Nonaffine displacements and the nonlinear response of a strained amorphous solid

Effect of nonaffine displacement on the mechanical performance of degraded PCL and its graphene composites: an atomistic investigation

Evaluating the mechanical properties of biodegradable implants can be challenging for in situ experiments and time-consuming for materials with a slow degradation rate, such as polycaprolactone (PCL). In this work, the effects of chain scission and water erosion on the mechanical properties of degraded PCL are investigated by molecular dynamics simulation. The decrease of the mechanical performance is correlated with the increase of the nonaffine displacement during the degradation. The nonaffine squared displacements (NSD) during the tensile deformation are calculated by subtracting the affine squared displacements from the mean squared displacements. After chain scission, short polymer chains increase the NSD of the system and weaken the modulus of the polymer matrix. The effect of the NSD is also observed in a water erosion model. When the bond break ratio is less than 5%, PCL still maintains a well-entangled network, which constrains the diffusion of the water molecules, resulting in a higher modulus of the erosion model than the chain scission model at a low degradation rate. The effect of NSD is also found in the PCL/graphene composites. For the degraded polymer chains, the diffusion of PCL is constrained by the graphene network, and such an effect increases during the degradation. As a result, the addition of graphene nanosheets slows down the decreasing trend of Young's modulus. Such findings can also explain the size effect of the graphene reinforcement on the mechanical properties of the polymer composites. This work provides atomistic insights into the mechanical property evolution during polymer degradation, revealing the possibility of tuning the mechanical performance by controlling the diffusion, which could be beneficial for the design and lifetime prediction of degradable implants.

Nonlinear elasticity, yielding, and entropy in amorphous solids

The holographic duality has proven successful in linking seemingly unrelated problems in physics. Recently, intriguing correspondences between the physics of soft matter and gravity are emerging, including strong similarities between the rheology of amorphous solids, effective field theories for elasticity, and the physics of black holes. However, direct comparisons between theoretical predictions and experimental/simulation observations remain limited. Here, we study the effects of nonlinear elasticity on the mechanical and thermodynamic properties of amorphous materials responding to shear, using effective field and gravitational theories. The predicted correlations among the nonlinear elastic exponent, the yielding strain/stress, and the entropy change due to shear are supported qualitatively by simulations of granular matter models. Our approach opens a path toward understanding the complex mechanical responses of amorphous solids, such as mixed effects of shear softening and shear hardening, and offers the possibility to study the rheology of solid states and black holes in a unified framework.

Theory of sound attenuation in amorphous solids from nonaffine motions

We present a theoretical derivation of acoustic phonon damping in amorphous solids based on the nonaffine response formalism for the viscoelasticity of amorphous solids. The analytical theory takes into account the nonaffine displacements in transverse waves and is able to predict both the ubiquitous low-energy diffusive damping ∼k², as well as a novel contribution to the Rayleigh damping ∼k⁴at higher wavevectors and the crossover between the two regimes observed experimentally. The coefficient of the diffusive term is proportional to the microscopic viscous (Langevin-type) damping in particle motion (which arises from anharmonicity), and to the nonaffine correction to the static shear modulus, whereas the Rayleigh damping emerges in the limit of low anharmonicity, consistent with previous observations and macroscopic models. Importantly, thek⁴Rayleigh contribution derived here does not arise from harmonic disorder or elastic heterogeneity effects and it is the dominant mechanism for sound attenuation in amorphous solids as recently suggested by molecular simulations.

Rejuvenation and shear banding in model amorphous solids

We measure the local yield stress, at the scale of small atomic regions, in a deeply quenched two-dimensional glass model undergoing shear banding in response to athermal quasistatic deformation. We find that the occurrence of essentially a single plastic event suffices to bring the local yield stress distribution to a well-defined value for all strain orientations, thus essentially erasing the memory of the initial structure. It follows that in a well-relaxed sample, plastic events cause the abrupt (nucleation-like) emergence of a local softness contrast and thus precipitate the formation of a band, which, in its early stages, is measurably softer than the steady-state flow. Moreover, this postevent yield stress ensemble presents a mean value comparable to that of the inherent states of a supercooled liquid around the mode-coupling temperature T_{MCT}. This, we argue, explains that the transition between brittle and ductile yielding in amorphous materials occurs around a comparable parent temperature. Our data also permit to capture quantitatively the contributions of pressure and density changes and demonstrate unambiguously that they are negligible compared with the changes of softness caused by structural rejuvenation.

