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Energy release control for numerical simulations of failure in quasi-brittle solids. (English) Zbl 1047.74551
Summary: A path-following constraint is developed which is based on the energy release during failure. This makes it applicable to the simulation of quasi-brittle materials when no previous knowledge is available on the failure behaviour of a body and, consequently, indirect displacement control methods like CMOD cannot be applied. The constraint is derived from the first principle of thermodynamics for a finite-element discretization of a solid with a continuum damage model. The performance of the constraint is demonstrated by means of a bending test on a single-edge-notched beam.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
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[1] Riks, An incremental approach to the solution of snapping and buckling problems, International Journal of Solids and Structures 15 pp 529– (1979) · Zbl 0408.73040
[2] Ramm, Nonlinear Finite Element Analyses in Structural Mechanics (1981)
[3] Crisfield, Non-Linear Finite Element Analysis of Solids and Structures (1991) · Zbl 0809.73005
[4] de Borst, Computation of post-bifurcation and post-failure behaviour of strain-softening solids, Computers and Structures 25 pp 211– (1987) · Zbl 0603.73046
[5] Geers, Enhanced solution control for physically and geometrically non-linear problems Part I-The subplane control approach, International Journal for Numerical Methods in Engineering 46 pp 177– (1999) · Zbl 0957.74034
[6] Geers, Enhanced solution control for physically and geometrically non-linear problems Part II-Comparative performance analysis, International Journal for Numerical Methods in Engineering 46 pp 205– (1999) · Zbl 0957.74034
[7] Lemaitre, Mechanics of Solids Materials (1990) · doi:10.1017/CBO9781139167970
[8] Simo, Finite deformation post-buckling analysis involving inelasticity and contact constraints, International Journal of Numerical Methods in Engineering 23 pp 779– (1986) · Zbl 0584.73045
[9] Crisfield, A fast incremental/iterative solution procedure that handles ’snap-through’, Computers and Structures 13 pp 55– (1981) · Zbl 0479.73031
[10] Peerlings, Gradient-enhanced damage modelling of concrete fracture, Mechanics of Cohesive-Frictional Materials 3 pp 323– (1998)
[11] de Vree, Comparison of nonlocal approaches in continuum damage mechanics, Computers and Structures 55 pp 581– (1995) · Zbl 0919.73187
[12] Schlangen E Experimental and numerical analysis of fracture processes in concrete 1993
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