Related papers: Incorporating Deformation Energetics in Long-Term …
This paper derives a finite-strain plate theory consistent with the principle of stationary three-dimensional (3-D) potential energy under general loadings with a third-order error. Staring from the 3-D nonlinear elasticity (with both…
We propose bending energies for isotropic elastic plates and shells. For a plate, we define and employ a surface tensor that symmetrically couples stretch and curvature such that any elastic energy density constructed from its invariants is…
We study abstract linear and nonlinear evolutionary systems with single or multiple delay feedbacks, illustrated by several concrete examples. In particular, we assume that the operator associated with the undelayed part of the system…
The long-term goal of this project is the non-perturbative renormalization of the energy-momentum tensor in the 2d $O(3)$ non-linear sigma model using different methods which have been developed for QCD applications. As a first step, we…
Faults are complex systems embedded in an evolving medium fractured by seismic ruptures. This off-fault damage zone is shown to be thermo-hydro-mechano-chemically coupled to the main fault plane by a growing number of studies. Yet,…
An energy for first-order structured deformations in the context of periodic homogenization is obtained. This energy, defined in principle by relaxation of an initial energy of integral type featuring contributions of bulk and interfacial…
Many seemingly different macroscopic systems (magnets, ferroelectrics, CDW, vortices,..) can be described as generic disordered elastic systems. Understanding their static and dynamics thus poses challenging problems both from the point of…
We derive thermodynamically consistent models for diblock copolymer solutions coupled with the electric and magnetic field, respectively. These models satisfy the second law of thermodynamics and therefore are therefore thermodynamically…
This paper presents a detailed study on analytical solutions to a general nonlinear boundary-value problem in finite deformation theory. Based on canonical duality theory and the associated pure complementary energy principle in nonlinear…
Interacting defect systems are ubiquitous in materials under realistic scenarios, yet gaining an atomic-level understanding of these systems from a computational perspective is challenging - it often demands substantial resources due to the…
A simple and effective approach to thermodynamics is suggested, which solves the major difficulties in the traditional presentation of the subject. The internal energy is introduced from the behavior of deformable bodies, whereas the…
Computational studies of the thermodynamic properties of materials at the mesoscopic and macroscopic scales -- involving lengths and times of at least $\mu$m and $\mu$s, respectively -- rely on a coarse-graining approximation such that only…
This paper concerns with finite element approximations of a quasi-static poroelasticity model in displacement-pressure formulation which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To…
The strain states of the components of pseudomorphic superlattices can be accurately modeled analytically through the application of linear elasticity. In this particular case of GaN/AlN 'free-standing' superlattices, the predictions…
Railway transition zones (RTZs) experience higher rates of degradation compared to open tracks, which leads to increased maintenance costs and reduced vailability. Despite existing literature on railway track assessment and maintenance,…
Nematic elastomers and glasses deform spontaneously when subjected to temperature changes. This property can be exploited in the design of heterogeneously patterned thin sheets that deform into a non-trivial shape when heated or cooled. In…
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…
These lectures present the analysis of stability and control of long time behavior of PDE models described by nonlinear evolutions of hyperbolic type. Specific examples of the models under consideration include: (i) nonlinear systems of…
Deep eutectic solvents (DESs) have gained attention in recent years as attractive alternatives to traditional solvents. There is a growing number of publications dealing with the thermodynamic modeling of DESs highlighting the importance of…
We develop a three-timescale framework for modelling climate change and introduce a space-heterogeneous one-dimensional energy balance model. This model, addressing temperature fluctuations from rising carbon dioxide levels and the…