{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T09:11:33Z","timestamp":1776417093689,"version":"3.51.2"},"reference-count":45,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T00:00:00Z","timestamp":1774483200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"publisher","award":["DP230100749"],"award-info":[{"award-number":["DP230100749"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Engineering Fracture Mechanics"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1016\/j.engfracmech.2026.112110","type":"journal-article","created":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T17:53:30Z","timestamp":1774461210000},"page":"112110","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Proposal of an adaptive stiffness-scaled analysis procedure for dynamic analysis of rate-dependent fracture in quasi-brittle materials"],"prefix":"10.1016","volume":"339","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6106-3414","authenticated-orcid":false,"given":"Saeed Mohammadzadeh","family":"Chianeh","sequence":"first","affiliation":[]},{"given":"Luming","family":"Shen","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2950-2237","authenticated-orcid":false,"given":"Daniel","family":"Dias-da-Costa","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"1\u20132","key":"10.1016\/j.engfracmech.2026.112110_b1","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/s10704-012-9768-1","article-title":"A non-iterative approach for the modelling of quasi-brittle materials","volume":"178","author":"Gra\u00e7a-e Costa","year":"2012","journal-title":"Int J Fract"},{"key":"10.1016\/j.engfracmech.2026.112110_b2","doi-asserted-by":"crossref","DOI":"10.1016\/j.engfracmech.2022.108955","article-title":"A novel, total-iterative approach to model quasi-brittle materials","volume":"277","author":"Alfaiate","year":"2023","journal-title":"Eng Fract Mech"},{"issue":"1","key":"10.1016\/j.engfracmech.2026.112110_b3","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s10704-013-9851-2","article-title":"Generalisation of non-iterative methods for the modelling of structures under non-proportional loading","volume":"182","author":"Gra\u00e7a-e Costa","year":"2013","journal-title":"Int J Fract"},{"key":"10.1016\/j.engfracmech.2026.112110_b4","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2024.117263","article-title":"Maximum energy dissipation-based incremental approach for structural analyses involving discrete fracture propagation in quasi-brittle materials","volume":"431","author":"Chianeh","year":"2024","journal-title":"Comput Methods Appl Mech Engrg"},{"key":"10.1016\/j.engfracmech.2026.112110_b5","series-title":"Sequentially linear analysis for simulating brittle failure","author":"Van de Graaf","year":"2017"},{"issue":"1\u20132","key":"10.1016\/j.engfracmech.2026.112110_b6","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/s10704-018-0270-2","article-title":"On the use of non-iterative methods in cohesive fracture","volume":"210","author":"Alfaiate","year":"2018","journal-title":"Int J Fract"},{"key":"10.1016\/j.engfracmech.2026.112110_b7","doi-asserted-by":"crossref","DOI":"10.1016\/j.engfracmech.2022.108531","article-title":"A damage-driven integration scheme in physically non-linear transient analysis for quasi-brittle materials","volume":"269","author":"Yu","year":"2022","journal-title":"Eng Fract Mech"},{"issue":"4","key":"10.1016\/j.engfracmech.2026.112110_b8","first-page":"495","article-title":"Extended implicit integration process by utilizing nonlinear dynamics in finite element","volume":"64","author":"Mohammadzadeh","year":"2017","journal-title":"Struct Eng Mech Int\u2019l J"},{"issue":"10","key":"10.1016\/j.engfracmech.2026.112110_b9","doi-asserted-by":"crossref","DOI":"10.1142\/S1758825118501065","article-title":"A novel sub-stepping method with numerical dissipation control for time integration of highly flexible