When simulating the process from elastic–plastic deformation, damage to failure in a metal structure collision, it is necessary to use the large shell element due to the calculation efficiency, but this would affect the accuracy of damage evolution simulation. The compensation algorithm adjusting failure strain according to element size is usually used in the damage model to deal with the problem. In this paper, a new nonlinear compensation algorithm between failure strain and element size was proposed, which was incorporated in the damage model GISSMO (Generalized incremental stress state dependent damage model) to characterize ductile fracture. And associated material parameters were calibrated based on tensile experiments of aluminum alloy specimens with notches. Simulation and experimental results show that the new compensation algorithm significantly reduces the dependence of element size compared with the constant failure strain model and the damage model with the linear compensation algorithm. During the axial splitting process of a circular tubular structure, the new compensation algorithm keeps the failure prediction errors low over the stress states ranging from shear to biaxial tension, and achieves the objective prediction of the damage evolution process. This study demonstrates how the compensation algorithm resolves the contradiction between large element size and fracture prediction accuracy, and this facilitates the use of the damage model in ductile fracture prediction for engineering structures.

For design and application of particulate reinforced metal matrix composites (PRMMCs), it is essential to predict the material strengths and understand how do they relate to constituents and microstructural features. To this end, a computational approach consists of the direct methods, homogenization, and statistical analyses is introduced in our previous studies. Since failure of PRMMC materials are often caused by time-varied combinations of tensile and shear stresses, the established approach is extended in the present work to take into account of these situations. In this paper, ultimate strengths and endurance limits of an exemplary PRMMC material, WC-Co, are predicted under three independently varied tensile and shear stresses. In order to cover the entire load space with least amount of weight factors, a new method for generating optimally distributed weight factors in an n dimensional space is formulated. Employing weight factors determined by this algorithm, direct method calculations were performed on many statistically equivalent representative volume elements (SERVE) samples. Through analyzing statistical characteristics associated with results the study suggests a simplified approach to estimate the material strength under superposed stresses without solving the difficult high dimensional shakedown problem.