# zbMATH — the first resource for mathematics

Smeared cracking, plasticity, creep, and thermal loading - A unified approach. (English) Zbl 0607.73109
A recently proposed smeared crack model which properly handles nonorthogonal cracks is further elaborated. It is proved that the model obeys the principle of material frame-indifference and some comments on possible stress-strain laws within a smeared crack are made. Algorithms are presented or indicated for the combination of plasticity and possibly multiple crack formation, for the combination of viscoelasticity and cracking, and for the combination of cracking and temperature-dependent material properties and phenomena like thermal dilatation and shrinkage.

##### MSC:
 74R05 Brittle damage 74S30 Other numerical methods in solid mechanics (MSC2010) 74S99 Numerical and other methods in solid mechanics 74C99 Plastic materials, materials of stress-rate and internal-variable type
Full Text:
##### References:
 [1] Ngo, D.; Scordelis, A.C., Finite element analysis of reinforced concrete beams, J. amer. concrete inst., 64, 152-163, (1967) [2] Nilson, A.H., Non-linear analysis of concrete by the finite element method, J. amer. concrete inst., 65, 757-766, (1968) [3] Saouma, V.E.; Ingraffea, A.R., Fracture mechanics analysis of discrete cracking, (), 413-436 [4] Blaauwendraad, J.; Grootenboer, H.J., Essentials for discrete crack analysis, (), 263-272 [5] Rashid, Y.R., Analysis of prestressed concrete pressure vessels, Nucl. engrg. design, 7, 334-344, (1968) [6] Suidan, M.; Schnobrich, W.C., Finite element analysis of reinforced concrete, ASCE J. struct. div., 99, 2109-2122, (1973) [7] Bergan, P.G.; Holand, I., Nonlinear finite element analysis of concrete structures, Comput. meths. appl. mech. engrg., Comput. meths. appl. mech. engrg., 18, 443-467, (1979) · Zbl 0398.73080 [8] Mehlhorn, G., On the application of the finite element method for analysing reinforced concrete plates and planar structures—A survey of some research activities by the Darmstadt group, (), 159-190 [9] Rots, J.G.; Nauta, P.; Kusters, G.M.A.; Blaauwendraad, J., Smeared crack approach and fracture localization in concrete, Heron, 30, 1, 1-48, (1985) [10] Rots, J.G., Strain-softening analysis of concrete fracture specimens, (), 115-126 [11] Cope, R.J.; Rao, P.V.; Clark, L.A.; Norris, P., Modelling of reinforced concrete behaviour for finite element analysis of bridge slabs, (), 457-470 [12] Crisfield, M.A., Accelerated solution techniques and concrete cracking, Comput. meths. appl. mech. engrg., 33, 585-607, (1982) · Zbl 0478.73088 [13] De Borst, R.; Nauta, P., Smeared crack analysis of reinforced concrete beams and slabs failing in shear, (), 261-273, Part 1 [14] De Borst, R.; Nauta, P., Non-orthogonal cracks in a smeared finite element model, Engrg. comput., 2, 35-46, (1985) [15] De Borst, R., Non-linear analysis of frictional materials, () [16] De Borst, R.; Van Den Berg, P., Analysis of creep and cracking in concrete members, (), 527-538 [17] Bažant, Z.P.; Oh, B., Crack band theory for fracture of concrete, RILEM materials and structures, 16, 155-177, (1983) [18] Bažant, Z.P.; Chern, J.C., Strain-softening with creep and exponential algorithm, ASCE J. engrg. mech., 111, 391-415, (1985) [19] Bažant, Z.P., Discussion on session 2, structural modelling for numerical analysis, (), 482 [20] Truesdell, C.; Noll, W., The non-linear field theories of mechanics, () · Zbl 0779.73004 [21] Besseling, J.F., A theory of elastic, plastic and creep deformation of an initially isotropic material showing strain hardening, creep recovery and secondary creep, J. appl. mech., 25, 529-536, (1958) · Zbl 0084.20501 [22] Dill, E.H., Rate formulations of nonlinear solid mechanics for the finite element method, Comput. & structures, 19, 51-56, (1984) · Zbl 0548.73050 [23] Reinhardt, H.W.; Walraven, J.C., Cracks in concrete subject to shear, ASCE J. struct. div., 108, 207-224, (1982) [24] Hillerborg, A.; Modeer, M.; Petersson, P.E., Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cement and concrete res., 6, 773-782, (1976) [25] Kolmar, W.; Mehlhorn, G., Comparison of shear stiffness formulation for cracked reinforced concrete elements, (), 133-147, Part 1 [26] Litton, R.W., A contribution to the analysis of concrete structures under cyclic loading, () [27] Ebbinghaus, P., Herleitung eines verfahrens zur berechnung von stahlbetonscheiben unter berücksichtigung der rissentwicklung, () [28] Kristjansson, R., Physikalisch und geometrisch nichtlineare berechnung von stahlbetonplatten mit hilfe finiter elemente, () [29] Krieg, R.D.; Krieg, D.B., Accuracies of numerical solution methods for the elastic-perfectly plastic model, J. pressure vessel technol., 99, 510-515, (1977) [30] Schreyer, H.L.; Kulak, R.F.; Kramer, J.M., Accurate numerical solution for elasto-plastic models, J. pressure vessel technol., 101, 226-234, (1979) [31] Nayak, G.C.; Zienkiewicz, O.C., Elasto-plastic stress analysis. A generalization for various constitutive relations including strain softening, Internat. J. numer. meths. engrg., 5, 113-135, (1972) · Zbl 0241.73034 [32] Owen, D.R.J.; Figueiras, J.A.; Damjanić, F., Finite element analysis of reinforced and prestressed concrete structures including thermal loading, Comput. meths. appl. mech. engrg., 41, 323-366, (1983) · Zbl 0517.73069 [33] Bažant, Z.P.; Wu, S.T., Rate-type creep law for aging concrete based on Maxwell chain, RILEM materials and structures, 7, 45-60, (1974) [34] Argyris, J.H.; Vaz, L.E.; Willam, K.J., Improved solution methods for inelastic rate problems, Comput. meths. appl. mech. engrg., 16, 231-277, (1978) · Zbl 0405.73068 [35] Taylor, R.L.; Pister, K.S.; Goudreau, G.L., Thermomechanical analysis of viscoelastic solids, Internat. J. numer. meths. engrg., 2, 45-59, (1970) · Zbl 0252.73006 [36] Rashid, Y.R., Nonlinear analysis of two-dimensional problems in concrete creep, J. appl. mech., 39, 475-482, (1972) · Zbl 0237.73098 [37] Anderson, C.A., Numerical creep analysis of structures, (), 259-303 [38] Argyris, J.H.; Pister, K.S.; Szimmat, J.; Willam, K.J., Unified concepts of constitutive modelling and numerical solution methods for concrete creep problems, Comput. meths. appl. mech. engrg., 10, 199-246, (1977) · Zbl 0353.73038
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.