Fusion of facial regions using color information in a forensic scenario

Comunicación presentada en: 18th Iberoamerican Congress on Pattern Recognition, CIARP 2013; Havana; Cuba; 20-23 November 2013The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-41827-3_50This paper reports an analysis of the benefits of using color information on a region-based face recognition system. Three different color spaces are analysed (RGB, YCbCr, lαβ) in a very challenging scenario matching good quality mugshot images against video surveillance images. This scenario is of special interest for forensics, where examiners carry out a comparison of two face images using the global information of the faces, but paying special attention to each individual facial region (eyes, nose, mouth, etc.). This work analyses the discriminative power of 15 facial regions comparing both the grayscale and color information. Results show a significant improvement of performance when fusing several regions of the face compared to just using the whole face image. A further improvement of performance is achieved when color information is consideredThis work has been partially supported by contract with Spanish Guardia Civil and projects BBfor2 (FP7-ITN-238803), bio-Challenge (TEC2009-11186), Bio Shield (TEC2012-34881), Contexts (S2009/TIC-1485), TeraSense (CSD2008-00068) and "Cátedra UAM-Telefónica

Identification using face regions: Application and assessment in forensic scenarios

This is the author’s version of a work that was accepted for publication in Forensic Science International. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Forensic Science International, 23, 1-3, (2013) DOI: 10.1016/j.forsciint.2013.08.020This paper reports an exhaustive analysis of the discriminative power of the different regions of the human face on various forensic scenarios. In practice, when forensic examiners compare two face images, they focus their attention not only on the overall similarity of the two faces. They carry out an exhaustive morphological comparison region by region (e.g., nose, mouth, eyebrows, etc.). In this scenario it is very important to know based on scientific methods to what extent each facial region can help in identifying a person. This knowledge obtained using quantitative and statical methods on given populations can then be used by the examiner to support or tune his observations. In order to generate such scientific knowledge useful for the expert, several methodologies are compared, such as manual and automatic facial landmarks extraction, different facial regions extractors, and various distances between the subject and the acquisition camera. Also, three scenarios of interest for forensics are considered comparing mugshot and Closed-Circuit TeleVision (CCTV) face images using MORPH and SCface databases. One of the findings is that depending of the acquisition distances, the discriminative power of the facial regions change, having in some cases better performance than the full face

Progress in Forensic Genetics: New Markers Validation Studies and Population Data

Los objetivos de esta tesis son: - validar una pentaplex de nueva generación que incluya los cinco nuevos marcadores recomendados por el Consejo de la Unión Europea para la extensión del lo European Standard Set (ESS) mediante evaluación del nivel de información de los datos y del éxito del análisis sobre una amplia gama de muestras forenses y también comparar su funcionamiento con el que de otros equipos disponibles comercialmente. - crear una base de datos demográfica útil en forense que incluye una estimación de la frecuencia de cada allelo posible y genotipo (o haplotipo), estudiando la variabilidad en el Área mediterránea de 15 STRs autosómicosl bien establecidos juntos con los 5 nuevos marcadores EES, el sumamente discriminante SE33 y algún STRs de los chromosomes sexuales comúnemente usados en la investigación forense. Finalmente pretendemos evaluar la variabilidad de la 52 SNPplex recientemente introducida para usos forense

Beyond DNA : an epigenetic approach to identical twin identification.

For more than two decades, DNA analysis has helped forensic scientists link suspects to a crime. Often times, DNA evidence is one of the most impactful pieces of evidence available. However, there is still one thing that traditional DNA analysis cannot accomplish - differentiating DNA from identical twins. With identical twins becoming more common than in the past and with numerous examples of cases being dropped because an identical twin was implicated, it would benefit the forensic science community to find a solution to this problem. The goal of this project was to see if the conventional forensic science techniques of cycle sequencing and capillary electrophoresis could be used to distinguish twins via DNA methylation analysis. It was found that the use of cycle sequencing and capillary electrophoresis for the analysis of DNA methylation extracted from human cells was problematic. While small successes were achieved in analyzing the methylation, the results were not consistent. Thus, while cycle sequencing and capillary electrophoresis are convenient and cost efficient for the forensic science community, they may not the best instruments for this problem. The PRKCA locus was shown to be a strong candidate locus that could be targeted by cycle sequencing or high-throughput sequencing technology. Therefore, rather than using an expensive and time-consuming method such as ultra-deep next generation sequencing to differentiate identical twins, the forensic science community should identify several key loci, such as the PRKCA gene analyzed in this study, for DNA methylation analysis

