GRIFFITH THEORY OF BRITTLE FRACTURE REVISITED: MERITS AND DRAWBACKS

Abstract

A VARIATIONAL REFORMULATION OF GRI±TH'S THEORY OF BRITTLE FRACTURE IS PROPOSED. AT THE EXPENSE OF A SLIGHT DEPARTURE FROM THE CLASSICAL THEORY, THE NEW FORMULATION DECISIVELY ADDRESSES THREE MAJOR ISSUES: CRACK INITIATION, CRACK PATH, AND SMOOTHNESS OF THE CRACK EVOLUTION. THE NEW FORMULATION IS AMENABLE TO NUMERICAL IMPLEMENTATION; A SIMULATION QUALITATIVELY IN AGREEMENT WITH EXPERIMENTAL DATA IS PRESENTED. THAT COMPUTATION IS WELL BEYOND THE SCOPE OF THE CLASSICAL THEORY AND DEMONSTRATES THE °EXIBILITY OF THE APPROACH. EXTENSIONS OF THE FORMULATION THAT CURE THE WEAKNESSES OF THE PROPOSED MODEL ARE SUGGESTED. IN THIS SHORT PAPER, WE ¯RST BRIE°Y DESCRIBE IN SECTION 1 THE VARIATIONAL FORMULATION THAT WE PROPOSE FOR QUASISTATIC BRITTLE FRACTURE EVOLUTION. OUR FORMULATION IS VERY CLOSE TO THE SPIRIT OF GRI±TH'S APPROACH TO BRITTLE FRACTURE [11], AND ONLY SLIGHTLY DEPARTS FROM THE CLASSICAL THEORY. IN SECTION 2, WE PRESENT A COMPUTATION THAT ILLUSTRATES THE REACH OF THE MODEL. FINALLY, SECTION 3 ZEROES IN ON THE DRAWBACKS OF THE FORMULATION AND ON POSSIBLE REMEDIES; IT FOCUSSES ON THE USE OF OTHER SURFACE ENERGIES.