Bio

Professor Christensen's research is concerned with the mechanics of materials. The behavior of polymers and polymeric fiber composites are areas of specialization. Of particular interest is the field of micro-mechanics that focuses on materials' functionality at intermediate-length scales between atomic and the usual macro scale. Applicable techniques involve the methods of homogenization for all types of composite materials. The intended outcomes of his research are useful means of characterizing the yielding, damage accumulation, and failure behavior of modern materials. A related website has been developed to provide critical evaluations for the mathematical failure criteria used with the various classes of engineering materials. Most of these materials types are employed in aerospace structures and products.

Academic Appointments

Honors & Awards

  • Nadai Medal, American Society of Mechanical Engineers (2006)

Boards, Advisory Committees, Professional Organizations

  • member, National Academy of Engineering (2013 - Present)

Professional Education

  • DEng, Yale (1961)

Contact

  • Academic
    christensen@stanford.edu
    University - Emeritus faculty Department: Aeronautics and Astronautics Position: Retiree
    • DURAND 387A
    • 4035
    • Stanford,  California  94305-4035 
    (650) 723-0062 (fax)

Additional Info

  • Mail Code: 4035

Links

2022-23 Courses

All Publications

  • An evaluation of the failure modes transition and the Christensen ductile/brittle failure theory using molecular dynamics PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Christensen, R., Li, Z., Gao, H. 2018; 474 (2219)

    View details for DOI 10.1098/rspa.2018.0361

    View details for Web of Science ID 000451779700004

  • The ductile/brittle transition provides the critical test for materials failure theory PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Christensen, R. M. 2018; 474 (2210)

    View details for DOI 10.1098/rspa.2017.0817

    View details for Web of Science ID 000426468200021

  • Why progress on the failure of fiber composite materials has been so retarded JOURNAL OF REINFORCED PLASTICS AND COMPOSITES Christensen, R. M. 2017; 36 (22): 1615–17

    View details for DOI 10.1177/0731684417733550

    View details for Web of Science ID 000414035500001

  • Materials Failure Theory and Applications, Change Is Coming JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY-TRANSACTIONS OF THE ASME Christensen, R. M. 2017; 139 (4)

    View details for DOI 10.1115/1.4036587

    View details for Web of Science ID 000425743400005

  • Failure Theory/Failure Criteria for Fiber Composite Laminates JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME Christensen, R. M., Lonkar, K. 2017; 84 (2)

    View details for DOI 10.1115/1.4035119

    View details for Web of Science ID 000396028400009

  • Perspective on Materials Failure Theory and Applications JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME Christensen, R. M. 2016; 83 (11)

    View details for DOI 10.1115/1.4034122

    View details for Web of Science ID 000385453800001

  • The Theoretical Measure of the Ductility of Failure for All Isotropic Materials in All States of Stress JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME Christensen, R. M. 2016; 83 (6)

    View details for DOI 10.1115/1.4033279

    View details for Web of Science ID 000378407200001

  • Evaluation of Ductile/Brittle Failure Theory and Derivation of the Ductile/Brittle Transition Temperature JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME Christensen, R. M. 2016; 83 (2)

    View details for DOI 10.1115/1.4032014

    View details for Web of Science ID 000367373500001

  • A New Theory of Strain Hardening and its Consequences for Yield Stress and Failure Stress CMC-COMPUTERS MATERIALS & CONTINUA Christensen, R. M. 2015; 47 (1): 45-63

    View details for Web of Science ID 000375367000004

  • The size dependence of tensile strength for brittle isotropic materials and carbon fiber composite materials COMPOSITES SCIENCE AND TECHNOLOGY Christensen, R., Miyano, Y., Nakada, M. 2015; 106: 9-14

    View details for DOI 10.1016/j.compscitech.2014.10.015

    View details for Web of Science ID 000347868200019

  • The effect on knee-joint load of instruction in analgesic use compared with neuromuscular exercise in patients with knee osteoarthritis: study protocol for a randomized, single-blind, controlled trial (the EXERPHARMA trial) TRIALS Clausen, B., Holsgaard-Larsen, A., Sondergaard, J., Christensen, R., Andriacchi, T. P., Roos, E. M. 2014; 15

    View details for DOI 10.1186/1745-6215-15-444

    View details for Web of Science ID 000345129100001

  • Failure Mechanics-Part II: The Central and Decisive Role of Graphene in Defining the Elastic and Failure Properties for all Isotropic Materials JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME Christensen, R. M. 2014; 81 (11)

