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Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. I: Fundamentals. II: Numerical simulation. (English) Zbl 0888.73018
The paper addresses standard constitutive equations to model strong discontinuities (cracks, shear bands, slip lines, etc.) in solid mechanics. The strong discontinuity analysis is introduced, and a link between continuum and discrete approaches to the strain localization phenomena is obtained. Applications to standard continuum damage and elastoplastic constitutive equations are presented. Relevant aspects of the numerical simulation of the problem are presented in part II.

##### MSC:
 74C99 Plastic materials, materials of stress-rate and internal-variable type 74R99 Fracture and damage 74S05 Finite element methods applied to problems in solid mechanics
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##### References:
 [1] Hill, J. Mech. Phys. Solids 16 pp 1– (1962) · Zbl 0111.37701 [2] Dvorkin, Int. J. numer. methods eng. 30 pp 541– (1990) · Zbl 0729.73209 [3] ’Numerical methods to simulate softening and fracture of concrete’, in: G. C. Sih and A. Di Tomaso (eds.), Fracture Mechanics of Concrete: Structural Application and Numerical Calculation, 1985, pp. 141-170. [4] and , ’Analysis of concrete fracture with an embedded crack approach’. in: et al. (eds.), Proc. EURO-C 1994 Computer Modelling of Concrete Structures, Pineridge Press, Swansea, 1994, 343-352. [5] Belytschko, Comput. Methods Appl. Mech. Eng. 70 pp 59– (1988) · Zbl 0653.73032 [6] Oliver, Int. J. numer. methods eng. 28 pp 461– (1989) · Zbl 0676.73066 [7] , and , ’Isotropic damage models and smeared crack analysis of concrete’, in: et. al. (eds.), Proc. SCI-C Computer Aided Analysis and Design of Concrete Structures, Pineridge Press, Swansea, 1990, pp. 945-951. [8] Zienkiewicz, Int. J. numer. methods eng. 19 pp 127– (1995) · Zbl 0819.73069 [9] Cabot, J. Eng. Mech. ASCE 113 pp 1512– (1987) [10] , and ’Computational modelling of localisation of deformation’, in et. al., (eds.), Proc. 3rd Conf. on Computational Plasticity: Fundamentals and Applications, Pineridge Press, Swansea, 1992, pp. 483-508. [11] Needleman, Comput. Methods. Appl. Mech. Eng. 67 pp 69– (1988) · Zbl 0618.73054 [12] Simo, Comput. Mech. 12 pp 277– (1993) · Zbl 0783.73024 [13] and , ’Modelling strong discontinuities by means of strain softening constitutive equations’, in: et. al. (eds.), Proc. EURO-C 1994 Computer Modelling of Concrete Structures, Pineridge Press, Swansea, 1994, pp. 363-372. [14] and , ’A new approach to the analysis and simulation of strong discontinuities’, in: et. al., (eds.), Fracture and Damage in Quasibrittle Structures, E & FN Spon, 1994, pp. 25-39. [15] ’Continuum modelling of strong discontinuities in solid mechanics’, in: et. al. (eds.), Proc. COMPLAS IV, 4th Int. Conf. on Computational Plasticity, Pineridge Press, Swansea, 1995, pp. 455-479. [16] and ’Embedded localization band based on regularized strong discontinuity’, in et al. (eds.), Proc. COMPLAS IV, 4th Int. Conf. on Computational Plasticity, Pineridge Press, Swansea, 1995, pp. 599-610. [17] and , ’Recent advances in the analysis and numerical simulation of strain localization in inelastic solids’, et. al., (eds.), Proc. COMPLAS IV 4th Int. Conf. on Computational Plasticity, Pineridge Press, Swansea, 1995, pp. 547-561. [18] and , ’Bifurcation analysis of tangential material operators’, in: et. al. (eds.), Proc. NUMETA-87 Transient/Dynamic Analysis of Constitutive Laws for Engineering Materials, C4/1-C4/13, Martinus Nijhoff Publishers, Dordrecht, 1987. [19] Ottosen, Int. J. Solids Struct. 27 pp 401– (1991) · Zbl 0738.73021 [20] Larsson, Int. J. numer. methods eng. 36 pp 2087– (1993) · Zbl 0794.73074 [21] Runesson, Int. J. Plasticity 7 pp 99– (1991) · Zbl 0761.73035
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