Giuseppe Cocchetti

Elastic¿plastic and limit-state analyses of frames with softening plastic-hinge models by mathematical programming

Abstract Frames (and more general beam systems) subjected to monotonic loading are modelled by conventional finite elements with the traditional assumption of possible plastic deformations concentrated in pre-selected “critical sections”. The inelastic behaviour of these beam sections, i.e. the development of “plastic hinges”, is described by piece-wise-linear constitutive models allowing for hardening and/or softening, in terms of generalized stresses and conjugate kinematic variables. The following topics are discussed: step-by-step analysis methods, both “exact” and stepwise holonomic; path bifurcations and overall stability; limit and deformation analyses combined, as an optimization problem under complementarity constraints apt to compute the safety factor (with respect to global or local failures); numerical tests of nonconventional algorithms by means of simple representative applications. The objective of the paper is to provide a unified methodology and to propose novel procedures for inelastic analyses of frames up to failure, in the light of recent results in mathematical programming, particularly on complementarity theory.

Poroelastic finite element analysis of a bone specimen under cyclic loading.

It had been suggested that the fluid embodied in bone lacunar-canalicular porosity may play an important role in bone remodelling [Weinbaum et al., 1994. Journal of Biomechanics 27, 339-360]. In this paper a finite element model of a poroelastic prismatic solid of rectangular cross-section is considered to simulate bone behaviour, precisely as in the previous work by Zhang and Cowin [Zhang and Cowin, 1994. Journal of Mechanical Physics of Solids 42, 1575-1599]. This solid is subject to combined cyclic axial and bending loads at its end. The objectives of the study are: (1) to verify the accuracy of the simplifying hypotheses underlying the analytical solutions established by the above authors; (2) to provide further insight into the behaviour of that solid; (3) to test the advantages in generality and versatility and the computing costs of general-purpose finite element codes in poroelastic analysis. The study is parametric with respect to the fluid leakage coefficient, to the ratio of the bending moment and axial load, and to the ratio of the characteristic relaxation time of the pore pressure over the excitation period. Results show that, for all the cases considered, the pore pressure distribution along the section height of the poroelastic beam exhibits a very good matching with previous analytical results. Stresses transversal with respect to the beam axis (assumed as constant or zero in previous analytical solutions) are evaluated. The analysis pointed out that: (1) the effects due to end-loads with zero resultants practically extinguish within a distance from the beam end almost equal to a typical length of the cross-section; (2) cross-sections remain plane above that distance; (3) the transversal total stresses are three orders of magnitude lower than axial stress.

MECHANICAL CHARACTERIZATION OF MATERIALS AND DIAGNOSIS OF STRUCTURES BY INVERSE ANALYSES: SOME INNOVATIVE PROCEDURES AND APPLICATIONS

A survey is presented herein of some recent research contributions to the methodology of inverse structural analysis based on statical tests for diagnosis of possibly damaged structures and for mechanical characterization of materials in diverse industrial environments. The following issues are briefly considered: identifications of parameters in material models and of residual stresses on the basis of indentation experiments; mechanical characterization of free-foils and laminates by cruciform and compression tests and digital image correlation measurements; diagnosis, both superficially and in depth, of concrete dams, possibly affected by alkali-silica-reaction or otherwise damaged.

Shakedown analysis in poroplasticity by linear programming

Static (lower bound) and kinematic (upper bound) theorems for shakedown analysis (and limit analysis as special case) are presented for two-phase, fully saturated poroplastic solids in a context characterized by the following features: quasi-static, non-associative, non-softening (perfect or hardening) poroplasticity; piecewise linearized yield loci and hardening; constant permeability (linear fluid transport law); small deformations; non-traditional Galerkin finite element discretization. With reference to cyclic (periodic) external actions, numerical examples centred on linear programming evidence the computational potentialities and limitations of ‘direct’ (non-evolutive) methods of integrity assessment according to limit-state design concepts in poroplasticity. Copyright

A rigorous bound on error in backward-difference elastoplastic time-integration

Abstract The finite element analysis of elastoplastic structures requires in general a time-stepping procedure and, in most cases, the integration of the constitutive law within each time-step has to be carried out by numerical integration. The error associated to this numerical integration depends on the degree of non-linearity of the structural response and can be used as an indicator for the adaptive definition of the time-step size. Based on Martin’s and Ortiz theorem on minimum total work, a simple estimate of the integration error associated to a backward-difference scheme for elastoplastic models is derived. It is shown that the proposed estimate is a rigorous upper bound on the error in the case of assigned constant strain rate. Finally, a simple strategy for the automatic definition of the time-step size is proposed. The estimator and the adaptive strategy are validated by application to problems with a perfectly plastic material model.

