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The deformations [Formula: see text] are chosen so that [Formula: see text] and [Formula: see text]. We provide conditions on [Formula: see text] under which the upscaling \u201c[Formula: see text]\u201d results in a macroscale energy that depends through [Formula: see text] on (1) the jumps [Formula: see text] of g and the \u201cdisarrangement field\u201d[Formula: see text], (2) the \u201chorizon\u201d r, and (3) the weighting function [Formula: see text] for microlevel averaging of [Formula: see text]. We also study the upscaling \u201c[Formula: see text]\u201d followed by spatial localization \u201c[Formula: see text]\u201d and show that this succession of processes results in a purely local macroscale energy [Formula: see text] that depends through [Formula: see text] upon the jumps [Formula: see text] of g and the \u201cdisarrangement field\u201d[Formula: see text] alone. In special settings, such macroscale energies [Formula: see text] have been shown to support the phenomena of yielding and hysteresis, and our results provide a broader setting for studying such yielding and hysteresis. As an illustration, we apply our results in the context of the plasticity of single crystals.<\/jats:p>","DOI":"10.1177\/1081286520973245","type":"journal-article","created":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T12:09:33Z","timestamp":1607602173000},"page":"963-997","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":4,"title":["Upscaling and spatial localization of non-local energies with applications to crystal plasticity"],"prefix":"10.1177","volume":"26","author":[{"given":"Jos\u00e9","family":"Matias","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3528-6152","authenticated-orcid":false,"given":"Marco","family":"Morandotti","sequence":"additional","affiliation":[{"name":"Dipartimento di Scienze Matematiche \u201cG. L. Lagrange,\u201d Politecnico di Torino, Torino, Italy"}]},{"given":"David R.","family":"Owen","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7419-300X","authenticated-orcid":false,"given":"Elvira","family":"Zappale","sequence":"additional","affiliation":[{"name":"Dipartimento di Ingegneria Industriale, Universit\u00e0 degli Studi di Salerno, Fisciano, Italy"}]}],"member":"179","published-online":{"date-parts":[[2020,12,6]]},"reference":[{"key":"bibr1-1081286520973245","doi-asserted-by":"publisher","DOI":"10.1177\/108128659900400304"},{"key":"bibr2-1081286520973245","doi-asserted-by":"publisher","DOI":"10.1177\/1081286502007002225"},{"key":"bibr3-1081286520973245","doi-asserted-by":"publisher","DOI":"10.1007\/s002050050036"},{"key":"bibr4-1081286520973245","doi-asserted-by":"publisher","DOI":"10.1007\/BF00375133"},{"key":"bibr5-1081286520973245","unstructured":"Del Piero G, Owen DR. 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