{"id":680,"date":"2014-02-11T16:52:24","date_gmt":"2014-02-11T21:52:24","guid":{"rendered":"https:\/\/my.vanderbilt.edu\/mcml\/?page_id=680"},"modified":"2014-02-11T16:52:24","modified_gmt":"2014-02-11T21:52:24","slug":"failure-prediction-of-composites-under-uncertainty","status":"publish","type":"page","link":"https:\/\/my.vanderbilt.edu\/mcml\/cv\/failure-prediction-of-composites-under-uncertainty\/","title":{"rendered":"Failure Prediction of Composites under Uncertainty"},"content":{"rendered":"<h4><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 18px\">Research Sponsor: <\/span><\/h4>\n<li><font color=\"black\" size=\"3\" face=\"Baskerville, Georgia, Arial, Garamond\"> National Defense Science and Engineering Graduate Fellowship <\/font>\n<\/li>\n<li><font color=\"black\" size=\"3\" face=\"Baskerville, Georgia, Arial, Garamond\"> Air Force Research Laboratory. Program Director: Dr. Stephen Clay <\/font>\n<\/li>\n<h4><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 18px\">Investigators: <\/span><\/h4>\n<p><font color=\"black\" size=\"3\" face=\"Baskerville, Georgia, Arial, Garamond\"> Michael J. Bogdanor and Caglar Oskay <\/font><br \/>\n<!--...................................................................................--><\/p>\n<h2>Motivation<\/h2>\n<li> <span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\"> Composites provide cutting edge performance by offering high strength to weight ratios, superior energy absorption behavior and significant customizability. <\/span>\n<\/li>\n<li> <span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Composites also present a number of research challenges and opportunities in:<\/span>\n<ul>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">modeling their inherent multiscale nature,<\/span><\/li>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">capturing the complex interacting failure modes,<\/span><\/li>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">extending models to rate-dependent loadings, and<\/span><\/li>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">incorporating the high variability from manufacturing and the nature of the material in failure predictions.<\/span><\/li>\n<\/ul>\n<p><!--...................................................................................--><\/p>\n<h2>Research Goal and Objectives<\/h2>\n<h4><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 18px\">Goals:<\/span><\/h4>\n<ul>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Gain a fundamental understanding of the sources of uncertainty in composite structures at all meaningful size scales.<\/span><\/li>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Gain a fundamental understanding of the mechanical phenomena at the micro- and macroscale  which govern failure response for fiber reinforced polymer composites.<\/span><\/li>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Implement a failure prediction methodology which incorporates stochastic effects. beginning at the microscopic constituent scale and propagating up to the macroscopic structural scale.<\/span><\/li>\n<\/ul>\n<h4><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 18px\">Objectives &#8211; Mechanical modeling of composite structures:<\/span><\/h4>\n<ul>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Implement a rate-dependent damage evolution law for modeling of constituent material response.<\/span><\/li>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Employ reduced order homogenization to efficiently capture the multiscale behavior of the composites.<\/span><\/li>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Utilize parallel computing structures to further speed up multiscale analyses.<\/span><\/li>\n<\/ul>\n<h4><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 18px\">Objectives &#8211; Uncertainty Quantification<\/span><\/h4>\n<ul>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Calibrate constituent material parameters from experimental results from laminated composites using Bayesian methods.<\/span><\/li>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Make stochastic predictions of laminated composite failure from the calibrated constituent parameters.<\/span><\/li>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Characterize the length scale effects in the spatial variability of underlying material parameters.<\/span><\/li>\n<\/ul>\n<p><!--...................................................................................