Current genetic methodologies in the identification of disaster victims and in forensic analysis

This review presents the basic problems and currently available molecular techniques used for genetic profiling in disaster victim identification (DVI). The environmental conditions of a mass disaster often result in severe fragmentation, decomposition and intermixing of the remains of victims. In such cases, traditional identification based on the anthropological and physical characteristics of the victims is frequently inconclusive. This is the reason why DNA profiling became the gold standard for victim identification in mass-casualty incidents (MCIs) or any forensic cases where human remains are highly fragmented and/or degraded beyond recognition. The review provides general information about the sources of genetic material for DNA profiling, the genetic markers routinely used during genetic profiling (STR markers, mtDNA and single-nucleotide polymorphisms [SNP]) and the basic statistical approaches used in DNA-based disaster victim identification. Automated technological platforms that allow the simultaneous analysis of a multitude of genetic markers used in genetic identification (oligonucleotide microarray techniques and next-generation sequencing) are also presented. Forensic and population databases containing information on human variability, routinely used for statistical analyses, are discussed. The final part of this review is focused on recent developments, which offer particularly promising tools for forensic applications (mRNA analysis, transcriptome variation in individuals/populations and genetic profiling of specific cells separated from mixtures)

Advances in Forensic Genetics

The book has 25 articles about the status and new directions in forensic genetics. Approximately half of the articles are invited reviews, and the remaining articles deal with new forensic genetic methods. The articles cover aspects such as sampling DNA evidence at the scene of a crime; DNA transfer when handling evidence material and how to avoid DNA contamination of items, laboratory, etc.; identification of body fluids and tissues with RNA; forensic microbiome analysis with molecular biology methods as a supplement to the examination of human DNA; forensic DNA phenotyping for predicting visible traits such as eye, hair, and skin colour; new ancestry informative DNA markers for estimating ethnic origin; new genetic genealogy methods for identifying distant relatives that cannot be identified with conventional forensic DNA typing; sensitive DNA methods, including single-cell DNA analysis and other highly specialised and sensitive methods to examine ancient DNA from unidentified victims of war; forensic animal genetics; genetics of visible traits in dogs; statistical tools for interpreting forensic DNA analyses, including the most used IT tools for forensic STR-typing and DNA sequencing; haploid markers (Y-chromosome and mitochondria DNA); inference of ethnic origin; a comprehensive logical framework for the interpretation of forensic genetic DNA data; and an overview of the ethical aspects of modern forensic genetics

Prognoses on DNA-based identification success rates of altered human remains using capillary electrophoresis and Next Generation Sequencing technologies

The DNA-based identification success of altered human remains relies on the condition of the collected tissue sample and the associated DNA quantity and quality. Due to tissue-specific differences in post-mortem DNA stability, sampling of the best-suited biological material is essential for successful and rapid identification. However, a large variety and partly contradicting recommendations on optimal material have been published so far. The observed insecurity in sampling strategies revealed the need for a broad and systematic approach in predicting short tandem repeat (STR) genotyping success rates in a wide range of tissue types. Therefore, the overarching aim of this thesis was to improve the DNA-based identification success of altered corpses by presenting novel recommendations and guidance for optimal tissue sampling according to the condition of the body. First, the current situation of identification processes in forensics casework was assessed by a retrospective study on the identification success of 402 altered human corpses over seven years (project I). The evaluation of medical as well as genetic reports revealed an increase in the examination of highly and profoundly decomposed corpses and challenges in molecular analyses of degraded and inhibited samples from altered remains. By comparing the number of successive and parallel PCR amplifications, the most unpredictable typing success and highest number of additional analyses were observed in muscle and bone samples. A comparison with previously published studies highlighted the challenges and insecurity in tissue sampling and the need for standardized guidelines. Furthermore, during project II, the reliability of novel DNA sequencing methods was assessed by validating the MiSeq FGx system for Next Generation Sequencing (NGS) of casework samples and optimizing the sequencing workflow for samples of altered remains. The extensive evaluation of sensitivity, concordance to currently used methods and reproducibility, among others, displayed the technology as robust and implementable in forensic routine casework. Additionally, the applicability of phenotype and biogeographic ancestry prediction was demonstrated in challenging samples of altered corpses. However, as the optimization results revealed, an additional PCR purification step, an increased pooling volume and a reduction of adapter volumes for DNA input concentrations ≥ 31.2 pg is recommended for sequencing highly degraded and inhibited samples. Finally, based on the outcomes of projects I and II, the multicentre study concludes with the presentation of novel recommendations on alteration-specific optimal tissue types for first-attempt identification of altered human remains in project III. By providing an easy and rapid scoring system, a precise assessment of the corpse alteration progress is enabled. Furthermore, the systematic approach included the comparison of DNA quantity, integrity and resulting STR profile completeness in an exceptional high number of 1698 DNA extracts from 949 samples of 19 different tissue types. Thereby, standard capillary electrophoresis as well as forthcoming NGS methods were used and the impact of DNA extraction methods was assessed. The final and first-time prognoses on genotyping success of a wide range of tissues separated for two DNA extraction methods (purifying and non-purifying) and two sets of STR loci (22 loci and 16 loci of the extended European Standard Set) provide guidance that improves the first-attempt DNA-based identification success of altered corpses