structures","volume":"10","author":"Mohammadzadeh","year":"2018","journal-title":"Int J Appl Mech"},{"issue":"1","key":"10.1016\/j.engfracmech.2026.112110_b10","first-page":"91","article-title":"Performances of non-dissipative structure-dependent integration methods","volume":"65","author":"Chang","year":"2018","journal-title":"Struct Eng Mech"},{"issue":"1","key":"10.1016\/j.engfracmech.2026.112110_b11","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1002\/cnm.649","article-title":"Energy release control for numerical simulations of failure in quasi-brittle solids","volume":"20","author":"Guti\u00e9rrez","year":"2004","journal-title":"Commun Numer Methods Eng"},{"issue":"9","key":"10.1016\/j.engfracmech.2026.112110_b12","doi-asserted-by":"crossref","first-page":"1269","DOI":"10.1002\/nme.1620190902","article-title":"An arc-length method including line searches and accelerations","volume":"19","author":"Crisfield","year":"1983","journal-title":"Internat J Numer Methods Engrg"},{"issue":"4","key":"10.1016\/j.engfracmech.2026.112110_b13","doi-asserted-by":"crossref","DOI":"10.1115\/1.4006992","article-title":"A unified library of nonlinear solution schemes","volume":"64","author":"Leon","year":"2011","journal-title":"Appl Mech Rev"},{"issue":"1","key":"10.1016\/j.engfracmech.2026.112110_b14","article-title":"Improved staggered algorithm for phase-field brittle fracture with the local arc-LengthMethod","volume":"134","author":"Wu","year":"2023","journal-title":"CMES Comput Model Eng Sci"},{"issue":"9","key":"10.1016\/j.engfracmech.2026.112110_b15","doi-asserted-by":"crossref","first-page":"1290","DOI":"10.1002\/nme.2447","article-title":"A dissipation-based arc-length method for robust simulation of brittle and ductile failure","volume":"77","author":"Verhoosel","year":"2009","journal-title":"Internat J Numer Methods Engrg"},{"key":"10.1016\/j.engfracmech.2026.112110_b16","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.finel.2015.12.005","article-title":"A fracture-controlled path-following technique for phase-field modeling of brittle fracture","volume":"113","author":"Singh","year":"2016","journal-title":"Finite Elem Anal Des"},{"key":"10.1016\/j.engfracmech.2026.112110_b17","doi-asserted-by":"crossref","DOI":"10.1016\/j.finel.2023.104084","article-title":"A dynamic description of the smoothing gradient damage model for quasi-brittle failure","volume":"230","author":"Vuong","year":"2024","journal-title":"Finite Elem Anal Des"},{"issue":"4","key":"10.1016\/j.engfracmech.2026.112110_b18","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1016\/S0022-5096(99)00028-9","article-title":"Numerical experiments in revisited brittle fracture","volume":"48","author":"Bourdin","year":"2000","journal-title":"J Mech Phys Solids"},{"key":"10.1016\/j.engfracmech.2026.112110_b19","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2020.113648","article-title":"Fracture of thermo-elastic solids: Phase-field modeling and new results with an efficient monolithic solver","volume":"376","author":"Mandal","year":"2021","journal-title":"Comput Methods Appl Mech Engrg"},{"key":"10.1016\/j.engfracmech.2026.112110_b20","first-page":"831","article-title":"Sequentially linear continuum model for concrete fracture","volume":"2","author":"Rots","year":"2001","journal-title":"Fract Mech Concr Struct"},{"issue":"7\u20138","key":"10.1016\/j.engfracmech.2026.112110_b21","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1002\/nag.371","article-title":"Regularized sequentially linear saw-tooth softening model","volume":"28","author":"Rots","year":"2004","journal-title":"Int J Numer Anal Methods Geomech"},{"issue":"4","key":"10.1016\/j.engfracmech.2026.112110_b22","doi-asserted-by":"crossref","first-page":"213","DOI":"10.12989\/cac.2006.3.4.213","article-title":"Saw-tooth softening\/stiffening-a stable computational procedure for rc structures","volume":"3","author":"Rots","year":"2006","journal-title":"Comput