Related papers: Finite plasticity in $P^T P$
The plasticity of amorphous solids undergoing shear is characterized by quasi-localized rearrangements of particles. While many models of plasticity exist, the precise relationship between plastic dynamics and the structure of a particle's…
We propose a simple and efficient scheme based on adaptive finite elements over conforming quadtree meshes for collapse plastic analysis of structures. Our main interest in kinematic limit analysis is concerned with both purely…
An $hp$-adaptive continuous Galerkin finite element method is developed to analyze a static anti-plane shear crack embedded in a nonlinear, strain-limiting elastic body. The geometrically linear material is described by a constitutive law…
Elasto-plastic models are among the most successful ways to study the critical properties of the plastic yielding transition of amorphous solids. Typically these models are studied under a condition of constant transition rates from one…
Following Brown[1], we construct composite operators for the scalar $\phi^3$ theory in six dimensions using renormalisation group methods with dimensional regularisation. We express bare scalar operators in terms of renormalised composite…
In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…
In this paper, finite element method is applied to Leland's model for numerical simulation of option pricing with transaction costs. Spatial finite element models based on P1 and/or P2 elements are formulated in combination with a…
A finite element framework is presented for the analysis of crack-tip phenomena in an elastic material containing a single edge crack under compressive loading. The mechanical response of the material is modeled by a nonlinear constitutive…
This paper is concerned with a shape optimization problem governed by a non-smooth PDE, i.e., the nonlinearity in the state equation is not necessarily differentiable. We follow the functional variational approach of [40] where the set of…
Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…
We propose an adaptive polygonal finite element formulation for collapse plastic analysis of solids. The article contributes into four crucial points: 1) Wachspress shape functions at vertex and bubble nodes handled at a primal-mesh level;…
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…
We study a shape evolution framework in which the deformation of shapes from time t to t + dt is governed by a regularized anisotropic elasticity model. More precisely, we assume that at each time shapes are infinitesimally deformed from a…
We consider the problem of matching two shapes assuming these shapes are related by an elastic deformation. Using linearized elasticity theory and the finite element method we seek an elastic deformation that is caused by simple external…
Models which allow an explicit application to structurally modulated substances are reviewed within the frame of a symmetry-based approach starting from discrete lattice theory. Focus is set on models formulated in terms of local variables…
This paper discusses a general formulation of the material point method in the context of additive decomposition rate-independent plasticity. The process of generating the weak form shows that volume integration over deforming particles can…
Precipitation of fine particles into the base material of a metal is a potent strengthening mechanism. This is numerically analyzed within a continuum framework based on a higher order strain gradient plasticity theory and by use of an…
We give a method for modeling solid objects undergoing large spatially varying and/or anisotropic strains, and use it to reconstruct human anatomy from medical images. Our novel shape deformation method uses plastic strains and the Finite…
The constitutive relation of the quasi-static deformation on two dimensional packed samples of polygons is calculated using molecular dynamic simulations. The stress values at which the system remains stable are bounded by a failure…
We investigate variational problems in large-strain magnetoelasticity, both in the static and in the quasistatic setting. The model contemplates a mixed Eulerian-Lagrangian formulation: while deformations are defined on the reference…