Summary In this work, a decoupled computational homogenization method for nonlinear elastic materials is proposed using neural networks. In this method, the effective potential is represented as a response surface parameterized by the macroscopic strains and some microstructural parameters. The discrete values of the effective potential are computed by finite element method through random sampling in the parameter space, and neural networks are used to approximate the surface response and to derive the macroscopic stress and tangent tensor components. We show through several numerical convergence analyses that smooth functions can be efficiently evaluated in parameter spaces with dimension up to 10, allowing to consider three‐dimensional representative volume elements and an explicit dependence of the effective behavior on microstructural parameters like volume fraction. We present several applications of this technique to the homogenization of nonlinear elastic composites, involving a two‐scale example of heterogeneous structure with graded nonlinear properties. Copyright © 2015 John Wiley & Sons, Ltd.

This paper couples bulk damage modeling and cohesive zone modeling to get the benefits of both. Damage brings the directionality for the crack propagation as well as the possibility of crack branching while cohesive zone modeling allows for an explicit discrete crack modeling. The coupling is made easy through the Thick Level Set approach. The originality is that the coupling induces concurrent development of bulk and interface degradation.

International audienceUsing thin reinforcements is a common way to strengthen structures, as in reinforced concrete for example. From a numerical point of view, dealing with these reinforcements is tedious, because of their diameter which is usually small compared to the characteristic dimensions of the structures, therefore requiring very fine meshes to represent them accurately. In this paper, a new approach allowing to mix a volumic and a lineic modeling of the reinforcements is proposed. Fine meshes with a volumic representation of the reinforcements are used in the zones of interest of the structure, whereas coarser meshes associated to lineic elements are used in the rest of the structure in order to decrease the computing times. A methodology to ensure the transition between both modeling is proposed, so that the results in the zones of interest are similar to the results that would be obtained with a full volumic representation of the reinforcements. The efficiency of the method is illustrated on several examples, involving linear elasticity and plasticity