Computational mechanics balance laws

General physical laws often state that quantities like mass, energy, and momentum are conserved. In computational mechanics, the most important of these balance laws pertains to linear momentum (when reckoned per unit volume, linear momentum may be expressed as the material density p times velocity v). The balance equation for linear momentum may be considered as a generalization of Newton s second law, which states that mass times acceleration equals total force. As we saw in the previous section, stresses in a material produce tractions, which may be considered as internal forces. In addition, external forces such as gravity may contribute to the total force. These are commonly reckoned per unit mass and are usually referred to as body forces to distinguish them from tractions, which may be considered as surface forces. For a one-dimensional motion, balance of linear momentum requires that (37,38)... 

To sum up, the realistic as-woven geometry of the 3D warp interlock fabrics should be well represented in numerical model, and the variation of the cross-sectional shape of the yams should be taken into account. The identification of a material s mechanical behaviour law is often difficult to achieve for a 3D warp interlock structure. It should highlight here that the computational cost of the forming simulation of the thick warp interlock preform is more important as compared to the 2D fabric therefore, it should find a good balance between forming simulation accuracy and computational efficiency. 

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