A combined reduced order‐full order methodology for the solution of 3D magneto‐mechanical problems with application to magnetic resonance imaging scanners

The design of a new magnetic resonance imaging (MRI) scanner requires multiple numerical simulations of the same magneto‐mechanical problem for varying model parameters, such as frequency and electric conductivity, in order to ensure that the vibrations, noise, and heat dissipation are minimized. The high computational cost required for these repeated simulations leads to a bottleneck in the design process due to an increased design time and, thus, a higher cost. To alleviate these issues, the application of reduced order modeling techniques, which are able to find a general solution to high‐dimensional parametric problems in a very efficient manner, is considered. Building on the established proper orthogonal decomposition technique available in the literature, the main novelty of this work is an efficient implementation for the solution of 3D magneto‐mechanical problems in the context of challenging MRI configurations. This methodology provides a general solution for varying parameters of interest. The accuracy and efficiency of the method are proven by applying it to challenging MRI configurations and comparing with the full‐order solution

Mechanical characterization of anisotropic elasto-plastic materials by indentation curves only

Anisotropy, usually orthotropy, arises in structural materials, particularly metals, due to production processes like laminations and concerns primarily parameters which govern the plastic behavior. Identification of such parameters is investigated here by a novel approach with the following features: experimental data provided by indentation curves only (not by imprint geometry); indenter shape with elliptical cross-section derived from classical conical or spherical shape and optimized by sensitivity analyses; indentation test repeated in near places after indenter rotation; deterministic inverse analyses centered on discrepancy function minimization and made computationally economical by an ‘a priori’ model reduction procedure

Identification of residual stresses by instrumented elliptical indentation and inverse analysis

The residual stress tensor near the surface of a metal structural component or products of metallurgical processes (particularly welding) is considered in view of the estimation of its governing components. These are: the two principal stresses if the directions are “a priori” known as assumed here for the preliminary optimization of the indenter shape; otherwise two normal stresses and a shear stress according to a preselected reference system. In both situations the material is assumed to be endowed with known elastic–plastic properties. The novel parameter identification procedure investigated herein can be outlined as follows, when the unknown stresses are three: an instrumented indenter is adopted with elliptical section across the axis of an originally conical, or, as an alternative, of an originally spherical shape; three indentations are performed with the ellipse axis rotated by 45° in a sequence, in three locations near to each other at minimal distances apt to avoid interference; the three digitalized indentation curves (loading–unloading force versus penetration) are the source of the experimental data set used as input of inverse analysis; this is carried out by a fast method consisting of finite element simulations of the tests, “proper orthogonal decomposition”, “radial basis function” interpolation, and a first-order algorithm for the minimization of the discrepancy function. When the unknowns are the two principal stresses (directions known) two orthogonal indentations turn out to be sufficient

Corrigendum to “Identification of residual stresses by instrumented elliptical indentation and inverse analysis” [Mech. Res. Commun. 41 (2012) 21–29]

The residual stress tensor near the surface of a metal structural component or products of metallurgical processes (particularly welding) is considered in view of the estimation of its governing components. These are: the two principal stresses if the directions are "a priori" known as assumed here for the preliminary optimization of the indenter shape; otherwise two normal stresses and a shear stress according to a preselected reference system. In both situations the material is assumed to be endowed with known elastic-plastic properties. The novel parameter identification procedure investigated herein can be outlined as follows, when the unknown stresses are three: an instrumented indenter is adopted with elliptical section across the axis of an originally conical, or, as an alternative, of an originally spherical shape; three indentations are performed with the ellipse axis rotated by 45° in a sequence, in three locations near to each other at minimal distances apt to avoid interference; the three digitalized indentation curves (loading-unloading force versus penetration) are the source of the experimental data set used as input of inverse analysis; this is carried out by a fast method consisting of finite element simulations of the tests, "proper orthogonal decomposition", "radial basis function" interpolation, and a first-order algorithm for the minimization of the discrepancy function. When the unknowns are the two principal stresses (directions known) two orthogonal indentations turn out to be sufficient

Mechanical characterization of anisotropic elasto-plastic materials by indentation curves only

Anisotropy, usually orthotropy, arises in structural materials, particularly metals, due to production processes like laminations and concerns primarily parameters which govern the plastic behavior. Identification of such parameters is investigated here by a novel approach with the following features: experimental data provided by indentation curves only (not by imprint geometry); indenter shape with elliptical cross-section derived from classical conical or spherical shape and optimized by sensitivity analyses; indentation test repeated in near places after indenter rotation; deterministic inverse analyses centered on discrepancy function minimization and made computationally economical by an a priori model reduction procedure

