Gradient damage models coupled with plasticity and their application to dynamic fragmentation

Arthur Geromel Fischer (1) , Jean-Jacques Marigo (1)

1 LMS - Laboratoire de mécanique des solides

This chapter explains the development of the so‐called "gradient damage models" and their extension to ductile materials and dynamic loading. It presents the construction of gradient damage models for brittle softening materials based on the principle of minimum energy. The chapter discusses the main hypothesis and the need for regularization. It then briefly discusses the von Mises plasticity criterion and how to take it into account. The chapter briefly discusses the numerical implementation and shows a few examples and results using the FEniCS library and an industrial code. It considers the case of small strains theory and an isotropic material. The chapter reviews variational approach used to describe damage evolution for a quasi‐static loading. It expresses that the evolution of the plasticity minimizes the energy. The chapter concerns the study of the fragmentation of a cylinder under a strong internal pressure.

Mots clés: Plasticity; Damage; Variational approach; Dynamical fracture; Fragmentation

Domaines: Mécanique des solides [physics.class-ph]

Arthur Geromel Fischer, Jean-Jacques Marigo. Gradient damage models coupled with plasticity and their application to dynamic fragmentation. David Edward Lambert, Crystal L. Pasiliao, Benjamin Erzar, Benoit Revil‐Baudard, Oana Cazacu. Dynamic Damage and Fragmentation, Wiley Online Library, chapter 3, pp. 95-141, 2019, 9781786304087. ⟨10.1002/9781119579311.ch3⟩. ⟨hal-02043778⟩