The Utilization of Volatile Organic Compounds and Human Leukocyte Antigen Genes for Ethnic-Specific Differentiation within Target Populations

Human scent has been previously defined as a complex mixture of volatile organic compounds (VOCs) detected in the headspace above a scent sample. Humans generate odor from several areas of the body including hair, mouth, hand, axillae, and foot. Due to the novelty of human scent research, human scent evidence has been undervalued in the court of law. However, this type of evidence has significant value when physical evidence is not available at crime scenes. To increase the individualization and differentiation power of human scent evidence, this study aimed to further investigate the identification of chemical signatures within axillae of specific ethnicities (Caucasian, Hispanic, and African American) and determine if ethnic-specific genetic signatures are present among Human Leukocyte Antigen (HLA) genes. During the study, the axillae of 68 participants were investigated. Upon collection, samples were extracted using Headspace Solid Phase Micro extraction (HS-SPME) and solvent extraction. The samples were analyzed using Gas Chromatography- Mass Spectrometry (GC-MS). The utilization of SPME immediately followed by solvent extraction complements the extraction of both semi-volatile and non-volatile compounds, thus filling in the gaps of the compounds that could not be recovered using HS-SPME alone. The samples were evaluated statistically via logistic regression and Receiving Operating Characteristic (ROC) curves to evaluate the performance and prediction power of VOCs for ethnicity inferences. The study concluded that logistic regression served as an efficient model predicting the VOCs capable of class characteristic determination when comparing ethnicities. The HLA gene complex was evaluated to determine its contribution to human scent and the ability to differentiate between ethnicities. Using buccal swabs extracted from 31 subjects, five genes were successfully amplified using Multiplex Polymerase Chain Reaction (Multiplex PCR). The Multiplex PCR products were analyzed using capillary electrophoresis. The genotype frequencies were observed, and linear discriminant analysis (LDA) was performed to assess the ability of predicting ethnicity using genotype frequencies of individuals. Four of the five genes predicted ethnicity at 80% or greater accuracy, which validates that the HLA genes (D6S2925, D6S2937, D6S2917, and D6S2787), coupled to the VOCs, can be used as a biomarker for class characteristic determination of an individual

