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A stress equilibration procedure for linear elasticity is proposed and analyzed in this paper with emphasis on the behavior for (nearly) incompressible materials. Based on the displacement-pressure approximation computed with a stable…
We present a new method for the approximate solution of the strongly coupled, nonlinear stress-diffusion problem that appears when modeling hydrogen transport in metals. The most salient feature of the proposed approximation is that it is…
We consider a system of evolutionary equations that is capable of describing certain viscoelastic effects in linearized yet nonlinear models of solid mechanics. The essence of the paper is that the constitutive relation, involving the…
The size-dependent bending behavior of nano-beams is investigated by the modified nonlocal strain gradient elasticity theory. According to this model, the bending moment is expressed by integral convolutions of elastic flexural curvature…
We present a geometrically exact nonlinear analysis of elastic in-plane beams in the context of finite but small strain theory. The formulation utilizes the full beam metric and obtains the complete analytic elastic constitutive model by…
In this article we consider the linear elasticity problem in an axisymmetric three dimensional domain, with data which are axisymmetric and have zero angular component. The weak formulation of the the three dimensional problem reduces to a…
A quasistatic nonlinear model for finite-strain poro-visco-elasticity is considered in the Lagrangian frame using Kelvin-Voigt rheology. The model consists of a mechanical equation which is coupled to a diffusion equation with a degenerate…
In this paper, we consider weak solutions of the Euler-Lagrange equation to a variational energy functional modeling the geometrically nonlinear Cosserat micropolar elasticity of continua in dimension three, which is a system coupling…
The classical continuum models used for the woven fabrics do not fully describe the whole set of phenomena that occur during the testing of those materials. This incompleteness is partially due to the absence of energy terms related to some…
This paper proposes a low order geometrically exact flexible beam formulation based on the utilisation of generic beam shape functions to approximate distributed kinematic properties of the deformed structure. The proposed nonlinear beam…
This manuscript explores a variational quantum formulation for nonlinear elasticity problems arising from hyperelastic material models, targeting near term noisy intermediate scale quantum (NISQ) devices. The approach leverages the…
We consider an application of variational-wavelet approach to nonlinear collective models of beam/plasma physics: Vlasov/Boltzmann-like reduction from general BBGKY hierachy. We obtain fast convergent multiresolution representations for…
When an optical beam propagates through a turbulent medium such as the atmosphere or ocean, the beam will become distorted. It is then natural to seek the best or optimal beam that is distorted least, under some metric such as intensity or…
Recently, the authors have proposed a novel all-angle beam contact (ABC) formulation that combines the advantages of existing point and line contact models in a variationally consistent manner. However, the ABC formulation has so far only…
In a previous work (arXiv:0902.3750 [hep-th]) we studied the world-sheet conformal invariance for superstrings in type IIB R-R plane-wave in semi-light-cone gauge. Here we give further justification to the results found in that work through…
The spectral decomposition of a symmetric, second-order tensor is widely adopted in many fields of Computational Mechanics. As an example, in elasto-plasticity under large strain and rotations, given the Cauchy deformation tensor, it is a…
The accurate modeling of the mechanical behavior of rubber-like materials under multi-axial loading constitutes a long-standing challenge in hyperelastic material modeling. This work employs deep symbolic regression as an interpretable…
The second gradient model of poromechanics, introduced in Part I, is here linearized in the neighborhood of a prestressed reference configuration to be applied to the one-dimensional consolidation problem originally considered by Terzaghi…
We prove the existence of a weak solution to the three-dimensional steady compressible isentropic Navier-Stokes equations in bounded domains for any specific heat ratio \gamma > 1. Generally speaking, the proof is based on the new weighted…
This study provides an abstract framework to analyze mixed formulations in viscoelasticity, in the classic saddle point form. Standard hypothesis for mixed methods are adapted to the Volterra type equations in order to obtain stability of…