{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T01:59:21Z","timestamp":1776131961000,"version":"3.50.1"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2013,11,24]],"date-time":"2013-11-24T00:00:00Z","timestamp":1385251200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Engineering with Computers"],"published-print":{"date-parts":[[2015,4]]},"DOI":"10.1007\/s00366-013-0342-x","type":"journal-article","created":{"date-parts":[[2013,11,23]],"date-time":"2013-11-23T04:24:50Z","timestamp":1385180690000},"page":"193-213","source":"Crossref","is-referenced-by-count":37,"title":["Verification tests in solid mechanics"],"prefix":"10.1007","volume":"31","author":[{"given":"K.","family":"Kamojjala","sequence":"first","affiliation":[]},{"given":"R.","family":"Brannon","sequence":"additional","affiliation":[]},{"given":"A.","family":"Sadeghirad","sequence":"additional","affiliation":[]},{"given":"J.","family":"Guilkey","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,11,24]]},"reference":[{"key":"342_CR1","first-page":"84","volume":"5","author":"D Appelo","year":"2009","unstructured":"Appelo D, Anders PN (2009) A stable finite difference method for the elastic wave equation on complex geometries with free surfaces. Commun Comput Phys 5:84\u2013107","journal-title":"Commun Comput Phys"},{"issue":"10","key":"342_CR2","doi-asserted-by":"crossref","first-page":"4057","DOI":"10.1016\/j.cma.2004.03.002","volume":"193","author":"I Babuska","year":"2004","unstructured":"Babuska I, Tinsley OJ (2004) Verification and validation in computational engineering and science: basic concepts. Comput Methods Appl Mech Eng 193:(10)4057\u20134066","journal-title":"Comput Methods Appl Mech Eng"},{"key":"342_CR3","unstructured":"Banerjee B (2006) Method of manufactured solutions. http:\/\/imechanica.org\/node\/1357"},{"key":"342_CR4","first-page":"477","volume":"5","author":"SG Bardenhagen","year":"2004","unstructured":"Bardenhagen SG, Kober EM (2004) The generalized interpolation material point method. CMES Comput Model Eng Sci 5:477\u2013495","journal-title":"CMES Comput Model Eng Sci"},{"key":"342_CR5","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1007\/s004660050263","volume":"20","author":"RC Batra","year":"1997","unstructured":"Batra RC, Liang XQ (1997) Finite dynamic deformations of smart structures. Comput Mech 20:427\u2013438","journal-title":"Comput Mech"},{"key":"342_CR6","doi-asserted-by":"crossref","first-page":"1992","DOI":"10.1016\/j.cma.2010.02.017","volume":"199","author":"M Benes","year":"2010","unstructured":"Benes M, Matous K (2010) Asynchronous multi-domain variational integrators for nonlinear hyperelastic solids. Comput Methods Appl Mech Eng 199:1992\u20132013","journal-title":"Comput Methods Appl Mech Eng"},{"key":"342_CR7","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1007\/s10704-009-9398-4","volume":"163","author":"RM Brannon","year":"2010","unstructured":"Brannon RM, Leelavanichkul S (2010) A multi-stage return algorithm for solving the classical damage component of constitutive models for rocks, ceramics, and other rock-like media. Int J Fract 163:133\u2013149","journal-title":"Int J Fract"},{"key":"342_CR8","unstructured":"Brannon RM, Kamojjala K, Sadeghirad A (2011) Establishing credibility of particle methods through verification testing. In: II international conference on particle-based methods\u2014fundamentals and applications"},{"key":"342_CR9","doi-asserted-by":"crossref","unstructured":"Brannon RM, Fossum AF, Strack OE (2009) Kayenta: theory and user\u2019s guide. Technical Report SAND2009-2282, USDOE","DOI":"10.2172\/984159"},{"key":"342_CR10","first-page":"876","volume":"95","author":"TA Brunner","year":"2006","unstructured":"Brunner TA (2006) Development of a grey nonlinear thermal radiation diffusion verification problem. Trans Am Nuclear Soc 95:876\u2013878","journal-title":"Trans Am Nuclear Soc"},{"key":"342_CR11","doi-asserted-by":"crossref","first-page":"5109","DOI":"10.1016\/j.cma.2005.01.001","volume":"194","author":"CD Foster","year":"2005","unstructured":"Foster CD, Regueiro RA, Fossum AF, Borja RI (2005) Implicit numerical integration of a three-invariant, isotropic\/kinematic hardening cap plasticity model for geomaterials. Comput Methods Appl Mech Eng 194:5109\u20135138","journal-title":"Comput Methods Appl Mech Eng"},{"key":"342_CR12","unstructured":"Guilkey J, Harman T, Luitjens J, Schmidt J, Thornock J, de St Germain JD, Shankar S, Peterson