This study addresses the application of the modified Constitutive Relation Error to field identification problems in the framework of elastostatics. We show how relevant is the addition of a gradient-penalizing regularization term (in norm 1 or 2 ), and emphasize the role played by unreliable boundary conditions. This leads to the proposition of a method using two parameters, for which automatic determination is addressed. All theoretical assessments are illustrated on experimental data. The test-problem consists in the identification of the heterogeneous fiber-orientation in a woven fabric composite from a unique quasi-static tensile test with digital image correlation.

The internal structure of composite materials is modified during manufacturing. The formation of woven prepregs or dry preforms changes the angle between the warp and weft yarns. The damage behaviour of the consolidated composite is modified by these changes of angle. It is important when designing a composite part to consider this modification when calculating the damage in order to achieve a correct dimensioning. In this paper, a damage calculation approach of the consolidated textile composite that takes into account the change in orientation of the yarns due to forming is proposed. The angles after forming are determined by a simulation of the draping based on a hypoelastic behaviour of the woven fabric reinforcement. Two orthogonal frames based on the warp and weft directions of the textile reinforcement are used for the objective integration of stresses. Damage analysis of the cured woven composite with non-perpendicular warp and weft directions is achieved by replacing it with two equivalent Unidirectional (UD) plies representing the yarn directions. For each ply, a model based on Continuum Damage Mechanics (CDM) describes the progressive damage. Two examples are presented, a bias extension specimen and the hemispherical forming coupon. In both cases, the angles between the warp and weft yarns are changed. It is shown that the damage calculated by taking into account these angle changes is greatly modified.

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The failure of laminated composite structures is linked to the numerous mechanisms that can appear during the material degradation phase under loading. The approach proposed here is to use Continuum Damage Mechanics to describe the matrix degradation at the ply scale and a non-local criterion, called Fracture Characteristic Volume (FCV), to predict the failure in the fiber direction. The FCV is a circular cylinder with a thickness equal to that of the ply where it is applied. The criterion is defined by comparing an average value inside the FCV, the stress in the fiber direction for example, to a maximum allowable value. This approach has been validated for the prediction of failure for complex geometries with stress concentrations in tension. The objective of this paper is to study the effectiveness of this criterion on different laminates and concentration types in the case of compression.