Quasi-non-destructive Small Punch and Hole Drilling tests extended to the assessment of both material properties and residual stresses

Small punch (SP) tests and Hole Drilling (HD) tests are at present frequently applied in diverse industrial contexts, the former for mechanical characterization of structural metals and the latter for the determination of parameters governing residual stresses near the surfaces. Both experiments are standardized in national and international codes, can be performed “in situ” and are regarded as “quasi-non-destructive” because almost negligible are the damages caused in the tested structural components. The innovative developments to be presented in this communication can be outlined as follows. (a) The extraction of specimens for SP tests is exploited for identification of parameters governing the residual stresses and the consequent displacements around the generated cavity are measured by Digital Image Correlation (DIC) cameras, employable to other purposes as well. A finite element (FE) model elaborated once for all and employed for back analysis leading from measured displacements to the residual stress parameters by exploiting the material properties estimated by a preceding backanalysis resting on experimental data measured by the SP test carried out as second experiment on the extracted specimens. (b) An usual HD test is performed; by DIC (no longer strain gauges) displacements are measured due to consequent changes of residual stresses; an indenter is employed for indentation (IND) either on the hole bottom or on the hole wedges (depending on the chosen geometry) and the digitalized “indentation curves” are used as input of inverse analysis based on test simulation by FE modelling; the material properties (elasticity and plasticity) quantified by the so assessed parameters are employed for another backanalysis which is based on HD test simulation by another computational FE model and which leads from DIC measurements of displacements earlier generated by the HD test to the sought residual stress parameters. Both diagnostic methods (a) and (b) are almost non destructive; the FE models and the inverse analyses (centered on “discrepancy minimization” by mathematical programming or genetic algorithms) can rest on software “a priori” elaborated once-for-all; the experimental instruments, except the SP one, can be portable and employed “in situ”, The above circumstances make economically advantageous the here proposed novelties in the methodology of structural diagnosis on metallic plant components

Diagnostic inverse structural analyses based on indentation curves alone and novel indenter geometries

Non-destructive indentation tests are experiments with origin in hardness testing and at present of growing multiplicity of applications. The developments presented here (and at present research subjects in our team) are characterized by the following features: experimental data extracted only from indentation curves; novel indenter geometries optimized by sensitivity analyses; parameter identifications by a deterministic approach and by preliminary model reduction apt to make economical and fast the discrepancy minimization algorithm. The estimates provided by the innovative inverse analysis procedures concern: residual stresses or fracture parameters or parameters in anisotropic plasticity models

Assessment of residual stresses and mechanical characterization of materials by hole drilling and indentation tests combined and by inverse analysis

Hole Drilling (HD) tests are frequently employed as quasi-non-destructive experiments, for assessments of residual stresses in metallic components of power plants and of other industrial structures. With respect to the present broadly standardized HD method, the following methodological developments are proposed and computationally validated in this paper: assessments of elastic and plastic parameters by indentation exploiting the hole generated by HD tests; employment of Digital Image Correlation (DIC) for full-field displacement measurements, instead of the strain measurements by gauge rosettes usually adopted so far; transitions from experimental data to sought parameters by inverse analyses based on computer simulations of both tests and on minimizations of a discrepancy function. Interactions between the two experiments are here investigated, besides the elastic parameters transition from indentation (IND) to HD test interpretation. The main advantage achievable by the procedure proposed herein is reduction of additional damage and cost due to usual experimental procedures for diagnosis of structural components (e.g. frequently adopted small punch experiments or laboratory tension tests). (C) 2015 Elsevier Ltd. All rights reserved

Estimation of residual stresses by inverse analysis based on experimental data from sample removal for “small punch” tests.

"Small Punch” (SP) tests, at present frequently employed for mechanical characterizations of structural metals, particularly for diagnosis of plant components, are here considered in view of employment also for assessments of stresses. In the procedure proposed herein the standardised sample removal from an in-service component for SP tests is exploited as external action altering the residual stress state possibly present near to the surface in the location considered. Full-field measurements of consequent displacements in the surrounding surface are employed as input for inverse analysis based on the following features: computer simulations of the sample removal as for its consequences due to relaxation of the preexisting stress state; "non-uniformity” of residual-stress dependence on depth described as layerdependent with uniformity in each layer of a pre-defined set of layers; "discrepancy function” minimization with employment of the elasticity parameters provided by the subsequent SP test. The advantages of the novel method consist of no-more need of traditional usual "Hole Drilling” (HD) tests or other tests for residual-stress estimation. The SP experimental procedure proposed herein for estimations of both stress state and elastic-plastic material properties would imply reductions of damages, costs and times in structural diagnoses