Search results for "Linear elasticity"
showing 10 items of 41 documents
A strain-difference-based nonlocal elasticity model
2004
Abstract A two-component local/nonlocal constitutive model for (macroscopically) inhomogeneous linear elastic materials (but constant internal length) is proposed, in which the stress is the sum of the local stress and a nonlocal-type stress expressed in terms of the strain difference field, hence identically vanishing in the case of uniform strain. Attention is focused upon the particular case of piecewise homogeneous material. The proposed model is thermodynamically consistent with a suitable free energy potential. It constitutes an improved form of the Vermeer and Brinkgreve [A new effective nonlocal strain measure for softening plasticity. In: Chambon, R., Desrues, J., Vardulakis, I. (E…
Physically-Based Approach to the Mechanics of Strong Non-Local Linear Elasticity Theory
2009
In this paper the physically-based approach to non-local elasticity theory is introduced. It is formulated by reverting the continuum to an ensemble of interacting volume elements. Interactions between adjacent elements are classical contact forces while long-range interactions between non-adjacent elements are modelled as distance-decaying central body forces. The latter are proportional to the relative displacements rather than to the strain field as in the Eringen model and subsequent developments. At the limit the displacement field is found to be governed by an integro-differential equation, solved by a simple discretization procedure suggested by the underlying mechanical model itself…
The mechanically-based approach to 3D non-local linear elasticity theory: Long-range central interactions
2010
Abstract This paper presents the generalization to a three-dimensional (3D) case of a mechanically-based approach to non-local elasticity theory, recently proposed by the authors in a one-dimensional (1D) case. The proposed model assumes that the equilibrium of a volume element is attained by contact forces between adjacent elements and by long-range forces exerted by non-adjacent elements. Specifically, the long-range forces are modelled as central body forces depending on the relative displacement between the centroids of the volume elements, measured along the line connecting the centroids. Further, the long-range forces are assumed to be proportional to a proper, material-dependent, dis…
On the hyperporous non-linear elasticity model for fusion-relevant pebble beds
2010
Abstract Packed pebble beds are particular granular systems composed of a large amount of small particles, arranged in irregular lattices and surrounded by a gas filling interstitial spaces. Due to their heterogeneous structure, pebble beds have non-linear and strongly coupled thermal and mechanical behaviours whose constitutive models seem limited, being not suitable for fusion-relevant design-oriented applications. Within the framework of the modelling activities promoted for the lithiated ceramics and beryllium pebble beds foreseen in the Helium-Cooled Pebble Bed breeding blanket concept of DEMO, at the Department of Nuclear Engineering of the University of Palermo (DIN) a thermo-mechani…
Crack growth in fillet welded steel joints subjected to membrane and bending loading modes
2020
Abstract The present paper presents the results from extensive studies of the fatigue damage evolution in fillet welded steel joints subjected to Constant Amplitude (CA) stress under membrane and bending loading modes. The welded joints in question are F class details (category 71) with plate thicknesses ranging from 25 to 32 mm. The steel quality is a medium strength carbon manganese steel. Crack growth histories for the shallow semi-elliptical shaped cracks emanating from the weld toe are obtained by an Alternating Current Potential Drop (ACPD) technique. These growth histories are presented in detail and modelled by Linear Elastic Facture Mechanics (LEFM). The calculations follow the rec…
A Theoretical Model to Evaluate the Compressive Behaviour of RС Jacketed Columns
2016
Reinforced concrete (RC) jacketing is becoming increasingly common among the different retrofit techniques for poor RC members, due to its economical and practical advantages. Experimental investigations in the literature have shown that the actual axial capacity of RC jacketed members can be substantially lower than that analytically evaluated by adapting the most common theoretical models for confined concrete. This fact can be explained by taking into account the presence of tensile stresses developing in the concrete, due to a mutual interaction between the inner core and the external jacket. This phenomenon is relevant especially in members where the concrete properties of the jacket a…
Limits of Sobolev homeomorphisms
2017
Let X; Y subset of R-2 be topologically equivalent bounded Lipschitz domains. We prove that weak and strong limits of homeomorphisms h: X (onto)-> Y in the Sobolev space W-1,W-p (X, R-2), p >= 2; are the same. As an application, we establish the existence of 2D-traction free minimal deformations for fairly general energy integrals. Peer reviewed
MAPPINGS OF FINITE DISTORTION: $L^n \log^{\alpha} L$ -INTEGRABILITY
2003
Recently, systematic studies of mappings of finite distortion have emerged as a key area in geometric function theory. The connection with deformations of elastic bodies and regularity of energy minimizers in the theory of nonlinear elasticity is perhaps a primary motivation for such studies, but there are many other applications as well, particularly in holomorphic dynamics and also in the study of first order degenerate elliptic systems, for instance the Beltrami systems we consider here.
Reliable measures of plastic deformations for elastic plastic structures in shakedown conditions
2020
A new formulation for evaluating reliable measures of the plastic deformations occurring in the transient phase of a structure in shakedown conditions is proposed. The structure is thought as constituted by elastic perfectly plastic material and subjected to a combination of fixed and cyclic loads. The proposed formulation consists in the search for the optimal plastic strain field that minimize a suitable objective function defining a strain energy measure related to the plastic strains at the shakedown limit. The typical self-stress field can be obtained as the elastic structural response to an assigned plastic strain field respecting appropriate ductility limits for the material. Without…
Isotropic p-harmonic systems in 2D Jacobian estimates and univalent solutions
2016
The core result of this paper is an inequality (rather tricky) for the Jacobian determinant of solutions of nonlinear elliptic systems in the plane. The model case is the isotropic (rotationally invariant) p-harmonic system ...