    View details for DOI 10.1115/1.4028407

    View details for Web of Science ID 000349190500001

  • Failure Mechanics-Part I: The Coordination Between Elasticity Theory and Failure Theory for all Isotropic Materials JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME Christensen, R. M. 2014; 81 (8)

    View details for DOI 10.1115/1.4027753

    View details for Web of Science ID 000338203600001

  • 2013 Timoshenko Medal Award Paper-Completion and Closure on Failure Criteria for Unidirectional Fiber Composite Materials JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME Christensen, R. M. 2014; 81 (1)

    View details for DOI 10.1115/1.4025177

    View details for Web of Science ID 000328262300011

  • The World Wide Failure Exercise II Examination of Results JOURNAL OF REINFORCED PLASTICS AND COMPOSITES Christensen, R. M. 2013; 32 (21): 1668-1672

    View details for DOI 10.1177/0731684413498634

    View details for Web of Science ID 000327378200009

  • A physically based cumulative damage formalism INTERNATIONAL JOURNAL OF FATIGUE Christensen, R. M. 2008; 30 (4): 595-602

    View details for DOI 10.1016/j.ijfatigue.2007.05.009

    View details for Web of Science ID 000257817700002

  • Observations on the definition of yield stress ACTA MECHANICA Christensen, R. M. 2008; 196 (3-4): 239-244

    View details for DOI 10.1007/s00707-007-0478-0

    View details for Web of Science ID 000254233500009

  • A comparison of open cell and closed cell properties for low-density materials JOURNAL OF MECHANICS OF MATERIALS AND STRUCTURES Christensen, R. M. 2007; 2 (7): 1299-1307

    View details for DOI 10.2140/jomms.2007.2.1299

    View details for Web of Science ID 000256406700007

  • A comprehensive theory of yielding and failure for isotropic materials JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY-TRANSACTIONS OF THE ASME Christensen, R. M. 2007; 129 (2): 173-181

    View details for DOI 10.1115/1.2712847

    View details for Web of Science ID 000246327500001

  • Deterministic and probabilistic lifetimes from kinetic crack growth-generalized forms INTERNATIONAL JOURNAL OF FRACTURE Christensen, R., Miyano, Y. 2007; 143 (1): 35-39

    View details for DOI 10.1007/s10704-006-9049-y

    View details for Web of Science ID 000245380000003

  • A comparative evaluation of three isotropic, two property failure theories Symposium on Current Trends in Mechanics Christensen, R. M. ASME. 2006: 852–59

    View details for DOI 10.1115/1.2173007

    View details for Web of Science ID 000240009700019

  • Stress intensity controlled kinetic crack growth and stress history dependent life prediction with statistical variability INTERNATIONAL JOURNAL OF FRACTURE Christensen, R., Miyano, Y. 2006; 137 (1-4): 77-87

    View details for DOI 10.1007/s10704-005-9062-6

    View details for Web of Science ID 000237133500005

  • YIELD FUNCTIONS AND PLASTIC POTENTIALS FOR BCC METALS AND POSSIBLY OTHER MATERIALS JOURNAL OF MECHANICS OF MATERIALS AND STRUCTURES Christensen, R. M. 2006; 1 (1): 183-200

    View details for DOI 10.2140/jomms.2006.1.183

    View details for Web of Science ID 000207728100008

  • Exploration of ductile, brittle failure characteristics through a two-parameter yield/failure criterion MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING Christensen, R. M. 2005; 394 (1-2): 417-424

    View details for DOI 10.1016/j.msea.2004.11.053

    View details for Web of Science ID 000228069000049

  • The three-dimensional analog of the classical two-dimensional truss system JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME Christensen, R. M. 2004; 71 (2): 285-287

    View details for DOI 10.1115/1.1651090

    View details for Web of Science ID 000221558500018

  • A probabilistic treatment of creep rupture behavior for polymers and other materials MECHANICS OF TIME-DEPENDENT MATERIALS Christensen, R. M. 2004; 8 (1): 1-15

    View details for Web of Science ID 000221390200001

  • Delamination failure investigation for out-of-plane loading in laminates JOURNAL OF COMPOSITE MATERIALS Christensen, R. M., DeTeresa, S. J. 2004; 38 (24): 2231-2238