Concr"},{"key":"10.1016\/j.engfracmech.2026.112110_b23","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.finel.2011.09.002","article-title":"Sequentially linear analysis of shear critical reinforced concrete beams without shear reinforcement","volume":"50","author":"Slobbe","year":"2012","journal-title":"Finite Elem Anal Des"},{"key":"10.1016\/j.engfracmech.2026.112110_b24","doi-asserted-by":"crossref","DOI":"10.1016\/j.engstruct.2021.112123","article-title":"A multi-surface interface model for sequentially linear methods to analyse masonry structures","volume":"238","author":"Pari","year":"2021","journal-title":"Eng Struct"},{"key":"10.1016\/j.engfracmech.2026.112110_b25","doi-asserted-by":"crossref","DOI":"10.1016\/j.ijimpeng.2021.104079","article-title":"Dynamic increase factor (DIF) for concrete in compression and tension in FE modelling with a local concrete model","volume":"163","author":"Li","year":"2022","journal-title":"Int J Impact Eng"},{"key":"10.1016\/j.engfracmech.2026.112110_b26","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2023.116540","article-title":"Dynamic fracture investigation of concrete by a rate-dependent explicit phase field model integrating viscoelasticity and micro-viscosity","volume":"418","author":"Hai","year":"2024","journal-title":"Comput Methods Appl Mech Engrg"},{"key":"10.1016\/j.engfracmech.2026.112110_b27","doi-asserted-by":"crossref","DOI":"10.1016\/j.tafmec.2023.103757","article-title":"Viscoelastic peridynamic fracture analysis for concrete beam with initial crack under impact","volume":"124","author":"Lu","year":"2023","journal-title":"Theor Appl Fract Mech"},{"key":"10.1016\/j.engfracmech.2026.112110_b28","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2024.116886","article-title":"Modeling the dynamic fracture of concrete\u2014A robust, efficient, and accurate mesoscale description","volume":"424","author":"Grunwald","year":"2024","journal-title":"Comput Methods Appl Mech Engrg"},{"key":"10.1016\/j.engfracmech.2026.112110_b29","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/j.engfracmech.2011.12.013","article-title":"A loading rate dependent cohesive model for concrete fracture","volume":"82","author":"Rosa","year":"2012","journal-title":"Eng Fract Mech"},{"key":"10.1016\/j.engfracmech.2026.112110_b30","doi-asserted-by":"crossref","DOI":"10.1016\/j.engfracmech.2025.110801","article-title":"A creep damage model for cracked concrete accounting for the rate of crack opening in a discrete strong discontinuity framework","author":"Chianeh","year":"2025","journal-title":"Eng Fract Mech"},{"key":"10.1016\/j.engfracmech.2026.112110_b31","article-title":"A viscous-cohesive model for concrete fracture in quasi-static loading rate","volume":"228","author":"Dos Santos","year":"2020","journal-title":"Eng Fract Mech"},{"key":"10.1016\/j.engfracmech.2026.112110_b32","series-title":"Energy principles and variational methods in applied mechanics","author":"Reddy","year":"2017"},{"key":"10.1016\/j.engfracmech.2026.112110_b33","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2020.113652","article-title":"A consistent finite element approach for dynamic crack propagation with explicit time integration","volume":"376","author":"Bybordiani","year":"2021","journal-title":"Comput Methods Appl Mech Engrg"},{"issue":"9","key":"10.1016\/j.engfracmech.2026.112110_b34","doi-asserted-by":"crossref","first-page":"1176","DOI":"10.1016\/j.engfracmech.2009.01.011","article-title":"A discrete strong discontinuity approach","volume":"76","author":"Dias-da Costa","year":"2009","journal-title":"Eng Fract Mech"},{"key":"10.1016\/j.engfracmech.2026.112110_b35","series-title":"Fib model code for concrete structures 2010","author":"Taerwe","year":"2013"},{"key":"10.1016\/j.engfracmech.2026.112110_b36","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1016\/j.ijsolstr.2020.04.018","article-title":"Visco-plasticity stress-based solid dynamics formulation and time-stepping