--><\/p>\n<h2>Uncertainty in Composites<\/h2>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-119\" src=\"https:\/\/my.vanderbilt.edu\/mcml\/wp-content\/uploads\/sites\/246\/2014\/02\/uqscales1.jpg\" alt=\"\" width=\"540\" \/><\/p>\n<h4><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 18px\">Macroscale &#8211; laminate and component<\/span><\/h4>\n<ul>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Natural frequencies, failure strength, buckling strength, fatigue life, interlaminar strength, and residual strength.<\/span><\/li>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Tools available (PICAN,IPACS) for stochastic analysis based on ply level randomness.<\/span><\/li>\n<\/ul>\n<h4><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 18px\">Mesoscale &#8211; ply and representative volume element<\/span><\/h4>\n<ul>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Uncertainty from fiber orientation, ply thickness, fiber length and volume ratio, fiber distribution, void volume ratio, inclusions, and debonding.<\/span><\/li>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Analytical methods (such as Tsai-Wu, Tsai-Hill, Mori-Tanaka) and numerical methods (computational homogenization) are used to characterize ply and RVE response.<\/span><\/li>\n<\/ul>\n<h4><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 18px\">Microscale &#8211; constituent materials<\/span><\/h4>\n<ul>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Uncertainty at microscale arises from randomness of the materials that make up the composite (fiber and matrix).<\/span><\/li>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">We characterize microscale uncertainty using nonparametric distributions of the parameters that govern the constituent response calibrated from experimental results.<\/span><\/li>\n<\/ul>\n<p><!--...................................................................................--><\/p>\n<h2>Experiments<\/h2>\n<p><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">A suite of experiments were conducted at the Air Force Research Laboratory.  These experiments were designed to calibrate the random constituent material parameters for the fiber and matrix in IM7\/977-3 fiber reinforced polymers and verify the calibrated simulation model against a more complex structure.<\/span><\/p>\n<figure id=\"attachment_816\" aria-describedby=\"caption-attachment-816\" style=\"width: 180px\" class=\"wp-caption alignleft\"><a href=\"https:\/\/cdn.vanderbilt.edu\/t2-my\/my-prd\/wp-content\/uploads\/sites\/246\/2014\/02\/zerotest.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-816\" src=\"https:\/\/cdn.vanderbilt.edu\/t2-my\/my-prd\/wp-content\/uploads\/sites\/246\/2014\/02\/zerotest-241x300.jpg\" alt=\"\" width=\"180\" height=\"224\" srcset=\"https:\/\/cdn.vanderbilt.edu\/t2-my\/my-prd\/wp-content\/uploads\/sites\/246\/2014\/02\/zerotest-241x300.jpg 241w, https:\/\/cdn.vanderbilt.edu\/t2-my\/my-prd\/wp-content\/uploads\/sites\/246\/2014\/02\/zerotest-523x650.jpg 523w, https:\/\/cdn.vanderbilt.edu\/t2-my\/my-prd\/wp-content\/uploads\/sites\/246\/2014\/02\/zerotest.jpg 945w\" sizes=\"auto, (max-width: 180px) 100vw, 180px\" \/><\/a><figcaption id=\"caption-attachment-816\" class=\"wp-caption-text\">Zero degree specimen uniaxial tension test.<\/figcaption><\/figure>\n<figure id=\"attachment_815\" aria-describedby=\"caption-attachment-815\" style=\"width: 180px\" class=\"wp-caption alignleft\"><a href=\"https:\/\/cdn.vanderbilt.edu\/t2-my\/my-prd\/wp-content\/uploads\/sites\/246\/2014\/02\/tpbtest.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-815\" src=\"https:\/\/cdn.vanderbilt.edu\/t2-my\/my-prd\/wp-content\/uploads\/sites\/246\/2014\/02\/tpbtest-250x300.jpg\" alt=\"\" width=\"180\" height=\"224\" \/><\/a><figcaption id=\"caption-attachment-815\" class=\"wp-caption-text\">Ninety degree specimen three point bending test.<\/figcaption><\/figure>\n<figure id=\"attachment_814\" aria-describedby=\"caption-attachment-814\" style=\"width: 180px\" class=\"wp-caption alignleft\"><a href=\"https:\/\/cdn.vanderbilt.edu\/t2-my\/my-prd\/wp-content\/uploads\/sites\/246\/2014\/02\/quasitest.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-814 \" style=\"margin-top: 1px;margin-bottom: 1px\" src=\"https:\/\/cdn.vanderbilt.edu\/t2-my\/my-prd\/wp-content\/uploads\/sites\/246\/2014\/02\/quasitest-249x300.jpg\" alt=\"\" width=\"180\" height=\"224\" \/><\/a><figcaption id=\"caption-attachment-814\" class=\"wp-caption-text\">Quasi-isotropic open hole uniaxial tension test.<\/figcaption><\/figure>\n<h2>Multiscale mechanical model<\/h2>\n<h4><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 18px\">Eigendeformation based reduced order homogenization<\/span><\/h4>\n<ul>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Computational homogenization analyzes the physical response of the microstructure (RVE) and incorporates this information at the macroscale.