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Examples of a non-segmented and of a segmented peening pattern. Both patterns make a flat square plate deform into a spherical patch (a) when applied from both sides of the plate. The non-segmented pattern (b) prescribes a gradual variation of the peening intensity over the plate, which is hardly reproducible with peening equipment. The segmented pattern (c) is reproducible because it consists of uniformly treated segments. Both patterns are discretized with triangular finite elements, and the effect of their application can be simulated using the eigenstrain approach. For this, one must establish in advance a one-to-one correspondence between the peening regimes or the intensities, and the induced eigenstrains.

Examples of a non-segmented and of a segmented peening pattern. Both patterns make a flat square plate deform into a spherical patch (a) when applied from both sides of the plate. The non-segmented pattern (b) prescribes a gradual variation of the peening intensity over the plate, which is hardly reproducible with peening equipment. The segmented pattern (c) is reproducible because it consists of uniformly treated segments. Both patterns are discretized with triangular finite elements, and the effect of their application can be simulated using the eigenstrain approach. For this, one must establish in advance a one-to-one correspondence between the peening regimes or the intensities, and the induced eigenstrains.

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Context 1
... solution to the inverse problem in peen forming is a map of local peening parameters (regimes) mapped over the initial geometry of the treated plate, which is called the peening pattern. For instance, Figure 1 shows two peening patterns that allow to shape a flat square plate into a spherical patch. The first steps towards numerical resolution of the inverse problem were made by VanLuchene et al. [4,5], who simulated the effect of peening using the peening-induced forces. ...
Context 2
... computed peening pattern is therefore a discrete map. In the general case, the eigenstrains prescribed to each element vary from one element to another, as it is illustrated in Figure 1 b). On the other hand, the practical conditions of physically applying the peening treatment limit this spatial variation. ...
Context 3
... a simpler and easier process, the segmented peening pattern must involve the fewest possible peening regimes while preserving the precision of the final shape. Figure 1 c) presents an example of a segmented pattern. In practice, such segmented patterns are usually applied using masks [27,28]. ...
Context 4
... eigenstrain value corresponds to a peening regime, so a clustering algorithm is able to prescribe the best suitable peening regime for each segment. This technique allowed, for example, to compute the pattern shown in Figure 1 (c) starting from the non-segmented pattern presented in Figure 1 (b). ...
Context 5
... eigenstrain value corresponds to a peening regime, so a clustering algorithm is able to prescribe the best suitable peening regime for each segment. This technique allowed, for example, to compute the pattern shown in Figure 1 (c) starting from the non-segmented pattern presented in Figure 1 (b). ...