Related papers: A unified model for stress-driven rearrangement in…
We demonstrate the continuous translational invariance of the energy of a capillary surface in contact with reconfigurable solid boundaries. We present a theoretical approach to find the energy-invariant equilibria of spherical capillary…
Dislocation based modeling of plasticity is one of the central challenges at the crossover of materials science and continuum mechanics. Developing a continuum theory of dislocations requires the solution of two long standing problems: (i)…
The governing equations of the variational approach to brittle and ductile fracture emerge from the minimization of a non-convex energy functional subject to irreversibility constraints. This results in a multifield problem governed by a…
Nonequilibrium dynamics at interfaces is generally driven by a chemical potential. Here we demonstrate a generic technique to derive the basic equations of motion, boundary conditions and the chemical potential in a consistent way from…
A boundary element formulation is developed to determine the complex stress intensity factors associated with cracks on the interface between dissimilar materials. This represents an extension of the methodology developed previously by the…
A robust $hp$-adaptive finite element framework is presented for the investigation of static cracks in materials characterized by complex, pointwise density variations. Within such heterogeneous media, the equilibrium equation governed by…
This paper presents a computational framework for the robust stiffness design of hyperelastic structures at finite deformations subject to various uncertain sources. In particular, the loading, material properties, and geometry…
Physics-informed neural networks provide a mesh-free framework for solving partial differential equation-governed problems in solid mechanics. However, most existing formulations in linear elasticity still learn the displacement field…
A confined incompressible elastic film does not deform uniformly when subjected to adhesive interfacial stresses but with undulations which have a characteristic wavelength scaling linearly with the thickness of the film. In the classical…
Remodelling is defined as an evolution of microstructure or variations in the configuration of the underlying manifold. The manner in which a biological tissue and its subsystems remodel their structure is treated in a continuum mechanical…
So far the problem of interface behavior upon phase transition has not yet acquired a satisfactory mathematical formulation due to a variety of the physical phenomena involved. Analytical solutions exist only for elementary problems…
Structure, function and dynamics of many biomolecular systems can be characterized by the energetic variational principle and the corresponding systems of partial differential equations (PDEs). This principle allows us to focus on the…
The present paper studies non-uniform plastic deformations of crystals undergoing anti-plane constrained shear. The asymptotically exact energy density of crystals containing a moderately large density of excess dislocations is found by the…
The morphology of crystalline thin films evolving on flat rigid substrates by condensation of extra film atoms or by evaporation of their own atoms in the surrounding vapor is studied in the framework of the theory of Stress Driven…
We present the formulation for finding the distribution of eigenstrains, i.e. the sources of residual stress, from a set of measurements of residual elastic strain (e.g. by diffraction), or residual stress, or stress redistribution, or…
In this contribution, a variational diffuse modeling framework for cracks in heterogeneous media is presented. A static order parameter smoothly bridges the discontinuity at material interfaces, while an evolving phase-field captures the…
In this paper, we present a novel interface-driven adaptive variational procedure using a fully Eulerian description of fluid-structure interaction. The proposed fully-Eulerian procedure involves a fixed background unstructured mesh on…
A variational modeling framework for hydraulically induced fracturing of elastic-plastic solids is developed in the present work. The developed variational structure provides a global minimization problem. While fracture propagation is…
Elasticity theory provides an accurate description of the long-wavelength vibrational dynamics of homogeneous crystalline solids, and with supplemental boundary conditions on the displacement field can also be applied to abrupt…
We investigate the stress-driven morphological instability of epitaxially growing multilayer films, which are coherent and dislocation-free. We construct a direct elastic analysis, from which we determine the elastic state of the system…