A linked FEM-damage percolation model of aluminum alloy sheet forming

A so-called damage percolation model is linked with a finite element model of a sheet forming process to offer a comprehensive study of ductile damage evolution. In the current study, a damage percolation code is linked with LS-DYNA, an explicit dynamic FEM code used to introduce local strain gradients and compliance effects due to damage-induced softening. The linked model utilizes a Gurson-based yield surface to account for the softening effects of void damage, while the local damage development and void linkage events are modeled using the damage percolation code. The percolation code accepts detailed second phase particle fields from image analysis of a 2.0×1.6 mm optical micrograph of AA5182 aluminum alloy sheet. The model is applied to a stretch-flange stamping process which is known to be a damage-sensitive operation. The critical conditions for fracture are predicted for various initial stretch flange hole sizes.     

Time-strain rate superposition for relaxation behavior of polyethylene pressure pipes

A new superposition principle based on time and strain rate is suggested as an alternative approach to construct a master curve of relaxation modulus versus time for polyethylene (PE) pressure pipe. The new approach uses results from a series of relaxation tests that reach the same relaxation strain at different strain rates (by varying the crosshead speed). Construction of the master curve for the relaxation modulus is first through horizontal shift using an expression similar to that for the time–temperature superposition principle. Then, a vertical shift is applied to generate a smooth curve profile. Such a time-strain rate superposition principle can serve as an alternative approach to construct a master curve for the long-term behavior of PE. The master curve shows two transitions for the rate of decrease of the relaxation modulus, instead of one transition reported before. The additional transition occurs within a short period after the relaxation strain is reached, and is detectable only if the initial strain rate is sufficiently low. Discovery of the new transition offers an additional perspective for studying mechanisms involved in the PE deformation.     

Characterization of the compressive deformation behavior with strain rate effect of low-density polymeric foams

This study investigates the compressive deformation behavior of a low-density polymeric foam at different strain rates. The material tested has micron-sized pores with a closed cell structure. The porosity is about 94%. During a uni-axial compressive test, the macroscopic stress–strain curve indicates a plateau region during plastic deformation. Finite Element Method (FEM) simulation was carried out, in which the yield criterion considered both components of Mises stress and hydrostatic stress. By using the present FEM and experimental data, we established a computational model for the plastic deformation behavior of porous material. To verify our model, several indentation experiments with different indenters (spherical indentation and wedge indentation) were carried out to generate various tri-axial stress states. From the series of experiments and computations, we observed good agreement between the experimental data and that generated by the computational model. In addition, the strain rate effect is examined for a more reliable prediction of plastic deformation. Therefore, the present computational model can predict the plastic deformation behavior (including time-dependent properties) of porous material subjected to uni-axial compression and indentation loadings.     

Electronic structure and optic absorption of phosphorene under strain

We studied the electronic structure and optic absorption of phosphorene (monolayer of black phosphorus) under strain. Strain was found to be a powerful tool for the band structure engineering. The in-plane strain in armchair or zigzag direction changes the effective mass components along both directions, while the vertical strain only has significant effect on the effective mass in the armchair direction. The band gap is narrowed by compressive in-plane strain and tensile vertical strain. Under certain strain configurations, the gap is closed and the energy band evolves to the semi-Dirac type: the dispersion is linear in the armchair direction and is gapless quadratic in the zigzag direction. The band-edge optic absorption is completely polarized along the armchair direction, and the polarization rate is reduced when the photon energy increases. Strain not only changes the absorption edge (the smallest photon energy for electron transition), but also the absorption polarization.     

A finite deformation theory of strain gradient plasticity

Plastic deformation exhibits strong size dependence at the micron scale, as observed in micro-torsion, bending, and indentation experiments. Classical plasticity theories, which possess no internal material lengths, cannot explain this size dependence. Based on dislocation mechanics, strain gradient plasticity theories have been developed for micron-scale applications. These theories, however, have been limited to infinitesimal deformation, even though the micro-scale experiments involve rather large strains and rotations. In this paper, we propose a finite deformation theory of strain gradient plasticity. The kinematics relations (including strain gradients), equilibrium equations, and constitutive laws are expressed in the reference configuration. The finite deformation strain gradient theory is used to model micro-indentation with results agreeing very well with the experimental data. We show that the finite deformation effect is not very significant for modeling micro-indentation experiments.     

