×

zbMATH — the first resource for mathematics

Gradient enhanced damage for quasi-brittle materials. (English) Zbl 0882.73057
Summary: Conventional continuum damage descriptions of material degeneration suffer from loss of well-posedness beyond a certain level of accumulated damage. As a consequence, numerical solutions are obtained which are unacceptable from a physical point of view. The introduction of higher-order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models. A consistent numerical solution procedure for the governing partial differential equations is presented, which is shown to be capable of properly simulating localization phenomena.

MSC:
74R99 Fracture and damage
74S05 Finite element methods applied to problems in solid mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bažant, J. Eng. Mech. 110 pp 1666– (1984) · doi:10.1061/(ASCE)0733-9399(1984)110:12(1666)
[2] Triantafyllidis, J. Elasticity 16 pp 225– (1986) · Zbl 0594.73044 · doi:10.1007/BF00040814
[3] Schreyer, J. Appl. Mech. 53 pp 791– (1986) · doi:10.1115/1.3171860
[4] Lasry, Int. J. Solids Struct. 24 pp 581– (1988) · Zbl 0636.73021 · doi:10.1016/0020-7683(88)90059-5
[5] de Borst, Eng. Comput. 10 pp 99– (1993) · doi:10.1108/eb023897
[6] Bažant, J. Appl. Mech. 55 pp 287– (1988) · Zbl 0663.73075 · doi:10.1115/1.3173674
[7] de Vree, Comput. Struct. 55 pp 581– (1995) · Zbl 0919.73187 · doi:10.1016/0045-7949(94)00501-S
[8] Aifantis, J. Eng. Mat. Technol. 106 pp 326– (1984) · doi:10.1115/1.3225725
[9] Mühlhaus, Int. J. Solids Struct. 28 pp 845– (1991) · Zbl 0749.73029 · doi:10.1016/0020-7683(91)90004-Y
[10] de Borst, Int. J. numer. methods eng. 35 pp 521– (1992) · Zbl 0768.73019 · doi:10.1002/nme.1620350307
[11] Simo, Int. J. Solids Struct. 23 pp 821– (1987) · Zbl 0634.73106 · doi:10.1016/0020-7683(87)90083-7
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.