{"id":3848,"date":"2015-11-12T10:17:12","date_gmt":"2015-11-12T15:17:12","guid":{"rendered":"http:\/\/mseas.mit.edu\/?p=3848"},"modified":"2015-11-12T10:17:12","modified_gmt":"2015-11-12T15:17:12","slug":"design-and-topology-optimization-for-wear-of-bi-composite-material-surfaces","status":"publish","type":"post","link":"https:\/\/mseas.mit.edu\/?p=3848","title":{"rendered":"Design and topology optimization for wear of bi-composite material surfaces"},"content":{"rendered":"Wear is the process of material removal under abrasion. Multi-material systems are characterized by non-uniform wear-rates that are leading to non-planar profiles under polishing.  Some recent iterative models have predicted with success the  well established experimental fact, that  under an initially uniform pressure load, multi-component wearing surfaces reach asymptotically a steady-state profile that continues to recess at a constant rate.  In a first part, a continuous model is derived from the original iterative scheme, and extrapolated to a mathematical, abstract, but versatile framework. It is shown that the steady-state can be computed directly by solving a time-independent elliptic partial differential equation, providing a substantial computational gain against the first iterative scheme. In a second part, this formulation is used to apply modern shape optimization methods to optimize wear performance of bi-material systems. Several objectives for systems undergoing wear are identified and formalized with shape derivatives. As an example, the unit-cell of 2D multi-material composites is optimized using a level-set based method. A minimum feature size must be taken into account to avoid the convergence of minimizing design sequences toward composite materials. To address this issue, a variant of a the level-set topology optimization method is developed . Through the use of a single updating equation, this scheme conveniently enforces volume equality constraints, controls the complexity of design features with a perimeter penalization, and nucleates material inclusions with the use of the topological gradient.\r\n\r\nKeywords: topology and shape optimization, wear, multi-composite surface, level-set methods.","protected":false},"excerpt":{"rendered":"<p>Wear is the process of material removal under abrasion. Multi-material systems are characterized by non-uniform wear-rates that are leading to non-planar profiles under polishing. Some recent iterative models have predicted with success the well established experimental fact, that under an initially uniform pressure load, multi-component wearing surfaces reach asymptotically a steady-state profile that continues to [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[168,7],"tags":[],"class_list":["post-3848","post","type-post","status-publish","format-standard","hentry","category-fall-2015","category-seminars"],"_links":{"self":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/3848","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3848"}],"version-history":[{"count":1,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/3848\/revisions"}],"predecessor-version":[{"id":3849,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/3848\/revisions\/3849"}],"wp:attachment":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3848"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3848"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3848"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}