    View details for DOI 10.1177/0021998304046431

    View details for Web of Science ID 000225868000005

  • Effective properties for single size, rigid spherical inclusions in an elastic matrix COMPOSITES PART B-ENGINEERING Christensen, R. M. 2004; 35 (6-8): 475-482

    View details for DOI 10.1016/j.compositesb.2004.04.008

    View details for Web of Science ID 000224020700005

  • A two-property yield, failure (fracture) criterion for homogeneous, isotropic materials JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY-TRANSACTIONS OF THE ASME Christensen, R. M. 2004; 126 (1): 45-52

    View details for DOI 10.1115/1.1631024

    View details for Web of Science ID 000188711800007

  • Failure plane orientations for transverse loading of a unidirectional fiber composite 14th United States National Congress of Theoretical and Applied Mechanics Christensen, R. M., DeTeresa, S. J. PERGAMON-ELSEVIER SCIENCE LTD. 2003: 7055–62

    View details for DOI 10.1016/S0020-7683(03)00354-8

    View details for Web of Science ID 000186437800011

  • Predicting failure in composite laminates using dissipated energy JOURNAL OF COMPOSITE MATERIALS Huang, H. S., Springer, G. S., Christensen, R. M. 2003; 37 (23): 2073-2099

    View details for DOI 10.1177/002199803035187

    View details for Web of Science ID 000186988000001

  • A possible limiting case behavior for brittle material fracture JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME Christensen, R. M. 2002; 69 (6): 772-774

    View details for DOI 10.1115/1.1483835

    View details for Web of Science ID 000179153900007

  • Failure criteria for isotropic materials, applications to low-density types INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES Christensen, R. M., Freeman, D. C., DeTeresa, S. J. 2002; 39 (4): 973-982

    View details for Web of Science ID 000174819500010

  • An evaluation of linear cumulative damage (Miner's Law) using kinetic crack growth theory MECHANICS OF TIME-DEPENDENT MATERIALS Christensen, R. M. 2002; 6 (4): 363-377

    View details for Web of Science ID 000179475700003

  • Compressive failure of composites using a matrix-controlled failure criterion with the kink band mechanism MECHANICS OF MATERIALS Christensen, R. M. 2000; 32 (9): 505-509

    View details for Web of Science ID 000088725000001

  • Yield functions, damage states, and intrinsic strength MATHEMATICS AND MECHANICS OF SOLIDS Christensen, R. M. 2000; 5 (3): 285-300

    View details for Web of Science ID 000167820500002

  • A general measure for the ductility of materials - Part II Applications JOURNAL OF MATERIALS SCIENCE LETTERS Christensen, R. M. 2000; 19 (16): 1465-1468

    View details for Web of Science ID 000088901300017

  • Basic two-dimensional core types for sandwich structures INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES Kim, B., Christensen, R. M. 2000; 42 (4): 657-676

    View details for Web of Science ID 000084844200002

  • Mechanics of cellular and other low-density materials INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES Christensen, R. M. 2000; 37 (1-2): 93-104

    View details for Web of Science ID 000083127400009

  • A general measure for the ductility of materials JOURNAL OF MATERIALS SCIENCE LETTERS Christensen, R. M. 1999; 18 (17): 1371-1373

    View details for Web of Science ID 000082123300003

  • The numbers of elastic properties and failure parameters for fiber composites JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY-TRANSACTIONS OF THE ASME Christensen, R. M. 1998; 120 (2): 110-113

    View details for Web of Science ID 000073137400003

  • Two theoretical elasticity micromechanics models JOURNAL OF ELASTICITY Christensen, R. M. 1998; 50 (1): 15-25

    View details for Web of Science ID 000075275900002

  • Yield functions failure criteria for isotropic materials PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Christensen, R. M. 1997; 453 (1962): 1473-1491

    View details for Web of Science ID A1997XK04800006

  • The kink band mechanism for the compressive failure of fiber composite materials JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME Christensen, R. M., DeTeresa, S. J. 1997; 64 (1): 1-6

    View details for Web of Science ID A1997WV16300001

  • Stress based yield/failure criteria for fiber composites INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES Christensen, R. M. 1997; 34 (5): 529-543

    View details for Web of Science ID A1997WB89300001

  • On the relationship of minimal conditions to low density material microstructures JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Christensen, R. M. 1996; 44 (12): 2113-?

    View details for Web of Science ID A1996VY93000008