algorithms for stiff case","volume":"196","author":"Nguyen","year":"2020","journal-title":"Int J Solids Struct"},{"key":"10.1016\/j.engfracmech.2026.112110_b37","doi-asserted-by":"crossref","DOI":"10.1016\/j.engstruct.2020.110526","article-title":"Nonlinear dynamic analysis of frames with isotropic and kinematic hardening\/softening","volume":"212","author":"Mohammadzadeh","year":"2020","journal-title":"Eng Struct"},{"key":"10.1016\/j.engfracmech.2026.112110_b38","series-title":"Dynamics of structures","author":"Chopra","year":"2012"},{"issue":"5","key":"10.1016\/j.engfracmech.2026.112110_b39","doi-asserted-by":"crossref","first-page":"978","DOI":"10.1111\/ffe.13174","article-title":"Loading-rate dependence of mode I crack growth in concrete","volume":"43","author":"Ma","year":"2020","journal-title":"Fatigue Fract Eng Mater Struct"},{"key":"10.1016\/j.engfracmech.2026.112110_b40","doi-asserted-by":"crossref","DOI":"10.1016\/j.tafmec.2023.103777","article-title":"Finite element modeling of dynamic fracture in concrete through the initial fracture toughness-based criterion and field variable transference technique","volume":"124","author":"Zhang","year":"2023","journal-title":"Theor Appl Fract Mech"},{"key":"10.1016\/j.engfracmech.2026.112110_b41","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.engfracmech.2015.09.002","article-title":"Dynamic fracture of concrete L-specimen: Experimental and numerical study","volume":"148","author":"O\u017ebolt","year":"2015","journal-title":"Eng Fract Mech"},{"issue":"3","key":"10.1016\/j.engfracmech.2026.112110_b42","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1002\/nme.2415","article-title":"Cracking node method for dynamic fracture with finite elements","volume":"77","author":"Song","year":"2009","journal-title":"Internat J Numer Methods Engrg"},{"key":"10.1016\/j.engfracmech.2026.112110_b43","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1016\/j.cma.2019.05.051","article-title":"Block coordinate descent energy minimization for dynamic cohesive fracture","volume":"354","author":"Hirmand","year":"2019","journal-title":"Comput Methods Appl Mech Engrg"},{"key":"10.1016\/j.engfracmech.2026.112110_b44","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1016\/j.cma.2019.01.026","article-title":"A phase-field formulation for dynamic cohesive fracture","volume":"348","author":"Geelen","year":"2019","journal-title":"Comput Methods Appl Mech Engrg"},{"issue":"1","key":"10.1016\/j.engfracmech.2026.112110_b45","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1007\/s10704-022-00635-1","article-title":"Simulation of dynamic brittle and quasi-brittle fracture: a revisited local damage approach","volume":"236","author":"Bui","year":"2022","journal-title":"Int J Fract"}],"container-title":["Engineering Fracture Mechanics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0013794426002729?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0013794426002729?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T08:16:51Z","timestamp":1776413811000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0013794426002729"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6]]},"references-count":45,"alternative-id":["S0013794426002729"],"URL":"https:\/\/doi.org\/10.1016\/j.engfracmech.2026.112110","relation":{},"ISSN":["0013-7944"],"issn-type":[{"value":"0013-7944","type":"print"}],"subject":[],"published":{"date-parts":[[2026,6]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Proposal of an adaptive stiffness-scaled analysis procedure for dynamic analysis of rate-dependent fracture in quasi-brittle materials","name":"articletitle","label":"Article Title"},{"value":"Engineering Fracture Mechanics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.engfracmech.2026.112110","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Authors. Published by Elsevier Ltd.","name":"copyright","label":"Copyright"}],"article-number":"112110"}}