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A description of macroscopic damage through microstructural relaxation. (English) Zbl 0948.74004
Summary: We present a flexible model for the description of damage in heterogeneous structural materials. The approach involves solving the equations of equilibrium, with unilateral constraints on the maximum attainable values of selected internal variables. Due to the unilateral constraints, the problem is nonlinear. Accordingly, a simple iterative algorithm is developed to solve this problem by (1) computing the internal fields with the initial undamaged microstructure and (2) reducing the material stiffness at locations where the constraints are violated. This process is repeated until a solution, with a corresponding microstructure that satisfies the equations of equilibrium and the constraints, is found. The corresponding microstructure is the final ‘damaged’ material. As an application, the method is used in an incremental fashion to generate response curves describing the progressive macroscopic damage for a sample of commonly used fibre-reinforced aluminum/boron composite. The results are compared with laboratory experiments and with computational results using standard numerical methods.

74A45 Theories of fracture and damage
74A60 Micromechanical theories
74S05 Finite element methods applied to problems in solid mechanics
Full Text: DOI
[1] Kyono, ASTM STP 964 pp 409– (1986)
[2] Brockenbrough, Acta Metall. Mater. 39 pp 735– (1991)
[3] Damage Mechanics, North-Holland, Amsterdam, 1996.
[4] and , ’Paradoxes in the application of thermo-dynamics to strained solids’, in and (eds.), A Critical Review of Thermodynamics, Mono-Book Corp., Baltimore, MD, 1970, pp. 275-298.
[5] Hill, SIAM J. Appl. Math. 25 pp 448– (1973) · Zbl 0275.73028
[6] and , Mechanics of Solid Material, Cambridge University Press, Cambridge, 1990.
[7] Lemaitre, Comput. Meth. Appl. Mech. Engng. 51 pp 31– (1985) · Zbl 0546.73085
[8] Ladaveze, J. Engng. Mat. Tech. 116 pp 331– (1994)
[9] ’Elements of homogenization for inelastic solids’, in and (eds.), Homogenization Techniques for Composite Media, Lecture Note in Physics, vol. 272, Springer, Berlin, 1987, pp. 193-278.
[10] , , and , Impact Dynamics, Wiley, New York, 1982.
[11] Topics on the Numerical Analysis and Simulation of Plasticity, Elsevier Science, 1998, to appear.
[12] Böhm, Mater. Sci. Engng. A135 pp 185– (1991)
[13] Cherepanov, USSR J. Appl. Math. Mech. Transl. 31 pp 504– (1967)
[14] ’A path independent integral and the approximate analysis of strain concentration by notches and cracks’, J. Appl. Mech., 379-386 (1968).
[15] Griffith, Phil. Trans. Roy. Soc. London A221 pp 163– (1921)
[16] Introduction to Continuum Damage Mechanics, Martinus Nijoff, Dordrecht, 1986.
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