A cohesive approach to thin-shell fracture and fragmentation

We develop a finite-element method for the simulation of dynamic fracture and fragmentation of thin-shells. The shell is spatially discretized with subdivision shell elements and the fracture along the element edges is modeled with a cohesive law. In order to follow the propagation and branching of cracks, subdivision shell elements are pre-fractured ab initio and the crack opening is constrained prior to crack nucleation. This approach allows for shell fracture in an in-plane tearing mode, a shearing mode, or a bending of hinge mode. The good performance of the method is demonstrated through the simulation of petalling failure experiments in aluminum plates.

[1]  T. Wierzbicki.  Petalling of plates under explosive and impact loading , 1999 .

[2]  Joe Warren,et al.  Subdivision Methods for Geometric Design: A Constructive Approach , 2001 .

[3]  R. Borst.  The zero-normal-stress condition in plane-stress and shell elastoplasticity , 1991 .

[4]  Werner Goldsmith,et al.  Petalling of thin, metallic plates during penetration by cylindro-conical projectiles , 1985 .

[5]  J. Rice,et al.  The Part-Through Surface Crack in an Elastic Plate , 1972 .

[6]  M. Ortiz,et al.  A material‐independent method for extending stress update algorithms from small-strain plasticity to finite plasticity with multiplicative kinematics , 1992 .

[7]  T. Wierzbicki,et al.  Large deformation of thin plates under localised impulsive loading , 1996 .

[8]  W. Q. Shen.  A study on the failure of circular plates struck by masses. Part 2: theoretical analysis for the onset of failure , 2002 .

[9]  Peter Hansbo,et al.  A discontinuous Galerkin method¶for the plate equation , 2002 .

[10]  E. Ramm,et al.  Shell theory versus degeneration—a comparison in large rotation finite element analysis , 1992 .

[11]  Subra Suresh,et al.  Statistical Properties of Residual Stresses and Intergranular Fracture in Ceramic Materials , 1993 .

[12]  M. Ortiz,et al.  Subdivision surfaces: a new paradigm for thin‐shell finite‐element analysis , 2000 .

[13]  J. Z. Zhu,et al.  The finite element method , 1977 .

[14]  Michael Ortiz,et al.  An Efficient Adaptive Procedure for Three-Dimensional Fragmentation Simulations , 2001, Engineering with Computers.

[15]  Michael Ortiz,et al.  Fully C1‐conforming subdivision elements for finite deformation thin‐shell analysis , 2001, International Journal for Numerical Methods in Engineering.

[16]  C. S. White,et al.  Elastic-Plastic Line-Spring Finite Elements for Surface-Cracked Plates and Shells , 1982 .

[17]  E. Ramm,et al.  Three‐dimensional extension of non‐linear shell formulation based on the enhanced assumed strain concept , 1994 .

[18]  M. Ortiz,et al.  FINITE-DEFORMATION IRREVERSIBLE COHESIVE ELEMENTS FOR THREE-DIMENSIONAL CRACK-PROPAGATION ANALYSIS , 1999 .

[19]  P. Krysl,et al.  Finite element simulation of ring expansion and fragmentation: The capturing of length and time scales through cohesive models of fracture , 1999 .

[20]  Viggo Tvergaard,et al.  Effect of Strain Dependent Cohesive Zone Model on Predictions of Interface Crack Growth , 1996 .

[21]  W. Q. Shen,et al.  A study on the failure of circular plates struck by masses. Part 1: experimental results , 2002 .

[22]  M. Ortiz,et al.  Solid modeling aspects of three-dimensional fragmentation , 1998, Engineering with Computers.

[23]  Hyungyil Lee,et al.  Line-spring finite element for fully plastic crack growth-II. Surface-cracked plates and pipes , 1998 .

[24]  A. Needleman.  A Continuum Model for Void Nucleation by Inclusion Debonding , 1987 .

[25]  Norman A. Fleck,et al.  Ballistic impact of polycarbonate—An experimental investigation , 1993 .

[26]  A. Needleman.  An analysis of decohesion along an imperfect interface , 1990 .

[27]  P. Krysl,et al.  Finite Element Simulation of Ring Expansion and Fragmentation , 1999 .

[28]  Young Hoon Moon,et al.  Estimation of hole flangeability for high strength steel plates , 2002 .

[29]  M. Ortiz,et al.  Computational modelling of impact damage in brittle materials , 1996 .

[30]  Charles T. Loop,et al.  Smooth Subdivision Surfaces Based on Triangles , 1987 .

[31]  C. Fond,et al.  Experimental and numerical analysis of the impact behaviour of polycarbonate and polyurethane multilayer , 2000 .

[32]  S. Timoshenko,et al.  THEORY OF PLATES AND SHELLS , 1959 .

[33]  I. Babuska,et al.  Nonconforming Elements in the Finite Element Method with Penalty , 1973 .

[34]  J. C. Simo,et al.  On stress resultant geometrically exact shell model. Part I: formulation and optimal parametrization , 1989 .

[35]  Xiaopeng Xu,et al.  Numerical simulations of fast crack growth in brittle solids , 1994 .

[36]  Peter Schröder,et al.  Integrated modeling, finite-element analysis, and engineering design for thin-shell structures using subdivision , 2002, Comput. Aided Des..