Precursors of fluidisation in the creep response of a soft glass

Via extensive numerical simulations, we study the fluidisation process of dense amorphous materials subjected to an external shear stress, using a three-dimensional colloidal glass model. In order to disentangle possible boundary effects from finite size effects in the process of fluidisation, we implement a novel geometry-constrained protocol with periodic boundary conditions. We show that this protocol is well controlled and that the longtime fluidisation dynamics is, to a great extent, independent of the details of the protocol parameters. Our protocol, therefore, provides an ideal tool to investigate the bulk dynamics prior to yielding and to study finite size effects regarding the fluidisation process. Our study reveals the existence of precursors to fluidisation observed as a peak in the strain-rate fluctuations, that allows for a robust definition of a fluidisation time. Although the exponents in the power-law creep dynamics seem not to depend significantly on the system size, we reveal strong finite size effects for the onset of fluidisation.

Yielding of a model glass former: An interpretation with an effective system of icosahedra

We consider the yielding under simple shear of a binary Lennard-Jones glass former whose super-Arrhenius dynamics are correlated with the formation of icosahedral structures. We recast this glass former as an effective system of icosahedra [Pinney et al., J. Chem. Phys. 143, 244507 (2015)JCPSA60021-960610.1063/1.4938424]. Looking at the small-strain region of sheared simulations, we observe that shear rates affect the shear localization behavior particularly at temperatures below the glass transition as defined with a fit to the Vogel-Fulcher-Tamman equation. At higher temperature, shear localization starts immediately on shearing for all shear rates. At lower temperatures, faster shear rates can result in a delayed start in shear localization, which begins close to the yield stress. Building from a previous work which considered steady-state shear [Pinney et al., J. Chem. Phys. 143, 244507 (2015)JCPSA60021-960610.1063/1.4938424], we interpret the response to shear and the shear localization in terms of a local effective temperature with our system of icosahedra. We find that the effective temperatures of the regions undergoing shear localization increase significantly with increasing strain (before reaching a steady-state plateau).

Particle rearrangement and softening contributions to the nonlinear mechanical response of glasses

Amorphous materials such as metallic, polymeric, and colloidal glasses exhibit complex preparation-dependent mechanical response to applied shear. In particular, glassy solids yield, with a mechanical response that transitions from elastic to plastic, with increasing shear strain. We perform numerical simulations to investigate the mechanical response of binary Lennard-Jones glasses undergoing athermal, quasistatic pure shear as a function of the cooling rate R used to prepare them. The ensemble-averaged stress versus strain curve 〈σ(γ)〉 resembles the spatial average in the large size limit, which appears smooth and displays a putative elastic regime at small strains, a yielding-related peak in stress at intermediate strain, and a plastic flow regime at large strains. In contrast, for each glass configuration in the ensemble, the stress-strain curve σ(γ) consists of many short nearly linear segments that are punctuated by particle-rearrangement-induced rapid stress drops. To explain the nonlinearity of 〈σ(γ)〉, we quantify the shape of the small stress-strain segments and the frequency and size of the stress drops in each glass configuration. We decompose the stress loss [i.e., the deviation in the slope of 〈σ(γ)〉 from that at 〈σ(0)〉] into the loss from particle rearrangements and the loss from softening [i.e., the reduction of the slopes of the linear segments in σ(γ)], and then compare the two contributions as a function of R and γ. For the current studies, the rearrangement-induced stress loss is larger than the softening-induced stress loss, however, softening stress losses increase with decreasing cooling rate. We also characterize the structure of the potential energy landscape along the strain direction for glasses prepared with different R, and observe a dramatic change of the properties of the landscape near the yielding transition. We then show that the rearrangement-induced energy loss per strain can serve as an order parameter for the yielding transition, which sharpens for slow cooling rates and in large systems.