Related papers: Damage-driven fracture with low-order potentials: …
In this work, we study the effective behavior of a two-dimensional variational model within finite crystal plasticity for high-contrast bilayered composites. Precisely, we consider materials arranged into periodically alternating thin…
Soft polymers are ubiquitous materials in nature and as engineering materials with properties varying from rate-independent to rate-dependent. Current fracture toughness measures are non-unique for rate-dependent soft materials for varying…
In many scenarios -- when we bite food or during a crash -- fracture is inevitable. Finding solutions to steer fracture to mitigate its impact or turn it into a purposeful functionality, is therefore crucial. Strategies using composites,…
Nanochains of atoms, molecules and polymers have gained recent interest in the experimental sciences. This article contributes to an advanced mathematical modeling of the mechanical properties of nanochains that allow for heterogenities,…
We study the $\Gamma$-convergence of a class of elastica-type energies defined on immersed planar curves and depending on a small positive parameter $\epsilon$. As $\epsilon\to 0^+$, sequences with equibounded energy develop concentration…
The current microscopic picture of plasticity in amorphous materials assumes local failure events to produce displacement fields complying with linear elasticity. Indeed, the flow properties of nonaffine systems such as foams, emulsions and…
A novel general framework for the study of $\Gamma$-convergence of functionals defined over pairs of measures and energy-measures is introduced. This theory allows us to identify the $\Gamma$-limit of these kind of functionals by knowing…
The goal of the current work is to explore direction-dependent damage initiation and propagation within an arbitrary anisotropic solid. In particular, we aim at developing anisotropic cohesive phase-field (PF) damage models by extending the…
In this work we derive by Gamma-convergence techniques a model for brittle fracture linearly elastic plates. Precisely, we start from a brittle linearly elastic thin film with positive thickness $\rho$ and study the limit as $\rho$ tends to…
A geometrically nonlinear continuum mechanical theory is formulated for deformation and failure behaviors of amorphous polymers. The model seeks to capture material response over a range of loading rates, temperatures, and stress states…
Many studies investigated the application of statistical mechanics to damage phenomena. However, so far the association of damage with statistical mechanics is far from completely developed. One of the most successful approaches maps the…
A two-dimensional lattice model with bond disorder is used to investigate the fracture behaviour under stress-controlled conditions. Although the cumulative energy of precursors does not diverge at the critical point, its derivative with…
Extreme mechanical processes such as strong lattice distortion and bond breakage during fracture are ubiquitous in nature and engineering, which often lead to catastrophic failure of structures. However, understanding the nucleation and…
We show that critical systems of finite size develop a fractal structure in momentum space with anomalous dimension given in terms of the isotherm critical exponent delta of the corresponding infinite system. The associated power laws of…
This is the first in a series of two papers in which we derive a $\Gamma$-expansion for a two-dimensional non-local Ginzburg-Landau energy with Coulomb repulsion, also known as the Ohta-Kawasaki model in connection with diblock copolymer…
Recently the scaling laws describing the roughness development of fracture surfaces was proposed to be related to the macroscopic elastic energy released during crack propagation [Mor00]. On this basis, an energy-based asymptotic analysis…
We discuss the relevance of methods of graph theory for the study of damage in simple model materials described by the random fuse model. While such methods are not commonly used when dealing with regular random lattices, which mimic…
We review what is known about fracton phases of quantum matter. Fracton phases are characterized by excitations that exhibit restricted mobility, being either immobile under local Hamiltonian dynamics, or mobile only in certain directions.…
A state coupling between the hydrostatic (volumetric) and deviatoric parts of the free energy is introduced in a damage mechanics model relevant for the quasi-brittle materials. It is shown that it describes the large dilatancy of concrete…
In this paper we study the asymptotic behaviour of phase-field functionals of Am brosio and Tortorelli type allowing for small-scale oscillations both in the volume and in the diffuse surface term. The functionals under examination can be…