Finnish population genetics in a forensic context

Finland’s unusual history and resulting genetic structure have a number of consequences for the practical applications of genetic testing in Finland today, including forensic analysis. The objective of this study was to characterize coding and noncoding genetic variation in the Finnish gene pool using forensic markers, in order to improve the efficiency of forensic testing in Finland while simultaneously broadening our understanding of its history. Finland is characterized by a clear genetic delineation between Eastern and Western regions of the country, the origins of which have heretofore remained undetermined. Here, patterns of distribution observed in markers of prehistoric association suggest this delineation represents the vestiges of an ancient border between Mesolithic hunter-gatherer and Neolithic farmer populations, undetectable in other regions of Europe. This study provides further insight into the development of the current population structure and clarifies the resolution of uniparental marker variation in contemporary Finland, with implications for forensic applications such as ancestry- informative testing. Along with the aforementioned population stratification, Finland’s unusual history has also left its mark on the population in the form of reduced diversity, visible especially in the Y-chromosome. In order to improve the efficiency of Finnish Y-profiling, novel multiplex panels of highly polymorphic Y-microsatellite markers were developed and evaluated. The new 7- and 24-locus Y-STR panels demonstrate improved suitability for practical forensic applications, with enhanced discrimination power and a reduction in regional subdivision compared to commercial sets. In order to assess the applicability of a novel commercial panel of insertion-deletion markers in Finnish forensic profiling, the Investigator DIPplex kit was evaluated in the Finnish population. Earlier studies of the applicability of insertion/deletion polymorphisms as a tool of forensics had indicated that they were likely to be beneficial for casework analysis both in individual identification as well as the testing of familial relationships. The results suggest that while these markers were well suited for individualization purposes, they were inefficient for paternity testing in the Finnish population. These two studies highlight the need for careful population-specific validation of commercial marker sets widely in use in forensics. Historical population bottlenecks can result in the enrichment of mutations, including those with clinical effects. The assessment of metabolic gene ABCB1 polymorphisms in Finns found increased frequency of these mutations in comparison to other populations, suggesting that Finns may demonstrate an increased susceptibility to drug intoxication. A further investigation performed on post-mortem samples revealed a positive correlation between mutation frequency and level of blood digoxin, confirming previous results of the adverse effect of ABCB1 mutations on metabolic processes. These findings will aid forensic medicine by providing valuable additional evidence for molecular autopsies. A thorough understanding of underlying patterns of genetic variation and the history that created them is vital in recognizing the factors affecting practical forensic analysis today. In these studies, the deep genetic delineation between Eastern and Western regions of Finland was observed in a variety of forensic loci, and shown for the first time to extend also to mitochondrial markers, giving further evidence of its ancient history. The results of this thesis thus reveal new information about the history and demographics of the Finnish population while offering globally applicable improvements to forensic typing. The end result is more straightforward analysis and improved reliability for a spectrum of forensic applications ranging from individualization to cause of death determinations.Väitöskirjatutkimus käsittelee suomalaisen väestön populaatiogenetiikkaa oikeuslääketieteellisessä kontekstissa. Suomen omintakeinen historia on jättänyt jälkensä väestön geneettiseen rakenteeseen vaikuttaen siten myös oikeusgeneettiseen yksilöntunnistukseen suomalaisessa väestössä. Tämän tutkimuksen tarkoituksena on luonnehtia Suomen geneettistä muuntelua forensisilla DNA-merkeillä, tavoitteena lisätä oikeusgeneettisen testauksen tehokkuutta sekä tuottaa lisätietoa Suomen historian vaiheista. Aikaisemmissa tutkimuksissa havaittua selkeää geneettistä jakautumista itäisen ja läntisen Suomen välillä tarkasteltiin mitokondrio- ja Y-kromosomimerkeillä, tavoitteena alueellisen rajan alkuperän selkeytyminen. Kromosomimerkkien esihistoriallisten ryhmien jakolinjat viittaavat siihen, että jakautuminen edustaa muinaista rajaa mesoliittisten metsästäjä-keräilijä- ja neoliittisten maanviljelijäryhmien välillä. Tutkimus antaa lisätietoa nykyisen väestörakenteen kehityksestä ja valottaa sukulinjamarkkereiden jakautumaa Suomessa. Suomen väestölle ominaisen alhaisen Y-kromosomimuuntelun takia suomalaisessa oikeusgenetiikassa on tarve korkeamman erottelutehon Y-merkeille. Tehokkuuden parantamiseksi arvioimme uusien monimuotoisten Y-mikrosatelliittimarkkereiden soveltuvuutta suomalaiseen Y-profilointiin. Tutkimuksessa kehiteltiin uusi Y-tunnistepaneeli, jonka erotteluvoima suomalaisväestössä on parempi kuin esim. kaupallisissa Y-kromosomipaneeleissa. Myös uuden kaupallisen insertio-deleetiomarkkerisarjan soveltuvuutta isyystutkimukseen arvioitiin. Tulokset osoittavat, että vaikka markkerit sopivat hyvin yksilöllistämiseen suomalaisessa väestössä, niiden erotteluteho isyyskokeissa on selvästi alentunut muihin eurooppalaisiin verrattuna. Historialliset tapahtumat voivat vaikuttaa myös kliinisesti merkittävien mutaatioiden yleistymiseen. Muihin väestöihin verrattuna suomalaisilla havaittiin aineenvaihduntageeni ABCB1-mutaatioiden lisääntynyt esiintyminen, indikoiden kohonnutta myrkytysriskiä. Lisäksi post-mortem-näytteistä tehty geenityypitys paljasti positiivisen korrelaation mutaatiofrekvenssin ja veren digoksiinipitoisuuden välillä, vahvistaen aikaisempia havaintoja ABCB1-mutaatioiden negatiivisesta vaikutuksesta aineenvaihduntaan. Nämä tulokset tarjoavat arvokkaita lisätodisteita oikeuslääketieteellisiin tutkimuksiin. Tutkimuksen tulokset paljastavat uutta tietoa Suomen väestöhistoriasta ja tarjoavat globaalisti sovellettavia parannuksia rikosteknisiin tutkimuksiin. Tutkimustulokset auttavat oikeuslääketieteellisten sovellusten eri osa-alueita yksilöntunnistamisesta kuolemansyyn määrittämiseen, selkeyttäen analyysia ja kasvattaen luotettavuutta

