Eighty years of the finite element method: Birth, evolution, and future

WK Liu, S Li, HS Park - Archives of Computational Methods in …, 2022 - Springer
This document presents comprehensive historical accounts on the developments of finite
element methods (FEM) since 1941, with a specific emphasis on developments related to …

[HTML][HTML] Gradient elasticity in statics and dynamics: an overview of formulations, length scale identification procedures, finite element implementations and new results

H Askes, EC Aifantis - International Journal of Solids and Structures, 2011 - Elsevier
In this paper, we discuss various formats of gradient elasticity and their performance in static
and dynamic applications. Gradient elasticity theories provide extensions of the classical …

Gradient damage vs phase-field approaches for fracture: Similarities and differences

R de Borst, CV Verhoosel - Computer Methods in Applied Mechanics and …, 2016 - Elsevier
Gradient-enhanced damage models and phase-field models are seemingly very disparate
approaches to fracture. Whereas gradient-enhanced damage models find their roots in …

[KİTAP][B] Fracture and size effect in concrete and other quasibrittle materials

ZP Bazant, J Planas - 2019 - taylorfrancis.com
Fracture and Size Effect in Concrete and Other Quasibrittle Materials is the first in-depth text
on the application of fracture mechanics to the analysis of failure in concrete structures. The …

Gradient enhanced damage for quasi‐brittle materials

RHJ Peerlings, R de Borst… - … Journal for numerical …, 1996 - Wiley Online Library
Conventional continuum damage descriptions of material degeneration suffer from loss of
well‐posedness beyond a certain level of accumulated damage. As a consequence …

A reformulation of strain gradient plasticity

NA Fleck, JW Hutchinson - Journal of the Mechanics and Physics of Solids, 2001 - Elsevier
A class of phenomenological strain gradient plasticity theories is formulated to
accommodate more than one material length parameter. The objective is a generalization of …

Fundamental issues in finite element analyses of localization of deformation

R De Borst, LJ Sluys, HB Muhlhaus… - Engineering …, 1993 - emerald.com
Classical continuum models, ie continuum models that do not incorporate an internal length
scale, suffer from excessive mesh dependence when strain‐softening models are used in …

Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy

VG Kouznetsova, MGD Geers… - Computer methods in …, 2004 - Elsevier
This paper presents the detailed implementation and computational aspects of a novel
second-order computational homogenization procedure, which is suitable for a multi-scale …

A critical comparison of nonlocal and gradient-enhanced softening continua

RHJ Peerlings, MGD Geers, R de Borst… - International Journal of …, 2001 - Elsevier
Continuous models of material degradation may cease to produced meaningful results in
the presence of high strain gradients. These gradients may occur for instance in the …

[KİTAP][B] Bifurcation analysis in geomechanics

J Sulem, IG Vardoulakis - 1995 - taylorfrancis.com
This book examines the experimental and theoretical aspects of bifurcation analysis as
applied to geomechanics. Coverage includes basic continuum mechanics for dry and fluid …