<\/span><\/li>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">RVE is partitioned into parts in which stress and damage evolution are uniform throughout the part.<\/span><\/li>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Influence and homogenization information is precomputed to speed up microscale analysis.<\/span><\/li>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Continuum Damage Mechanics is employed to track damage and damage induced hardening as an internal state variable in the constituent materials of the composite.<\/span><\/li>\n<\/ul>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-119\" src=\"https:\/\/cdn.vanderbilt.edu\/t2-my\/my-prd\/wp-content\/uploads\/sites\/246\/2014\/02\/parts.jpg\" alt=\"\" width=\"540\" \/><\/p>\n<p><!--...................................................................................--><\/p>\n<h2>Bayesian Stochastic Parameter Calibration<\/h2>\n<p><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Bayesian analysis is a means of using conditional probabilities to investigate the relationships between events.  Bayesian parameter updating estimates posterior distributions of model parameters based on observed results.<\/span><\/p>\n<h4><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 18px\">Markov chain Monte Carlo simulation with Metropolis Hastings sampling (MCMC)<\/span><\/h4>\n<ul>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Accelerated sampling technique for calibration.<\/span><\/li>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Likelihood of parmameters calculated based on agreement with experimental results.<\/span><\/li>\n<\/ul>\n<h4><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 18px\">Gaussian Process (GP) surrogate models<\/span><\/h4>\n<ul>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Replace expensive models with accurate predictions which require significantly less computational effort.<\/span><\/li>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Captures nonlinear response and also is able to identify where the model makes weak or strong predictions.<\/span><\/li>\n<\/ul>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-119\" src=\"https:\/\/cdn.vanderbilt.edu\/t2-my\/my-prd\/wp-content\/uploads\/sites\/246\/2014\/02\/calibration.jpg\" alt=\"\" width=\"540\" \/><\/p>\n<p><!--...................................................................................--><\/p>\n<h2>Ongoing Work<\/h2>\n<ul>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Investigate spatial variability in material parameters and the length scale effects.<\/span><\/li>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Implement mechanical models which incorporate macroscopic discontinuities, such as the extended finite element model.<\/span><\/li>\n<li><span style=\"font-family: Baskerville,Georgia,Arial,Garamond;font-size: 16px\">Calibrate and include in the uncertainty model additional sources of uncertainty at higher scales (i.e. manufacturing error in the RVE and laminate).<\/span><\/li>\n<\/ul>\n<\/li>\n","protected":false},"excerpt":{"rendered":"<p>Research Sponsor: National Defense Science and Engineering Graduate Fellowship Air Force Research Laboratory. Program Director: Dr. Stephen Clay Investigators: Michael J. Bogdanor and Caglar Oskay Motivation Composites provide cutting edge performance by offering high strength to weight ratios, superior energy absorption behavior and significant customizability. Composites also present a number of research challenges and opportunities&#8230;<\/p>\n","protected":false},"author":529,"featured_media":788,"parent":5,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[],"class_list":["post-680","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/my.vanderbilt.edu\/mcml\/wp-json\/wp\/v2\/pages\/680","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/my.vanderbilt.edu\/mcml\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/my.vanderbilt.edu\/mcml\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/mcml\/wp-json\/wp\/v2\/users\/529"}],"replies":[{"embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/mcml\/wp-json\/wp\/v2\/comments?post=680"}],"version-history":[{"count":83,"href":"https:\/\/my.vanderbilt.edu\/mcml\/wp-json\/wp\/v2\/pages\/680\/revisions"}],"predecessor-version":[{"id":937,"href":"https:\/\/my.vanderbilt.edu\/mcml\/wp-json\/wp\/v2\/pages\/680\/revisions\/937"}],"up":[{"embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/mcml\/wp-json\/wp\/v2\/pages\/5"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/mcml\/wp-json\/wp\/v2\/media\/788"}],"wp:attachment":[{"href":"https:\/\/my.vanderbilt.edu\/mcml\/wp-json\/wp\/v2\/media?parent=680"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/mcml\/wp-json\/wp\/v2\/tags?post=680"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}