Statistical Assessment of the Significance of Fracture Fits in Trace Evidence

Fracture fits are often regarded as the highest degree of association of trace materials due to the common belief that inherently random fracturing events produce individualizing patterns. Often referred to as physical matches, fracture matches, or physical fits, these assessments consist of the realignment of two or more items with distinctive features and edge morphologies to demonstrate they were once part of the same object. Separated materials may provide a valuable link between items, individuals, or locations in forensic casework in a variety of criminal situations. Physical fit examinations require the use of the examiner’s judgment, which rarely can be supported by a quantifiable uncertainty or vastly reported error rates. Therefore, there is a need to develop, validate, and standardize fracture fit examination methodology and respective interpretation protocols. This research aimed to develop systematic methods of examination and quantitative measures to assess the significance of trace evidence physical fits. This was facilitated through four main objectives: 1) an in-depth review manuscript consisting of 112 case reports, fractography studies, and quantitative-based studies to provide an organized summary establishing the current physical fit research base, 2) a pilot inter-laboratory study of a systematic, score-based technique previously developed by our research group for evaluation of duct tape physical fit pairs and referred as the Edge Similarity Score (ESS), 3) the initial expansion of ESS methodology into textile materials, and 4) an expanded optimization and evaluation study of X-ray Fluorescence (XRF) Spectroscopy for electrical tape backing analysis, for implementation in an amorphous material of which physical fits may not be feasible due to lack of distinctive features. Objective 1 was completed through a large-scale literature review and manuscript compilation of 112 fracture fit reports and research studies. Literature was evaluated in three overall categories: case reports, fractography or qualitative-based studies, and quantitative-based studies. In addition, 12 standard operating protocols (SOP) provided by various state and federal-level forensic laboratories were reviewed to provide an assessment of current physical fit practice. A review manuscript was submitted to Forensic Science International and has been accepted for publication. This manuscript provides for the first time, a literature review of physical fits of trace materials and served as the basis for this project. The pilot inter-laboratory study (Objective 2) consisted of three study kits, each consisting of 7 duct tape comparison pairs with a ground truth of 4 matching pairs (3 of expected M+ qualifier range, 1 of the more difficult M- range) and 3 non-matching pairs (NM). The kits were distributed as a Round Robin study resulting in 16 overall participants and 112 physical fit comparisons. Prior to kit distribution, a consensus on each sample’s ESS was reached between 4 examiners with an agreement criterion of better than ± 10% ESS. Along with the physical comparison pairs, the study iii included a brief, post-study survey allowing the distributors to receive feedback on the participants’ opinions on method ease of use and practicality. No misclassifications were observed across all study kits. The majority (86.6%) of reported ESS scores were within ± 20 ESS compared to consensus values determined before the administration of the test. Accuracy ranged from 88% to 100%, depending on the criteria used for evaluation of the error rates. In addition, on average, 77% of ESS attributed no significant differences from the respective pre-distribution, consensus mean scores when subjected to ANOVA-Dunnett’s analysis using the level of difficulty as blocking variables. These differences were more often observed on sets of higher difficulty (M-, 5 out of 16 participants, or 31%) than on lower difficulty sets (M+ or M-, 3 out of 16 participants, or 19%). Three main observations were derived from the participant results: 1) overall good agreement between ESS reported by examiners was observed, 2) the ESS score represented a good indicator of the quality of the match and rendered low percent of error rates on conclusions 3) those examiners that did not participate in formal method training tended to have ESS falling outside of expected pre-distribution ranges. This interlaboratory study serves as an important precedent, as it represents the largest inter-laboratory study ever reported using