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


  • Emeritus Faculty, Acad Council, Aeronautics and Astronautics

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)

2018-19 Courses


All Publications


  • 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

  • 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
  • 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
  • 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
  • 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
  • A physically based cumulative damage formalism INTERNATIONAL JOURNAL OF FATIGUE Christensen, R. M. 2008; 30 (4): 595-602
  • Observations on the definition of yield stress ACTA MECHANICA Christensen, R. M. 2008; 196 (3-4): 239-244
  • 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
  • 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
  • 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

  • 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
  • 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
  • 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
  • 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
  • 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

  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • Yield functions, damage states, and intrinsic strength MATHEMATICS AND MECHANICS OF SOLIDS Christensen, R. M. 2000; 5 (3): 285-300
  • A general measure for the ductility of materials - Part II Applications JOURNAL OF MATERIALS SCIENCE LETTERS Christensen, R. M. 2000; 19 (16): 1465-1468
  • Basic two-dimensional core types for sandwich structures INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES Kim, B., Christensen, R. M. 2000; 42 (4): 657-676
  • Mechanics of cellular and other low-density materials INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES Christensen, R. M. 2000; 37 (1-2): 93-104
  • A general measure for the ductility of materials JOURNAL OF MATERIALS SCIENCE LETTERS Christensen, R. M. 1999; 18 (17): 1371-1373
  • 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
  • Two theoretical elasticity micromechanics models JOURNAL OF ELASTICITY Christensen, R. M. 1998; 50 (1): 15-25
  • 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
  • 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
  • Stress based yield/failure criteria for fiber composites INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES Christensen, R. M. 1997; 34 (5): 529-543
  • 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-?