According to this method, an nth order recursive meshfree gradient is formulated as an interpolation of the (n − 1)th order gradients by standard first order meshfree gradients, which finally can be expressed as a successive multiplication of standard first order meshfree gradients. Results indicate that MPM is capable of predicting the large deformation response and energy absorption properties of cellular structures.Ī general arbitrary order recursive gradient formulation is presented for meshfree approximation. Validation involves a comprehensive evaluation of different simulation parameters, namely model refinement, rate of loading and boundary conditions. The performance of the numeric models is evaluated using experimental measurements of the force-deformation curve and energy-absorption capacity. Experimental data in the literature is used, from which geometric and material properties of cellular systems (in the form of stacked tubes) are extracted and used to validate the numerical model. An in-house computer code is developed for this purpose. This study evaluates the performance of MPM for such simulations. These features make MPM attractive for the simulation of cellular structures under large deformations. At the same time, being a particle-based approach, it is also well-suited for problems involving large deformations and contact. As a simulation tool, the material point method (MPM) simplifies the creation of intricate geometries.

However, accurate simulation of the response of these materials and structures is rather complex. Cellular materials and structures have been shown to be highly effective in the context of energy absorption systems.

Meshfree particle methods pdf