Related papers: On the construction and properties of weak solutio…
Cavitation is a common damage mechanism in soft solids. Here, we study this using a phase-separation technique in stretched, elastic solids to controllably nucleate and grow small cavities by several orders of magnitude. The ability to make…
We prove the existence of a weak solution to the equations describing the inertial motions of a coupled system constituted by a rigid body containing a viscous compressible fluid. We then provide a weak-strong uniqueness result that allows…
An exact integro-differential equation for the conformal map from the unit circle to the boundary of an evolving cavity in a stressed 2-dimensional solid is derived. This equation provides an accurate description of the dynamics of…
Cavity growth in ductile metal materials under dynamic loading is investigated via the material point method. Two typical cavity effects in the region subjected to rarefaction wave are identified: (i) part of material particles flow away…
The understanding of dynamic failure in amorphous materials via the propagation of free boundaries like cracks and voids must go beyond elasticity theory, since plasticity intervenes in a crucial and poorly understood manner near the moving…
Cavitation in solids can be caused by tensile dead-load traction or impulse traction. The two different types of boundary conditions lead to different static and dynamic solutions. In addition, if the material is stochastic, i.e., the model…
We study the Cauchy problem for the compressible Euler equations in two spatial dimensions under any physical barotropic equation of state except that of a Chaplygin gas. We prove that the well-known phenomenon of shock formation in simple…
We revisit the classic problem of elastic cavitation within the framework of stochastic elasticity. For the deterministic elastic problem, involving homogeneous isotropic incompressible hyperelastic spheres under radially symmetric tension,…
Cavitation in soft elastomers and adhesives is often viewed as an elastic instability, commonly tied to the study of incompressible solids. It is the first step prior to fibrillation and ultimate failure in adhesives. Building on the work…
Amorphous solids are known to fail catastrophically and in some situations, nano-scaled cavities are believed to play a significant role in the failure. In a recent work, using numerical simulations, we have shown the correspondence between…
We propose a one-dimensional, nonconvex elastic constitutive model with higher gradients that can predict spontaneous fracture at a critical load via a bifurcation analysis. It overcomes the problem of discontinuous deformations without…
The notion of singular limiting induced from continuum solutions (slic-solutions) is applied to the problem of cavitation in nonlinear elasticity, in order to re-assess an example of non-uniqueness of entropic weak solutions (with…
Predicting the shape of a crater formed by high velocity impact is of interest in several fields. It can aid in design of more efficient protective structures, in forensic analysis of bullet holes, and in understanding the effects of…
This paper proposes a method for studying the early stages of the cavitation development in arbitrary, non-stationary conditions. This method is based on the comparison of the results of calculations in the framework of a theoretical model…
Soft polymer-based solid materials can be defined as solid materials with elastic moduli below 1 MPa. In order to obtain such a low modulus while retaining a solid character, all these materials are based on a network of fixed points…
In this paper we analyze an isothermal and isotropic model for viscoelastic media combining linearized perfect plasticity (allowing for concentration of plastic strain and development of shear bands) and damage effects in a dynamic setting.…
We consider quasi-static poroelastic systems with incompressible constituents. The nonlinear permeability is taken to be dependent on solid dilation, and physical types of boundary conditions (Dirichlet, Neumann, and mixed) for the fluid…
The main part of the thesis deals with continuously and discretely self-similar solutions and type II critical phenomena in a family of self-gravitating non-linear sigma-models. The phenomena strongly depend on the dimensionless coupling…
This paper addresses the construction and the stability of self-similar solutions to the isentropic compressible Euler equations. These solutions model a gas that implodes isotropically, ending in a singularity formation in finite time. The…
For one-dimensional vibrating cavity systems appearing in the standard illustration of the dynamical Casimir effect, we propose an approach to the construction of exact closed-form solutions. As new results, we obtain solutions that are…