A Cap-Model for Masonry-Like Material Constitutive Laws

An accurate description of the constitutive behaviour of masonry-like materials is an essential target for obtaining an effective analysis-tool of masonry structures. In this paper an idealized constitutive model of such materials is proposed taking into account some peculiar features of masonry: -i) a limited strength in compression; -ii) a very limited ability to withstand tensile stresses; -iii) a softening behaviour due to a progressive reduction of the tensile strength during a monotonically increasing loading.

Shakedown optimum design of reinforced concrete framed structures

Structures subjected to variable repeated loads can undergo the shakedown or adaptation phenomenon,-which prevents them from collapse but may cause lack of serviceability, for the plastic deformations developed, although finite, as shakedown occurrence postulates, may exceed some maximum values imposed by external ductility criteria. This paper is devoted to the optimal design of reinforced concrete structures, subjected to variable and repeated loads. For such structures the knowledge of the actual values taken by the plastic deformations, at shakedown occurrence, is a crucial issue. An approximate assessment of such plastic deformations is needed, which is herein provided in the shape of …

A thermodynamic approach to nonlocal plasticity and related variational principles

Elastic-plastic rate-independent materials with isotropic hardening/softening of nonlocal nature are considered in the context of small displacements and strains. A suitable thermodynamic framework is envisaged as a basis of a nonlocal associative plasticity theory in which the plastic yielding laws comply with a (nonlocal) maximum intrinsic dissipation theorem. Additionally, the rate response problem for a (continuous) set of (macroscopic) material particles, subjected to a given total strain rate field, is discussed and shown to be characterized by a minimum principle in terms of plastic coefficient. This coefficient and the relevant continuum tangent stiffness matrix are shown to admit, …

Internal-variable constitutive model for rate-independent plasticity with hardening saturation surface

An elastic-plastic material model with internal variables and thermodynamic potential, not admitting hardening states out of a saturation surface, is presented. The existence of such a saturation surface in the internal variables space — a consequence of the boundedness of the energy that can be stored in the material's internal micro-structure — encompasses, in case of general kinematic/isotropic hardening, a one-parameter family of envelope surfaces in the stress space, which in turn is enveloped by a limit surface. In contrast to a multi-surface model, noad hoc rules are required to avoid the intersection between the yield and bounding/envelope surface. The flow laws of the proposed mode…

Interaction Diagram of a Circular Bar in Torsion and Extension

For a circular bar of perfectly plastic material and subjected to a cyclically variable torque and a constant axial force, the interaction (or generalized Bree) diagram is derived by a direct method in which Melan’s theorem is used to locate the nonratchetting load boundary.

Mechanical testing and numerical modelling of pull-wound carbon-epoxy spinnaker poles

The paper deals with experimental testing and numerical simulation of the mechanical behaviour of multi-layer cylindrical coupons, of two different diameters, made in carbon-epoxy composite. The aim of the study is to provide a simple and effective numerical model that can be used as a design tool for structural elements having analogous geometrical and manufacturing characteristics. The numerical analysis, performed in the elastic regime with a standard finite element (FE) code, was strongly correlated with the laboratory determination of fibre-volume fractions and of some elastic parameters of the material system. Other parameters, like the shear modulus values G, were in fact appropriate…

A STRAIN-DIFFERENCE BASED NONLOCAL ELASTICITY THEORY FOR SMALL-SCALE SHEAR-DEFORMABLE BEAMS WITH PARAMETRIC WARPING

A strain-difference-based nonlocal elasticity model

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…

Shakedown of Structures Accounting for Damage Effects

Shakedown theory for elastic-plastic-damage materials is exposed. Two kinds of shakedown are considered: i) Enlarged shakedown (or simply shakedown), in which both plastic deformations and damage eventually cease, after which the structural response is purely elastic; ii) Weak-form shakedown, in which plastic deformations eventually cease together with their consequences (including ductile damage), not necessarily damage from other sources (which are however escluded by assumption). An (enlarged) shakedown static-type theorem is given for a class of D-stable structures. Sufficient theorems of weak-form shakedown are provided, i.e. a static-type one (quite similar to that of Hachemi and Weic…

Integral and differential approaches to Eringen's nonlocal elasticity models accounting for boundary effects with applications to beams in bending

Nonlinear finite element analysis of no-tension masonry structures

A numerical approach for structural analysis of masonry walls in plane stress conditions is presented. The assumption of a perfectly no-tension material (NTM) constitutive model, whose relevant equations are in the form of classical rate-independent associated flow laws of elastoplastic material, allows one to adopt numerical procedures commonly used in computational plasticity. An accuracy analysis on the integration algorithm employed in the solution of constitutive relations has been carried out. The results obtained for some relevant case-studies and their comparison with data, available in the literature show the effectiveness of the proposed method.

