Vladimir Buljak

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.

Assessment of elastic–plastic material parameters comparatively by three procedures based on indentation test and inverse analysis

Non-destructive indentation tests are more and more frequently employed for the mechanical characterization of structural metals. Three kinds of experimental data sets as inputs to inverse analyses for parameter identification are comparatively examined in this article: (A) indentation curve, namely the relationship between penetration of the indenter tip versus the force applied on it; (B) both this curve and imprint geometry; (C) imprint profile only. The comparisons are based on two different parameter identification procedures. The novel information source (C) turns out to be promising and advantageous in practical industrial applications for innovative diagnostic analysis methods centred on indentation.

Characterization of fracture properties of thin aluminuminclusions embedded in anisotropic laminate composites

The fracture properties of thin aluminum inclusions embedded in anisotropic paperboardcomposites, of interest for food and beverage packaging industry, can be determined by performing tensile testson non-conventional heterogeneous specimens. The region of interest of the investigated material samples ismonitored all along the experiment by digital image correlation techniques, which allow to recover qualitativeand quantitative information about the metal deformation and about the evolution of the damaging processesleading to the detachment of the inclusion from the surrounding laminate composite. The interpretation of thelaboratory results is supported by the numerical simulation of the tests.

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.

Proper Orthogonal Decomposition and Radial Basis Functions for Fast Simulations

Proper Orthogonal Decomposition (POD) is a powerful method for low-order approximation of some high dimensional processes. It is widely used in the situations where model reduction is required. The most favorable feature of the method is its optimality: it provides the most efficient way of capturing the dominant components of high-dimensional processes with, sometimes surprisingly small number of “modes”. This chapter will present an algorithm that combines POD with Radial Basis Functions (RBF) used for the interpolation of the data with previously reduced dimensionality by the POD.

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

Inverse Analysis: Introduction

Numerical simulations have been established as a powerful tool used in practically all fields of engineering and science. A large number of commercial codes is developed to solve the, so-called direct problems (or forward problems), which consist of finding the solution in terms of response fields when a complete set of input data defining uniquely the solution is known. Since these codes require the knowledge of some parameters on which the solution depends, sometime in engineering practice it is required to solve an inverse problem, defined as the one where some of the “effects” (responses) are known but not some of the “causes” leading to them, namely parameters on which the system depends. These problems are tackled within, relatively young and still growing scientific branch which in modern literature (e.g. [1–3]) is found under the name of Inverse Analyses.

Inverse Analyses in Structural Problems: Putting All the Pieces Together

Inverse analyses procedures in structural problems are usually designed in order to assess some of the unknown parameters. Up to now we already saw that, for a successful development of fully operative inverse analysis procedure, it is required to put together three different elements: experimental technique, numerical simulation of it, and an optimization algorithm. The most traditional approach to the inverse analyses procedures, when structural problems are in focus, assumes that the simulation of the experiment is done by finite element modeling. It is classical, and the most common way of proceeding since nowadays there are well developed FE techniques at our disposal which can be used to simulate even complicated phenomena that may take place in a selected experiment. Given the required repeatability of the simulations enforced by the adopted optimization algorithm, this approach may not be the most convenient for the routine use, as it can be time consuming. Therefore, a modern approach to inverse analyses goes in the direction of avoiding a need to perform FE simulations every time when the inverse problem needs to be solved. One of the possible solutions of this problem is based on POD-RBF algorithm described in Chap. 3. Its implementation within an inverse analyses procedure will be discussed in the subsequent chapter. This chapter will focus on a traditional approach relaying on FE simulations, as it is anyhow very important at least in some of the phases of procedure development.

Modern Approach to Inverse Analyses

By surveying the scientific literature, it can be observed that inverse problems are nowadays becoming more and more popular. Today, there are couple of international journals with high impact factors devoted to this class of problems. Apart of them there are many recently published books that are dealing with mathematical programming in the context of inverse analyses, several are cited within bibliography in previous chapters of this book.