a quantitative assessment of physical fits of duct tapes. In addition, the study provides valuable insights to move forward with the standardization of protocols of examination and interpretation. Objective 3 consisted of a preliminary study on the assessment of 274 total comparisons of stabbed (N=100) and hand-torn (N=174) textile pairs as completed by two examiners. The first 74 comparisons resulted in a high incidence of false exclusions (63%) on textiles prone to distortion, revealing the need to assess suitability prior to physical fit examination of fabrics. For the remaining dataset, five clothing items were subject to fracture of various textile composition and construction. The overall set consisted of 100 comparison pairs, 20 per textile item, 10 each per separation method of stabbed or hand-torn fractured edges, each examined by two analysts. Examiners determined ESS through the analysis of 10 bins of equal divisions of the total fracture edge length. A weighted ESS was also determined with the addition of three optional weighting factors per bin due to the continuation of a pattern, separation characteristics (i.e. damage or protrusions/gaps), or partial pattern fluorescence across the fractured edges. With the addition of a weighted ESS, a rarity ratio was determined as the ratio between the weighted ESS and non-weighted ESS. In addition, the frequency of occurrence of all noted distinctive characteristics leading to the addition of a weighting factor by the examiner was determined. Overall, 93% accuracy was observed for the hand-torn set while 95% accuracy was observed for the stabbed set. Higher misclassification in the hand-torn set was observed in textile items of either 100% polyester composition or jersey knit construction, as higher elasticity led to greater fracture edge distortion. In addition, higher misclassification was observed in the stabbed set for those textiles of no pattern as the stabbed edges led to straight, featureless bins often only associated due to pattern continuation. The results of this study are anticipated to provide valuable knowledge for the future development of protocols for evaluation of relevant features of textile fractures and assessments of the suitability for fracture fit comparisons. Finally, the XRF methodology optimization and evaluation study (Objective 4) expanded upon our group’s previous discrimination studies by broadening the total sample set of characterized iv tapes and evaluating the use of spectral overlay, spectral contrast angle, and Quadratic Discriminant Analysis (QDA) for the comparison of XRF spectra. The expanded sample set consisted of 114 samples, 94 from different sources, and 20 from the same roll. Twenty sections from the same roll were used to assess intra-roll variability, and for each sample, replicate measurements on different locations of the tape were analyzed (n=3) to assess the intra-sample variability. Inter-source variability was evaluated through 94 rolls of tapes of a variety of labeled brands, manufacturers, and product names. Parameter optimization included a comparison of atmospheric conditions, collection times, and instrumental filters. A study of the effects of adhesive and backing thickness on spectrum collection revealed key implications to the method that required modification to the sample support material Figures of merit assessed included accuracy and discrimination over time, precision, sensitivity, and selectivity. One of the most important contributions of this study is the proposal of alternative objective methods of spectral comparisons. The performance of different methods for comparing and contrasting spectra was evaluated. The optimization of this method was part of an assessment to incorporate XRF to a forensic laboratory protocol for rapid, highly informative elemental analysis of electrical tape backings and to expand examiners’ casework capabilities in the circumstance that a physical fit conclusion is limited due to the amorphous nature of electrical tape backings. Overall, this work strengthens the fracture fit research base by further developing quantitative methodologies for duct tape and textile materials and initiating widespread distribution of the technique through an inter-laboratory study to begin steps towards laboratory implementation. Additional projects established the current state of forensic physical fit to provide the foundation from which future quantitative work such as the studies presented here must grow and provided highly sensitive techniques of analysis for materials that present limited fracture fit capabilities