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The simulation of large deformation problems, involving complex history-dependent constitutive laws, is of paramount importance in several engineering fields. Particular attention has to be paid to the choice of a suitable numerical technique such that reliable results can be obtained. In this paper, a Material Point Method (MPM) and a Galerkin Meshfree Method (GMM) are presented and verified against classical benchmarks in solid mechanics. The aim is to demonstrate the good behavior of the methods in the simulation of cohesive-frictional materials, both in static and dynamic regimes and in problems dealing with large deformations. The vast majority of MPM techniques in the literatrue are based on some sort of explicit time integration. The techniques proposed in the current work, on the contrary, are based on implicit approaches, which can also be easily adapted to the simulation of static cases. The two methods are presented so as to highlight the similarities to rather than the differences from “standard” Updated Lagrangian (UL) approaches commonly employed by the Finite Elements (FE) community. Although both methods are able to give a good prediction, it is observed that, under very large deformation of the medium, GMM lacks robustness due to its meshfree natrue, which makes the definition of the meshless shape functions more difficult and expensive than in MPM. On the other hand, the mesh-based MPM is demonstrated to be more robust and reliable for extremely large deformation cases.

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In this work we apply a numerical inverse analysis procedure based on the ICME framework to ensure a required microstructure and combination of properties in the quenched plate. The microstructure is decided first, and the cooling profile needed to obtain such microstructure is then calculated using the CALPHAD approach. Subsequently, an inverse analysis of the heat transfer problem provides the description of the convection mechanism in quenching that results in the demanded cooling profile. An additional constraint is set on the through-thickness thermal gradient to achieve a homogeneous microstructure. Finally, the resultant microstructure is computed. By means of the proposed model we are able to retrieve the necessary quenching process parameters and to quantify the influence of these parameters on the temperature and microstructure distribution within the plate after the quenching.