J, Brownlee C (2009) Uintah User guide. SCI Institute Technical Report"},{"key":"342_CR13","unstructured":"Johnson GR, Cook WH (1983) A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: Proceedings of the 7th international symposium on ballistics, The Netherlands, pp 541\u2013547"},{"key":"342_CR14","unstructured":"Kamojjala K, Brannon RM (2011) Verification of frame indifference for complicated numerical constitutive models. In: ASME early career technical conference"},{"key":"342_CR15","volume-title":"Verification of computer codes in computational science and engineering","author":"P Knupp","year":"2003","unstructured":"Knupp P, Salari K (2003) Verification of computer codes in computational science and engineering. Chapman and Hall\/CRC, London"},{"key":"342_CR16","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1016\/j.ijplas.2008.08.003","volume":"25","author":"A Kossa","year":"2009","unstructured":"Kossa A, Szab\u00f3 L (2009) Exact integration of the von Mises elastoplasticity model with combined linear isotropic-kinematic hardening. Int J Plasticity 25:1083\u20131106","journal-title":"Int J Plasticity"},{"key":"342_CR17","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1007\/s10915-012-9624-5","volume":"55","author":"JE Kozdon","year":"2013","unstructured":"Kozdon JE, Dunham EM, Nordstrom J (2013) Simulation of dynamic earthquake ruptures in complex geometries using high-order finite difference method. J Sci Comput 55:92\u2013124","journal-title":"J Sci Comput"},{"key":"342_CR18","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1115\/1.3454568","volume":"99","author":"RD Krieg","year":"1977","unstructured":"Krieg RD, Krieg DB (1977) Accuracies of numerical solution methods for the elastic-perfectly plastic model. J Pressure Vessel Technol 99:510\u2013515","journal-title":"J Pressure Vessel Technol"},{"key":"342_CR19","first-page":"11","volume":"151","author":"C-S Kuo","year":"2010","unstructured":"Kuo C-S, Hu H-T, Lin R-M, Huang K-Y, Lin P-C, Zhong Z-C, Hseih M-L (2010) Biomechanical analysis of the lumbar spine on facet joint force and intradiscal pressure\u2014a finite element study. BMC Musculoskelet Disord 151:11","journal-title":"BMC Musculoskelet Disord"},{"key":"342_CR20","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.cma.2005.06.027","volume":"195","author":"E Love","year":"2006","unstructured":"Love E, Sulsky DL (2006) An unconditionally stable, energy-momentum consistent implementation of the material-point method. Comput Methods Appl Mech Eng 195:33\u201336","journal-title":"Comput Methods Appl Mech Eng"},{"key":"342_CR21","volume-title":"Introduction to the mechanics of a continuous medium","author":"LE Malverin","year":"1969","unstructured":"Malverin LE (1969) Introduction to the mechanics of a continuous medium. Prentice-Hall Inc., New Jersey"},{"key":"342_CR22","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/0010-4655(88)90026-4","volume":"48","author":"JJ Monaghan","year":"1988","unstructured":"Monaghan JJ (1988) Introduction to sph. Comput Phys Commun 48:89\u201396","journal-title":"Comput Phys Commun"},{"key":"342_CR23","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511760396","volume-title":"Verification and validation in scientific computing","author":"WL Oberkampf","year":"2010","unstructured":"Oberkampf WL, Roy CJ (2010) Verification and validation in scientific computing. Cambridge University Press, Cambridge"},{"key":"342_CR24","doi-asserted-by":"crossref","unstructured":"Oberkampf WL, Trucano TG, Hirsh C (2002) Verification and validation of modeling and simulation in computer ccience and engineering applications. In: Foundations of verification and validation in 21st century workshop","DOI":"10.2172\/793406"},{"key":"342_CR25","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/S0376-0421(02)00005-2","volume":"38","author":"WL Oberkampf","year":"2002","unstructured":"Oberkampf WL, Trucano TG (2002) Verification and validation in computational fluid dynamics. Progress Aerospace Sci 38:209\u2013272","journal-title":"Progress Aerospace Sci"},{"key":"342_CR26","unstructured":"Pautz SD (2001) Verification of transport codes by the method of manufactured solutions: the attila experience. In: Proceedings of ANS international meeting on mathematical methods for nuclear applications, Salt Lake City"},{"issue":"23","key":"342_CR27","doi-asserted-by":"crossref","first-page":"3937","DOI":"10.1002\/nme.1620362302","volume":"36","author":"MM