Related papers: Integral representation for a relaxed optimal desi…
In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…
The paper is devoted to the study of the unconditional extremal problem for a fractional linear integral functional defined on a set of probability distributions. In contrast to results proved earlier, the integrands of the integral…
Incompressible nonlinearly hyperelastic materials are rarely simulated in Finite Element numerical experiments as being perfectly incompressible because of the numerical difficulties associated with globally satisfying this constraint. Most…
The paper presents a micromechanical representation of deformation in 2D granular materials. The representation is a generalization of K. Bagi's work and is based upon the void-cell approach of M. Satake. The general representation applies…
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…
We consider the unit ball $\Omega\subset \mathbb{R}^N$ ($N\ge2$) filled with two materials with different conductivities. We perform shape derivatives up to the second order to find out precise information about locally optimal…
This study addresses the modelling of elastic bodies, particularly when the relaxed configuration is unknown or non-existent. We adopt the theory of initially stressed materials, incorporating the deformation gradient and stress state of…
To facilitate the design and optimization of nanomaterials for a given application it is necessary to understand the relationship between structure and physical properties. For large nanomaterials, there is imprecise structural information…
This work presents a scalable computational framework for optimal design under uncertainty with application to multi-material insulation components of building envelopes. The forward model consists of a multi-phase thermo-mechanical model…
Plasticity refers to thermodynamically irreversible deformation associated with a change of configuration of materials. Friction is a phenomenological law that describes the forces resisting sliding between two solids or across an embedded…
We use a power expansion representation of plane elasticity complex potentials due to Kolossov and Muskhelishvili, to compute the elastic fields induced by a localized plastic deformation event. Far from its center, the dominant…
We consider the problem of formulating perturbative expansions of the conformation tensor, which is a positive-definite tensor representing polymer deformation in viscoelastic flows. The classical approach does not explicitly take into…
Finite plasticity theories are still a subject of controversy and lively discussions. Among the approaches to finite elastoplasticity two became especially popular. The first, implemented in the commercial finite element codes, is based on…
We derive an exact closed-form representation for the Euclidean thermal Green function of the two-dimensional (2D) free massless scalar field in coordinate space. This can be interpreted as the real part of a complex analytic function of a…
The structure of the overall response of a metal polycrystal is analyzed under the assumption that activity on the slip systems of its constituents is governed by a generalized Schmid law. In the resulting macro-model of metal plasticity…
In this article we propose a discrete lattice model to simulate the elastic, plastic and failure behaviour of isotropic materials. Focus is given on the mathematical derivation of the lattice elements, nodes and edges, in the presence of…
We consider vectorial variational problems in nonlinear elasticity of the form $I[u]=\int W(Du)dx$, where $W$ is continuous on matrices with positive determinant and diverges to infinity long sequences of matrices whose determinant is…
We prove existence and uniqueness for solutions to equilibrium problems for free-standing, traction-free, non homogeneous crystals in the presence of plastic slips. Moreover we prove that this class of problems is closed under G-convergence…
The plastic component of the deformation gradient plays a central role in finite kinematic models of plasticity. However, its characterization has been the source of extended debates in the literature and many important issues still remain…
Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to nonlinear mechanics and nontrivial geometrical effects. While numeric approaches are successful, analytic tools and…