHPFRC composites and on their post-elastic evolution. Concrete matrix and fiber reinforcement have been modeled as brittle and elasto-plastic phases of a mixture, whose internal energies are enriched by non-local damage and plasticity contributions. The different failure mechanisms observed in experiments have been reproduced, including the ductile failure experienced by specimens with sufficiently high fiber dosage, which distinguishes for a strain-hardening phase of matrix multi- micro-cracking that anticipates material failure.

The Effects of Loading Conditions on the Behaviour of Fixed-Ended Plain Channel Columns.

The compressive behaviour of column members can be considerably affected by local buckling, material yielding and local end conditions. In this paper, the effects of the loading conditions at the ends of plain channel section columns subjected to uniformly compressed loading, and fixed conditions at the column ends with respect to global rotations, was examined. Finite element simulation was employed to look at the post-buckled response of thin-walled, plain channel section columns that covered the complete loading history of the compression columns from the onset of elastic local buckling through the nonlinear elastic and elastoplastic post-buckling phases of behaviour to final collapse and unloading. Two types of loading conditions were considered: the first was one that has been used practically in tests whereby one end is loaded with a moving top platen while the other end is fixed at the lower platen, but, for the second loading condition, both ends were loaded with equally moving top and lower platens. These two conditions were shown to lead to quite different characteristic interactive responses of the columns due to mode jumping in the buckling mode for the locally rotationally constrained case.

On interface conditions on a material singular surface

The presence of grain boundaries significantly influences the overall mechanical behavior of materials with an underlying crystalline microstructure. They act as an obstacle against the movement of dislocations and, thus, significantly contribute to size effects as for example the Hall–Petch effect. Hence, the thermodynamically consistent modeling of the behavior of the plastic slip at a grain boundary is of utmost interest. To this end, balance equations at a grain boundary are derived from an extended energy balance by means of invariance considerations. The grain boundary is considered as a material singular surface with own internal and kinetic energy as well as energy supply. Consequently, the balances at the grain boundary depend on its mean curvature. The framework presented is applied to a small strain slip gradient crystal plasticity theory, regarding single slip. Accounting for the derived balance equations, thermodynamically consistent flow rules for the plastic slip at the grain boundary are obtained by exploitation of the Coleman–Noll procedure. In this context, a classification of flow rules for the plastic slip at the grain boundary is provided. Finally, the distribution of the plastic slip is presented regarding a three-phase laminate material with two elastoplastic phases and one elastic phase. The two elastoplastic phases represent the grains of a bicrystal. A grain boundary effect is discussed which is based on a variation of the internal length scale in one of the two elastoplastic phases.

On periodic homogenization in perfect elasto-plasticity

The limit behavior of a periodic assembly of a finite number of elasto-plastic phases is investigated as the period becomes vanishingly small. A limit quasi-static evolution is derived through two-scale convergence techniques. It can be thermodynamically viewed as an elasto-plastic model, albeit with an infinite number of internal variables.

A combined incremental-secant mean-field homogenization scheme with per-phase residual strains for elasto-plastic composites

This paper presents an incremental secant mean-field homogenization (MFH) procedure for composites made of elasto-plastic constituents. In this formulation, the residual stress and strain states reached in the elasto-plastic phases upon a fictitious elastic unloading are considered as starting point to apply the secant method. The mean stress fields in the phases are then computed using secant tensors, which are naturally isotropic and enable to define the Linear–Comparison-Composite. The method, which remains simple in its formulation, is valid for general non-monotonic and non-proportional loading. It is applied on various problems involving elastic, elasto-plastic and perfectly-plastic phases, to demonstrate its accuracy compared to other existing MFH methods.

Failure Mechanics of Uniformly Compressed Thin-Walled Box-Section Struts

It is well known that the structural performance of thin-walled compression members is subject to the effects of local buckling and material yielding. Due to these effects, the compressive carrying capability of short strut members can be significantly reduced. This paper employs finite element simulation to examine the post-buckled response of thin-walled box-sections that covers complete loading history of the compression struts from the onset of elastic local buckling through the nonlinear elastic and elasto-plastic post-buckling phases of behaviour up to final collapse and unloading. A detailed account of the growth and redistribution of stresses on the surfaces is given in the paper. The results from finite element simulations are shown to compare well with the analytical method of analysis.

Equilibrium Conditions at a Solid-Solid Interface

We derive the thermodynamic conditions necessary for two elastoplastic solid phases to coexist in equilibrium. Beyond temperature, velocity, and traction continuity, these conditions require continuity of a generalization of the specific Gibbs free energy. We express this quantity in the Eulerian frame as well as the Lagrangian frame. We also show that two approaches in deriving the equilibrium conditions, one on the continuum level and the other on the atomistic scale, yield the same results. Finally, we discuss two possible interpretations for the Gibbs free energy, which lead to distinct generalizations, except in the case of inviscid fluids, where they coincide.

