A micro–meso-model of intra-laminar fracture in fiber-reinforced composites based on a discontinuous Galerkin/cohesive zone method

Abstract

The recently developed hybrid discontinuous Galerkin/extrinsic cohesive law framework is extended to the study of intra-laminar fracture of composite materials. Toward this end, micro-volumes of different sizes are studied. The method captures the debonding process, which is herein proposed to be assimilated to a damaging process, before the strain softening onset, and the density of dissipated energy resulting from the damage (debonding) remains the same for the different studied cell sizes. Finally, during the strain softening phase a micro-crack initiates and propagates in agreement with experimental observations. We thus extract a resulting mesoscale cohesive law, which is independent on the cell sizes, using literature methods.

Multiscale computational homogenization methods with a gradient enhanced scheme based on the discontinuous Galerkin formulation

“…The implementation is based on the partitioning of the mesh at the macro-scale. The connectivity between partitions is ensured using the face-based ghost method for discontinuous Galerkin method described in [35,36]. The elements of the macro-mesh are thus integrated in different processors.…”

“…Finally, the microscopic boundary value problem is solved by seeking the solution of the equilibrium state equation (17) with the constraints (24) and (27) and with the constitutive law (36). Equation (35) is satisfied automatically if the periodic constraints (24) and (27) are satisfied either by using the constraint elimination method or by using the Lagrange multipliers method, in which case the multipliers represent the boundary forces.…”

“…This confirms that the method is stable for the values of β larger than a constant. As the time requires to solve the macro-problem becomes negligible compared to the resolution of the micro-problems, the use of the FDG method is more advantageous since the method is amenable to an efficient parallel implementations using a face-based ghost method [35,36].…”

“…On the contrary, the FDG method suffers from an explosion in the number of degrees of freedom as the the shape functions are now discontinuous. Nevertheless the FDG formulation is advantageous in case of parallel implementations using face-based ghost elements [35,36]. 3-dimensional implementations of both the EDG and FDG methods are presented in this paper, showing that they can be integrated into conventional parallel finite element codes without significant effort.…”

Elastic damage to crack transition in a coupled non-local implicit discontinuous Galerkin/extrinsic cohesive law framework

“…Nevertheless the computational efficiency of the extrinsic approach is still challenging for 3D parallel applications as it requires mesh topology modifications on the fly. An energetically rigorous and computationally efficient way to introduce a CZM is to combine the extrinsic cohesive law with a discontinuous Galerkin (DG) approach [22,23,24,25,26,27]. With this hybrid DG/ECL method, interface elements are inserted between bulk elements at the beginning of the simulation, but the consistency and continuity during the pre-fracture stage are ensured by having recourse to the DG interface terms, contrarily to a classical intrinsic CZM.…”