A thermodynamically consistent formulation of nonlocal and gradient plasticity

Size effects of small-scale beams in bending addressed with a strain-difference based nonlocal elasticity theory

Abstract A strain-difference based nonlocal elasticity model devised by the authors elsewhere (Polizzotto et al., Int. J. Solids Struct. 25 (2006) 308–333) is applied to small-scale homogeneous beam models in bending under static loads in the purpose to describe the inherent size effects. With this theory —belonging to the strain-integral nonlocal model family, but exempt from anomalies typical of the Eringen nonlocal theory— the relevant beam problem is reduced to a set of three mutually independent Fredholm integral equations of the second kind (each independent of the beam’s ordinary boundary conditions, only one depends on the given load), which can be routinely solved numerically. Appl…

Numerical simulations of the mechanical characteristics of glass fibre reinforced C-profiles

A mechanical characterisation analysis on pultruded glass fibre reinforced C-shaped profiles, developed as modular construction elements to assemble fastening systems, such as doors, window frames and shutters is presented. The key idea is to perform the analysis, and all the related identification procedures of the material parameters, via a coupled approach, based on a limited number of standard laboratory tests and on the numerical finite element simulations of the same tests. The proposed approach allows one to identify all those material parameters which are difficult to detect, by means of simple laboratory experiments on specimens that are extracted from commercial products. It also …

Shakedown of Structures Subjected to Dynamic External Actions and Related Bounding Techniques

The shakedown theory for dynamic external actions is expounded considering elastic-plastic internal-variable material models endowed with hardening saturation surface and assuming small displacements and strains as long with negligible effects of temperature variations on material data. Two sorts of dynamic shakedown theories are presented, i.e.: i) Unrestricted dynamic shakedown, in which the structure is subjected to (unknown) sequences of short-duration excitations belonging to a known excitation domain, with no-load no-motion time periods in between and for which a unified framework with quasi-static shakedown is presented; and ii) Restricted dynamic shakedown, in which the structure is…

Shear Effects in Elastic Nanobeams

Small-scale, shear deformable nanobeams, subjected to quasi-static loads, are analyzed by a nonlocal (integral) elasticity model with the main goal to evaluate the influence of shear deformation on size effects. To this aim a warping parametric model is considered in order to obtain a continuous family of shear deformable beam models which span from the Euler-Bernoulli to the Thimoshenko beam model, passing from the Reddy model. The strain difference based nonlocal elasticity theory is applied under the hypotheses of small displacements and isotropic material. The results, obtained by analysing a cantilever nonlocal nanobeam, indicate that shear deformation has a considerable influence upon…

A nonhomogeneous nonlocal elasticity model

Nonlocal elasticity with nonhomogeneous elastic moduli and internal length is addressed within a thermodynamic framework suitable to cope with continuum nonlocality. The Clausius–Duhem inequality, enriched by the energy residual, is used to derive the state equations and all other thermodynamic restrictions upon the constitutive equations. A phenomenological nonhomogeneous nonlocal (strain difference-dependent) elasticity model is proposed, in which the stress is the sum of two contributions, local and nonlocal, respectively governed by the standard elastic moduli tensor and the (symmetric positive-definite) nonlocal stiffness tensor. The inhomogeneities of the elastic moduli and of the int…

Shakedown Analysis by Elastic Simulation

Shakedown analysis of elastic plastic structures is widely credited as a valuable analytical/numerical tool for design purposes. For complex structures and loading conditions, e. g. for fast breeder nuclear reactor plants, full inelastic analysis is rarely performed, practically never within the early stages of the design advancement and the inherent decision process. The essential information therein needed can in fact be obtained, at moderate computational costs, by application of the shakedown methods and rules, at least within some limits related to the present developments of shakedown theory and its applicability to practical engineering problems, see e. g. Ponter et al. (1990), Carte…

Strengthening of steel-reinforced concrete structural elements by externally bonded FRP sheets and evaluation of their load carrying capacity

Abstract The paper proposes a preliminary design tool for reinforced concrete (RC) elements strengthened by fiber-reinforced-polymer (FRP) sheets to be used in civil engineering applications and in particular in medical buildings. The design strategy is based on limit analysis theory and utilizes a numerical procedure which provides a direct method to determine peak load, failure mode and critical zones of the structural elements of interest.

Theorems of restricted dynamic shakedown

Abstract Dynamic shakedown for a rate-independent material with internal variables is addressed in the hypothesis that the load values are restricted to those of a specified load history of finite or even infinite duration, thus ruling out the possibility—typical of classical shakedown theory—of indefinite load repetitions. Instead of the usual approach to dynamic shakedown, based on the bounded plastic work criterion, another approach is adopted here, based on the adaptation time criterion. Static, kinematic and mixed-form theorems are presented, which characterize the minimum adaptation time (MAT), a feature of the structure-load system, but which are also able to assess whether plastic w…

The shakedown load boundary of an elastic-perfectly plastic structure

In the hypothesis of small displacements and combined time-variable/steady loads, the geometrical-mechanical properties of the shakedown load boundary are investigated. It is shown that, in the load space, the shakedown load boundary plays the role of yield surface, and that a certain plastic strain accumulation vector—characterizing some impending inadaptation collapse mechanism—obeys the normality rule, whereas a specific form of the maximum plastic work theorem constitutes an effective tool for the evaluation of the shakedown limit load corresponding to a specified inadaptation collapse mode. The equations governing the state of the structure at the shakedown limit are provided and the r…