{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,4]],"date-time":"2026-11-04T12:49:14Z","timestamp":1793796554515,"version":"4.6.1"},"reference-count":72,"publisher":"The Company of Biologists","issue":"13","license":[{"start":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T00:00:00Z","timestamp":1751846400000},"content-version":"vor","delay-in-days":6,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100004359","name":"Vetenskapsr\u00e5det","doi-asserted-by":"crossref","award":["2024-05045"],"award-info":[{"award-number":["2024-05045"]}],"id":[{"id":"10.13039\/501100004359","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,7,1]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n               <jats:p>In insect locomotion, the transmission of energy from muscles to motion is a process within which there are many sources of dissipation. One significant but understudied source is the structural damping within the insect exoskeleton itself: the thorax and limbs. Experimental evidence suggests that exoskeletal damping shows frequency (or rate) independence, but investigation into its nature and implications has been hampered by a lack methods for simulating the time-domain behaviour of this damping. Here, synergising and extending results across applied mathematics and seismic analysis, I provide these methods. Existing models of exoskeletal rate-independent damping are equivalent to an important singular integral in time: the Hilbert transform. However, these models are strongly noncausal, violating the directionality of time. I derive the unique causal analogue of these existing exoskeletal damping models, as well as an accessible approximation to them, as Hadamard finite-part integrals in time, and provide methods for simulating them. These methods are demonstrated on several current problems in insect biomechanics. Finally, I demonstrate, for the first time, that these rate-independent damping models show counterintuitive energetic properties \u2013 in certain cases, extending to violation of conservation of energy. This work resolves a key methodological impasse in the understanding of insect exoskeletal dynamics and offers new insights into the micro-structural origins of rate-independent damping as well as the directions required to resolve violations of causality and the conservation of energy in existing models.<\/jats:p>","DOI":"10.1242\/jeb.249940","type":"journal-article","created":{"date-parts":[[2025,6,9]],"date-time":"2025-06-09T12:40:15Z","timestamp":1749472815000},"source":"Crossref","is-referenced-by-count":6,"title":["Causal models of rate-independent damping in insect exoskeleta"],"prefix":"10.1242","volume":"228","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6102-1735","authenticated-orcid":false,"given":"Arion","family":"Pons","sequence":"first","affiliation":[{"name":"Chalmers University of Technology Division of Fluid Dynamics, Department of Mechanics and Maritime Sciences , , 412 96 Gothenburg ,","place":["Sweden"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"237","published-online":{"date-parts":[[2025,7,7]]},"reference":[{"key":"2025070706590611000_JEB249940C1","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1016\/j.asd.2016.08.001","article-title":"Effect of sample treatment on biomechanical properties of insect cuticle","volume":"46","author":"Aberle","year":"2017","journal-title":"Arthropod. 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