Size effects in generalised continuum crystal plasticity for two-phase laminates

The solutions of a boundary value problem are explored for various classes of generalised crystal plasticity models including Cosserat, strain gradient and micromorphic crystal plasticity. The considered microstructure consists of a two-phase laminate containing a purely elastic and an elasto-plastic phase undergoing single or double slip. The local distributions of plastic slip, lattice rotation and stresses are derived when the microstructure is subjected to simple shear. The arising size effects are characterised by the overall extra back stress component resulting from the action of higher order stresses, a characteristic length l c describing the size-dependent domain of material response, and by the corresponding scaling law l n as a function of microstructural length scale, l. Explicit relations for these quantities are derived and compared for the different models. The conditions at the interface between the elastic and elasto-plastic phases are shown to play a major role in the solution. A range of material parameters is shown to exist for which the Cosserat and micromorphic approaches exhibit the same behaviour. The models display in general significantly different asymptotic regimes for small microstructural length scales. Scaling power laws with the exponent continuously ranging from 0 to −2 are obtained depending on the values of the material parameters. The unusual exponent value −2 is obtained for the strain gradient plasticity model, denoted “ curl H p ” in this work. These results provide guidelines for the identification of higher order material parameters of crystal plasticity models from experimental data, such as precipitate size effects in precipitate strengthened alloys.

Plasticity-triggered architectural effects in periodic multilayers with wavy microstructures

Despite considerable presence of periodic multilayers with wavy architectures in nature and technology, little simulation data is available on their response. A recent investigation of wavy multilayers comprised of alternating elastic and elastic-perfectly plastic plies has revealed the important role that plasticity plays on their post-yield response relative to the corresponding flat configurations [Khatam, H., Pindera, M.-J., 2009b. Parametric finite-volume micromechanics of periodic materials with elastoplastic phases. Int. J. Plasticity 25 (7), 1386–1411]. Herein, we extend this investigation by considering the effect of elastic layer thickness on the post-yield response at several fixed elastic phase volume fractions using the parametric finite-volume direct averaging micromechanics (FVDAM) theory. The layer thickness is shown to have a substantial impact on the post-yield response whose extent depends on the loading mode and waviness amplitude, in contrast with the minimal impact on the homogenized elastic moduli. Decreasing the layer thickness at sufficiently high fixed volume fractions decreases the extent of strain hardening under transverse normal loading, as well as the maximum normal and shear stresses in the stiff layers, reducing the possibility of failure and thus potentially enhancing durability. The opposite holds under transverse shear loading for low waviness amplitudes. The presented results provide a framework for tailoring the elastoplastic response of multilayers with sinusoidally varying plies under different loading modes.

High-Fidelity Micromechanical Modeling of Continuously Reinforced Elastic Multiphase Materials Undergoing Finite Deformations

The purpose of this communication is twofold. First, we demonstrate the predictive capability of a recently extended micromechanics model known as the high-fidelity generalized method of cells, originally developed for unidirectionally reinforced periodic multiphase materials characterized by elastic or elasto-plastic phases undergoing infinitesimal deformation. The recent extension incorporates finite-deformation capabilities to enable modeling of heterogeneous materials such as fiber-reinforced rubbers or certain types of biological tissues characterized by potential-based, nonlinear elastic phases. The model's capability to accurately estimate both the homogenized nonlinear elastic response and the local stress fields in the individual phases is demonstrated by comparison with an exact elasticity solution for a porous composite with four different types of the matrix material under axisyrmnetric loading, and a finite-element analysis of a repeating unit cell representative of a unidirectionally reinforced periodic composite subjected to transverse loading. Second, we demonstrate the micromechanics model's utility as a subroutine in a structural analysis setting by implementing it into a specialized lamination theory framework in the absence of bending. Examples of the nonlinear response of families of [±θ]s lay-ups under biaxial inplane loading are provided, demonstrating how the developed model can be used either to validate or to construct macroscopic constitutive laws for materials, such as certain biological tissues, characterized by multi-directional reinforcement.

Deformation Characteristics of Crashworthy Thin-Walled Steel Tubes Subjected to Bending

The collapse behaviour and crashworthy characteristics of cantilever circular tubes subjected to bending are studied both theoretically and experimentally. Three different fixture devices were used and their effect on failure behaviour of the tube was investigated in detail. A theoretical method, proposed by Hodge, slightly modified, is used to analyse the elastic and elastoplastic phases of bending, while a rigid-perfectly plastic analysis is developed to describe the plastic bending phase. Agreement between experimental and theoretical results was found to be quite good.