Diffuse interface approach to brittle fracture

Self-organized mud cracking amplifies the resilience of an iconic "Red Beach" salt marsh

Self-organized patterning, resulting from the interplay of biological and physical processes, is widespread in nature. Studies have suggested that biologically triggered self-organization can amplify ecosystem resilience. However, if purely physical forms of self-organization play a similar role remains unknown. Desiccation soil cracking is a typical physical form of self-organization in coastal salt marshes and other ecosystems. Here, we show that physically self-organized mud cracking was an important facilitating process for the establishment of seepweeds in a "Red Beach" salt marsh in China. Transient mud cracks can promote plant survivorship by trapping seeds, and enhance germination and growth by increasing water infiltration in the soil, thus facilitating the formation of a persistent salt marsh landscape. Cracks can help the salt marsh withstand more intense droughts, leading to postponed collapse and faster recovery. These are indications of enhanced resilience. Our work highlights that self-organized landscapes sculpted by physical agents can play a critical role in ecosystem dynamics and resilience to climate change.

Different universality classes at the yielding transition of amorphous systems

We study the yielding transition of a two-dimensional amorphous system under shear by using a mesoscopic elasto-plastic model. The model combines a full (tensorial) description of the elastic interactions in the system and the possibility of structural reaccommodations that are responsible for the plastic behavior. The possible structural reaccommodations are encoded in the form of a "plastic disorder" potential, which is chosen independently at each position of the sample to account for local heterogeneities. We observe that the stress must exceed a critical value σ_{c} in order for the system to yield. In addition, when the system yields a flow curve (relating stress σ and strain rate γ[over ̇]) of the form γ[over ̇]∼(σ-σ_{c})^{β} is obtained. Remarkably, we observe the value of β to depend on some details of the plastic disorder potential. For smooth potentials a value of β≃2.0 is obtained, whereas for potentials obtained as a concatenation of smooth pieces a value β≃1.5 is observed in the simulations. This indicates a dependence of critical behavior on details of the plastic behavior. In addition, by integrating out nonessential, harmonic degrees of freedom, we derive a simplified scalar version of the model that represents a collection of interacting Prandtl-Tomlinson particles. A mean-field treatment of this interaction reproduces the difference of β exponents for the two classes of plastic disorder potentials and provides values of β that compare favorably with those found in the full simulations.

A phase field model coupling lithium diffusion and stress evolution with crack propagation and application in lithium ion batteries

Coupling effects among lithium diffusion, stress evolution and crack propagation have a significant effect on lithium diffusion and crack propagation.

The dynamics of rapid fracture: instabilities, nonlinearities and length scales

The failure of materials and interfaces is mediated by cracks, almost singular dissipative structures that propagate at velocities approaching the speed of sound. Crack initiation and subsequent propagation-the dynamic process of fracture-couples a wide range of time and length scales. Crack dynamics challenge our understanding of the fundamental physics processes that take place in the extreme conditions within the almost singular region where material failure occurs. Here, we first briefly review the classic approach to dynamic fracture, namely linear elastic fracture mechanics (LEFM), and discuss its successes and limitations. We show how, on the one hand, recent experiments performed on straight cracks propagating in soft brittle materials have quantitatively confirmed the predictions of this theory to an unprecedented degree. On the other hand, these experiments show how LEFM breaks down as the singular region at the tip of a crack is approached. This breakdown naturally leads to a new theoretical framework coined 'weakly nonlinear fracture mechanics', where weak elastic nonlinearities are incorporated. The stronger singularity predicted by this theory gives rise to a new and intrinsic length scale, ℓnl. These predictions are verified in detail through direct measurements. We then theoretically and experimentally review how the emergence of ℓnl is linked to a new equation for crack motion, which predicts the existence of a high-speed oscillatory crack instability whose wavelength is determined by ℓnl. We conclude by delineating outstanding challenges in the field.

Phase field modeling of fracture and stress-induced phase transitions

We present a continuum theory to describe elastically induced phase transitions between coherent solid phases. In the limit of vanishing elastic constants in one of the phases, the model can be used to describe fracture on the basis of the late stage of the Asaro-Tiller-Grinfeld instability. Starting from a sharp interface formulation we derive the elastic equations and the dissipative interface kinetics. We develop a phase field model to simulate these processes numerically; in the sharp interface limit, it reproduces the desired equations of motion and boundary conditions. We perform large scale simulations of fracture processes to eliminate finite-size effects and compare the results to a recently developed sharp interface method. Details of the numerical simulations are explained, and the generalization to multiphase simulations is presented.

Crack propagation as a free boundary problem

A sharp interface model of crack propagation as a phase transition process is discussed. We develop a multipole expansion technique to solve this free boundary problem numerically. We obtain steady state solutions with a self-consistently selected propagation velocity and shape of the crack, provided that elastodynamic effects are taken into account. Also, we find a saturation of the steady state crack velocity below the Rayleigh speed, tip blunting with increasing driving force, and a tip splitting instability above a critical driving force.

Morphologies of expansion ridges of elastic thin films onto a substrate

A model of a thin film elastically attached to a rigid substrate is considered. In the case in which the film expands relative to the substrate and assuming certain nonlinear elastic behavior of the film, expansion ridges may appear, in which the material collapses, and the density is higher on average. By studying numerically this process, the possible morphologies of these collapsed regions are presented. They range from circular spots and straight stripes, to wiggle polygonal patterns and ring-shaped domains. The similarity of some of these results with patterns observed in delamination of thin films and biphase epitaxial growth is emphasized.

Phase field modeling of fast crack propagation

We present a continuum theory which predicts the steady state propagation of cracks. The theory overcomes the usual problem of a finite time cusp singularity of the Grinfeld instability by the inclusion of elastodynamic effects which restore selection of the steady state tip radius and velocity. We developed a phase-field model for elastically induced phase transitions; in the limit of small or vanishing elastic coefficients in the new phase, fracture can be studied. The simulations confirm analytical predictions for fast crack propagation.

Intrinsically anomalous roughness of admissible crack traces in concrete

We study the roughness of postmortem cracks in concrete plates of different size. We find that the set of admissible crack paths exhibits an intrinsically anomalous roughness; nevertheless, any individual crack trace in concrete is essentially self-affine. We also find that both the local and the global amplitudes of crack traces are distributed according to a log-logistic distribution characterized by the same scaling exponent, whereas the mean-square width distribution is best fitted by the Pearson distribution, while the log-normal distribution also provides quite good adjustments and cannot be clearly rejected.