Calibration of brittle fracture models by sharp indenters and inverse analysis

In several engineering areas structural analyses concern also fracture processes of brittle materials and employ cohesive crack models. Calibrations of such models, i.e. identification of their parameters by tests, computer simulations of the tests and inverse analyses, have been investigated in the literature particularly with reference to non-destructive indentation tests at various scales.To this timely research, the following contributions are presented in this paper: a simple piecewise-linear cohesive crack model is considered for brittle materials (here glass, for example); for its calibration by “non-destructive” indentation tests novel shapes are attributed to instrumented indenters, in order to make fracture the dominant feature of the specimen response to the test; such shapes are comparatively examined and optimized by sensitivity analyses; a procedure for inverse analysis is developed and computationally tested, based on penetration versus increasing force only (no imprint measurements by profilometers) and is made “economical” (i.e. computationally fast, “in situ” by small computers) by model reduction through proper orthogonal decomposition in view of repeated industrial applications.

Mechanical Characterization of Foils with Compression in Their Planes

An experimental-computational procedure is proposed and numerically validated for combined compression and bending tests and for identification of parameters in anisotropic elastic-plastic material models of the mechanical behavior of foils, specifically of paperboards and laminates for liquid containers. From the experimental standpoint, the proposed technique generalizes the instrumentation and “modus operandi” of traditional uni-axial testing with the following novel provisions: the foil specimen is stabilized by two elastic “blocks” of a well known polymeric material (therefore, such system is called “sandwich” herein); “full-field” displacement measurements by a digital image correlation (DIC) technique are envisaged, and examined by sensitivity analyses with respect to the sought parameters; the experimental data provided by DIC might be enriched by the digitalized relationship between external loading and imposed displacements in the test; test simulations (“direct analyses”) are performed by finite element modeling and the sought parameters governing the specimen behavior are assessed by minimization of a discrepancy function (inverse analysis); the minimization by mathematical programming is made fast and economical by radial basis functions (RBF) interpolations based on preliminary proper orthogonal decomposition (POD).

A Domain Decomposition Method for the Simulation of Fracture in Polysilicon MEMS

In this paper, a domain decomposition approach is proposed to efficiently address the finite element simulation of fracture phenomena in polysilicon MEMS under impact dynamics. The analysis is performed at the microscale, i.e. at the level of the microstructural parts composing the microsystem, in order to simulate local failure mechanisms developing in critical regions.

Upper bounds on post-shakedown quantities in poroplasticity

In this paper various inequalities are established in coupled poroplasticity. These provide upper bounds that can be computed directly for various history-dependent post-shakedown quantities. The main features of the constitutive and computational models considered are as follows: two-phase material; full saturation; piecewise linearization of yield surfaces and hardening; associativity; linear Darcy law; finite element space-discretization in Prager’s generalized variables. The results achieved are illustrated by comparative numerical tests.

Materials Mechanical Characterizations and Structural Diagnoses by Inverse Analyses

Mechanical damages in structures, in structural components of plants and in industrial products usually imply changes of parameters which have central roles in computational modelling apt to assess safety margins with respect to service loading. Such parameters may depend also on the production processes in industrial environments. In this chapter, the parameter identification methodology by inverse analyses is dealt with under the following limitations: experiments at macroscale level, deterministic approaches, statical external actions and time independence in material behaviours. Semiempirical approaches frequently adopted in codes of practice are not dealt with here. The inverse analysis methods outlined here are centered on computational simulations of tests (namely, direct analyses), sensitivity analyses for the optimal design of experiments, model reduction procedures and other provisions apt to make fast and economical the parameter estimation in engineering practice. The applications summarized here as examples concern structural diagnoses based on indentation tests, in situ diagnostic experiments on concrete dams and laboratory mechanical characterization of membranes and laminates. Introductory Remarks The “inverse analysis”methodology is an area of applied sciences which at present is still growing as for improvements of procedures and as for variety of engineering applications. Inverse analysis is based on information concerning the response of a “system” to external actions and leads to the identification of some features of the system, usually parameters included in its modelling and, hence, in the computer simulation of the system response to those actions. In the present context of applied mechanics, the features to assess are usually either parameters contained in material constitutive models or stresses present in the system and included in the set of “parameters” to estimate or “identify.” The system may be a laboratory specimen or a structural component as industrial product; however, frequently, it consists of a structure possibly affected by damages due to deterioration in service. Therefore, inverse analysis is becoming central to “structural diagnosis” intended to provide a reliable basis for the subsequent “direct analyses” apt to assess “margins of safety” with respect to collapses or to substantial further structural damages (“admissible stress” criteria being superseded now in more and more industrial codes). *Email: giulio.maier@polimi.it Handbook of Damage Mechanics DOI 10.1007/978-1-4614-8968-9_33-1 # Springer Science+Business Media New York 2013