Rashid","year":"1993","unstructured":"Rashid MM (1993) Incremental kinematics for finite element applications. Int J Numer Methods Eng 36:(23)3937\u20133956","journal-title":"Int J Numer Methods Eng"},{"key":"342_CR28","unstructured":"Rieben R, White DA (2005) Verification of high-order mixed fem solution of transient magnetic diffusion problems. Technical report, Lawrence Livermore National Laboratory"},{"key":"342_CR29","unstructured":"Roache Patrick J (1999) Fundamentals of Verification and Validation, volume 41. SIAM, Editor: Mark Anisworth"},{"key":"342_CR30","volume-title":"Fundamentals of verification and validation","author":"PJ Roache","year":"2009","unstructured":"Roache Patrick J (2009) Fundamentals of verification and validation. Hermosa Publishers, Socorro"},{"key":"342_CR31","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1002\/fld.660","volume":"44","author":"CJ Roy","year":"2004","unstructured":"Roy CJ, Nelson CC, Smith TM, Ober CC (2004) Verification of euler\/navier stokes codes using the method of manufactured solutions. Int J Numer Methods Fluids 44:599\u2013620","journal-title":"Int J Numer Methods Fluids"},{"key":"342_CR32","doi-asserted-by":"crossref","first-page":"2131","DOI":"10.1016\/j.cma.2011.03.016","volume":"200","author":"CJ Roy","year":"2011","unstructured":"Roy CJ, Oberkampf WL (2011) A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing. Comput Methods Appl Mech Eng 200:2131\u20132144","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"22","key":"342_CR33","doi-asserted-by":"crossref","first-page":"1435","DOI":"10.1002\/nme.3110","volume":"86","author":"A Sadeghirad","year":"2011","unstructured":"Sadeghirad A, Brannon RM, Burghardt J (2011) A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations. Int J Numer Methods Eng 86(22):1435\u20131456","journal-title":"Int J Numer Methods Eng"},{"key":"342_CR34","doi-asserted-by":"crossref","first-page":"928","DOI":"10.1002\/nme.4526","volume":"95","author":"A Sadeghirad","year":"2013","unstructured":"Sadeghirad A, Brannon RM, Guilkey JE (2013) Second-order convected particle domain interpolation (CPDI2) with enrichment for weak discontinuities at material interfaces. Int J Numer Methods Eng 95:928\u2013952","journal-title":"Int J Numer Methods Eng"},{"key":"342_CR35","unstructured":"Schwer LE (2006) Guide for verification and validation in computational solid mechanics. In: The American Society of Mechanical Engineers"},{"key":"342_CR36","volume-title":"Computational inelasticity. Interdisciplinary applied mathematics: mechanics and materials","author":"JC Simo","year":"1998","unstructured":"Simo JC, Hughes TJR (1998) Computational inelasticity. Interdisciplinary applied mathematics: mechanics and materials. Springer, New York"},{"key":"342_CR37","first-page":"107","volume":"2","author":"M Steffen","year":"2008","unstructured":"Steffen M, Wallstedt PC, Guilkey JE, Kirby RM, Berzins M (2008) Examination and analysis of implementation choices within the material point method (mpm). Comput Model Eng Sci 2:107\u2013127","journal-title":"Comput Model Eng Sci"},{"key":"342_CR38","doi-asserted-by":"crossref","unstructured":"Tremblay D, Etienne S, Pelletier D (2006) Code verification and the method of manufactured solutions for fluid-structure interaction problems. In: 36th AIAA fluid dynamics conference, vol 2, pp 882\u2013892","DOI":"10.2514\/6.2006-3218"},{"key":"342_CR39","doi-asserted-by":"crossref","first-page":"9628","DOI":"10.1016\/j.jcp.2008.07.019","volume":"227","author":"PC Wallstedt","year":"2008","unstructured":"Wallstedt PC, Guilkey JE (2008) An evaluation of explicit time integration schemes for use with the generalized interpolation material point method. J Comput Phys 227:9628\u20139642","journal-title":"J Comput Phys"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-013-0342-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00366-013-0342-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-013-0342-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,4]],"date-time":"2019-08-04T00:37:49Z","timestamp":1564879069000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00366-013-0342-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,24]]},"references-count":39,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,4]]}},"alternative-id":["342"],"URL":"https:\/\/doi.org\/10.1007\/s00366-013-0342-x","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,11,24]]}}}