Bounds and estimates for the effect of strain gradients upon the effective plastic properties of an isotropic two-phase composite

Predictions are made for the size effect on strength of a random, isotropic two-phase composite. Each phase is treated as an isotropic, elastic-plastic solid, with a response described by a modified deformation theory version of the Fleck-Hutchinson strain gradient plasticity formulation (Fleck and Hutchinson, J. Mech. Phys. Solids 49 (2001) 2245). The essential feature of the new theory is that the plastic strain tensor is treated as a primary unknown on the same footing as the displacement. Minimum principles for the energy and for the complementary energy are stated for a composite, and these lead directly to elementary bounds analogous to those of Reuss and Voigt. For the case of a linear hardening solid, Hashin-Shtrikman bounds and self-consistent estimates are derived. A non-linear variational principle is constructed by generalising that of Ponte Castañeda (J. Mech. Phys. Solids 40 (1992) 1757). The minimum principle is used to derive an upper bound, a lower estimate and a self-consistent estimate for the overall plastic response of a statistically homogeneous and isotropic strain gradient composite. Sample numerical calculations are performed to explore the dependence of the macroscopic uniaxial response upon the size scale of the microstructure, and upon the relative volume fraction of the two phases.     

Consequences of a result on pure shear

If, in a continuum, the Cauchy stress tensor is traceless, the material is said to be in a state of “pure shear”. Here we derive consequences of a fundamental theorem concerning pure shear, in the contexts of infinitesimal strain, finite strain, and fluid motion.     

Modeling the response of filled elastomers at finite strains by rigid-rod networks

Summary  A constitutive model is developed for the isothermal response of particle-reinforced elastomers at finite strains. An amorphous rubbery polymer is treated as a network of long chains bridged to permanent junctions. A strand between two neighboring junctions is thought of as a sequence of rigid segments connected by bonds. In the stress-free state, a bond may be in one of two stable conformations: flexed and extended. The mechanical energy of a bond in the flexed conformation is treated as a quadratic function of the local strain, whereas that of a bond in the extended conformation is neglected. An explicit expression is developed for the free energy of a network. Stress–strain relations and kinetic equations for the concentrations of bonds in various conformations are derived using the laws of thermodynamics. In the case of small strains, these relations are reduced to the constitutive equation for the standard viscoelastic solid. At finite strains, the governing equations are determined by four adjustable parameters which are found by fitting experimental data in uniaxial tensile, compressive and cyclic tests. Fair agreement is demonstrated between the observations for several filled and unfilled rubbery polymers and the results of numerical simulation. We discuss the effects of the straining state, filler content, crosslink density and temperature on the adjustable constants. Received 3 January 2001; accepted for publication 12 July 2001     

Gradient plasticity modeling of geomaterials in a meshfree environment. Part I: Theory and variational formulation

Deformation and strength behavior of geomaterials in the pre- and post-failure regimes are of significant interest in various geomechanics applications. To address the need for development of a realistic constitutive framework, which allows for an accurate simulation of pre-failure response as well as an objective and meaningful post-failure response, a strain gradient plasticity model is formulated by incorporating the spatial gradients of elastic strain in the evolution of stress and gradients of plastic strain in the evolution of the internal variables. In turn, gradients of only kinematic variables are included in the constitutive equations. The resulting constitutive equations along with the balance of linear momentum for the continuum are cast as a coupled system of equations, with displacements and plastic multiplier appearing as the primary unknowns in the final governing integral equations. To avoid singular stress fields along element boundaries, a finite element discretization of the governing equations would require C² continuous displacements and C¹ continuous plastic multiplier, which is undesirable from a numerical implementation point of view. This issue is naturally resolved when a meshfree discretization is used. Hence the developed model is formulated within the framework of a meshfree environment. The new constitutive model allows an analysis of grain size effects on strength and dilatancy of rocks. The role and effectiveness of the new gradient terms on regularizing the underlying boundary value problems of geomechanics beyond the initiation of strain localization will be assessed in a future paper.     

A simple theory of strain gradient plasticity based on stress-induced anisotropy of defect diffusion

A new strain gradient plasticity theory is formulated to accommodate more than one material length parameter. The theory is an extension of the classical J₂ flow theory of metal plasticity to the micron scale. Distinctive features of the proposed theory as compared to other existing theories are the simplicities of mathematical formulation, numerical implementation and physical interpretation.