Microstructural scale effects in the nonlinear elastic response of bio-inspired wavy multilayers undergoing finite deformation

Abstract We discuss the nonlinear elastic response in scale invariant solids. Following previous work, we split the analysis into two basic options: according to whether scale invariance (SI) is a manifest or a spontaneously broken symmetry. In the latter case, one can employ effective field theory methods, whereas in the former we use holographic methods. We focus on a simple class of holographic models that exhibit elastic behaviour, and obtain their nonlinear stress-strain curves as well as an estimate of the elasticity bounds — the maximum possible deformation in the elastic (reversible) regime. The bounds differ substantially in the manifest or spontaneously broken SI cases, even when the same stress- strain curve is assumed in both cases. Additionally, the hyper-elastic subset of models (that allow for large deformations) is found to have stress-strain curves akin to natural rubber. The holographic instances in this category, which we dub black rubber, display richer stress- strain curves — with two different power-law regimes at different magnitudes of the strain.

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Nonlinear elastic response of single crystal Cu under uniaxial loading by molecular dynamics study

Materials Letters ◽

10.1016/j.matlet.2018.05.094 ◽

2018 ◽

Vol 227 ◽

pp. 236-239 ◽

Cited By ~ 8

Author(s):

Liang Zhang ◽

Cheng Lu ◽

Anh Kiet Tieu

Keyword(s):

Molecular Dynamics ◽

Single Crystal ◽

Uniaxial Loading ◽

Elastic Response ◽

Nonlinear Elastic

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A finite-deformation constitutive model of particle-binder composites incorporating yield-surface-free plasticity

Journal of Applied Mechanics ◽

10.1115/1.4052654 ◽

2021 ◽

pp. 1-32

Author(s):

Ankit Agarwal ◽

Marcial Gonzalez

Keyword(s):

Constitutive Model ◽

Yield Surface ◽

Finite Deformation ◽

Large Strain ◽

Elastic Response ◽

Rate Equations ◽

Internal Variables ◽

Model Parameters ◽

Stress Strain ◽

Stress Softening

Abstract We present a constitutive model for particle-binder composites that accounts for finite-deformation kinematics, nonlinear elasto-plasticity without apparent yield, cyclic hysteresis, and progressive stress-softening before the attainment of stable cyclic response. The model is based on deformation mechanisms experimentally observed during quasi-static monotonic and cyclic compression of mock Plastic-Bonded Explosives (PBX) at large strain. An additive decomposition of strain energy into elastic and inelastic parts is assumed, where the elastic response is modeled using Ogden hyperelasticity while the inelastic response is described using yield-surface-free endochronic plasticity based on the concepts of internal variables and of evolution or rate equations. Stress-softening is modeled using two approaches; a discontinuous isotropic damage model to appropriately describe the softening in the overall loading-unloading response, and a material scale function to describe the progressive cyclic softening until cyclic stabilization. A nonlinear multivariate optimization procedure is developed to estimate the elasto-plastic model parameters from nominal stress-strain experimental compression data. Finally, a correlation between model parameters and the unique stress-strain response of mock PBX specimens with differing concentrations of aluminum is identified, thus establishing a relationship between model parameters and material composition.

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Scale Effects in Orthotropic Composite Assemblies as Micropolar Continua: A Comparison between Weak- and Strong-Form Finite Element Solutions

Materials ◽

10.3390/ma12050758 ◽

2019 ◽

Vol 12 (5) ◽

pp. 758 ◽

Cited By ~ 11

Author(s):

Lorenzo Leonetti ◽

Nicholas Fantuzzi ◽

Patrizia Trovalusci ◽

Francesco Tornabene

Keyword(s):

Finite Element ◽

Scale Effects ◽

Kinematic Model ◽

Elastic Response ◽

Actual Behavior ◽

Orthotropic Composite ◽

Additional Degree ◽

Micropolar Continua ◽

Orthotropic Composites ◽

Micropolar Materials

The aim of the present work was to investigate the mechanical behavior of orthotropic composites, such as masonry assemblies, subjected to localized loads described as micropolar materials. Micropolar models are known to be effective in modeling the actual behavior of microstructured solids in the presence of localized loads or geometrical discontinuities. This is due to the introduction of an additional degree of freedom (the micro-rotation) in the kinematic model, if compared to the classical continuum and the related strain and stress measures. In particular, it was shown in the literature that brick/block masonry can be satisfactorily modeled as a micropolar continuum, and here it is assumed as a reference orthotropic composite material. The in-plane elastic response of panels made of orthotropic arrangements of bricks of different sizes is analyzed herein. Numerical simulations are provided by comparing weak and strong finite element formulations. The scale effect is investigated, as well as the significant role played by the relative rotation, which is a peculiar strain measure of micropolar continua related to the non-symmetry of strain and work-conjugated stress. In particular, the anisotropic effects accounting for the micropolar moduli, related to the variation of microstructure internal sizes, are highlighted.

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