Related papers: A variational principle for hardening elastoplasti…
While data-driven methods offer significant promise for modeling complex materials, they often face challenges in generalizing across diverse physical scenarios and maintaining physical consistency. To address these limitations, we propose…
Inspired by recent experimental observations of a harmonically excited elastic foil hovering near a wall while supporting substantial weight, we develop a theoretical framework that describes the underlying physical effects. Using…
This work discusses a variational approach to determining the time evolution operator. We directly see a glimpse of how a generalization of the quantum geometric tensor for unitary operators plays a central role in parameter evolution. We…
A self-consistent theory for the classical description of the interaction of light and matter at the nano-scale is presented, which takes into account spatial dispersion. Up to now, the Maxwell equations in nanostructured materials with…
We develop a fourth order accurate finite difference method for the three dimensional elastic wave equation in isotropic media with the piecewise smooth material property. In our model, the material property can be discontinuous at curved…
The two key phenomena occurring in the process of ceramic powder compaction are the progressive gain in cohesion and the increase of elastic stiffness, both related to the development of plastic deformation. The latter effect is an example…
In this paper we prove a two-dimensional existence result for a variational model of crack growth for brittle materials in the realm of linearized elasticity. Starting with a time-discretized version of the evolution driven by a prescribed…
Based on the mathematical-physical model of pavement mechanics, a multilayer elastic system with interlayer friction conditions is constructed. Given the complex boundary conditions, the corresponding variational inequalities of the partial…
A dynamic linear thermo-poroelasticity model, containing inertial and relaxation terms with second-order time derivatives, is investigated in this paper. The mathematical and numerical analysis of this model is performed in the frequency…
Heterogeneous materials, such as rocks and concrete, have a complex dynamics including hysteresis, nonlinear elasticity and viscoelasticity. It is very sensitive to microstructural changes and damage. The goal of this paper is to propose a…
Heterogeneous growth plays an important role in the shape and pattern formation of thin elastic structures ranging from the petals of blooming lilies to the cell walls of growing bacteria. Here we address the stability and regulation of…
The restricted strong convexity is an effective tool for deriving globally linear convergence rates of descent methods in convex minimization. Recently, the global error bound and quadratic growth properties appeared as new competitors. In…
We give a geometric description of variational principles in mechanics, with special attention to constrained systems. For the general case of nonholonomic constraints, a unified variational approach is given, and the equations of motion of…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
What characterises a solid is its way to respond to external stresses. Ordered solids, such crystals, display an elastic regime followed by a plastic one, both well understood microscopically in terms of lattice distortion and dislocations.…
We consider systematic numerical approximation of a viscoelastic phase separation model that describes the demixing of a polymer solvent mixture. An unconditionally stable discretisation method is proposed based on a finite element…
We present a new variational principle for linking models of beams and deformable solids, providing also its mathematical analysis. Despite the apparent differences between the two types of governing equations, it will be shown that the…
In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
The aim of this paper is to study the spatial behaviour of the solutions to the boundary-final value problems associated with the linear theory of elastic materials with voids. More precisely the present study is devoted to porous materials…