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This paper proposes a method to describe the bi-modular behavior of quasi-brittle materials. The approach is based on using multiple loading functions that are associated with the stress state of the material point. The model also includes degradation laws that control the evolution of the internal variables under tension and compression, which allows the representation of the material response with fidelity. The following approach outlines an objective methodology for improving classical models and provides a theoretical framework for developing new constitutive models. This work also presents an updated version of the Mazars damage model, with improved material parametrization through multiple damage laws. Similarly, the modified von Mises model has been extended to include different functions for damage evolution, combining exponential and continuum polynomial laws for tension and compression. A third model was developed to showcase the full potential of the proposed formulation. This model formulates the Lemaitre and Chaboche criterion, typically used for ductile materials, to describe quasi-brittle materials. The model provides a comprehensive characterization of the tension and compression behavior by utilizing various loading functions and multiple damage laws. Numerical simulations of experimental benchmarks are presented to show the performance of the proposal, including a nonlocal approach to avoid strain localization and mesh dependency problems. • A formulation to represent simply the bi-modularity of quasi-brittle materials by isotropic damage models is presented. • The proposal provides versatility to prescribe any damage law, especially with fill constitutive parameters. • The strategy is applied to classical models present in literature providing an enhancement of the model behavior. • The approach can be extended and applied to other models presented in the literature. [ABSTRACT FROM AUTHOR]

• A method of uncertainty analysis based on the MP-II model was proposed to examine a case of adhesive assembly. • Uncertainty transfer was constructed by a combination of finite-element simulation and a B-spline surrogate model. • The effect of the uncertainties of three types of bonding defects on the center-of-mass drift was understood. • The reliability index was improved and the parameter intervals of the bonding defects were optimized. Multi-source and strong uncertainties of the adhesive assembly process for high-precision inertial devices are critical issues that result in the current low assembly accuracy and poor assembly consistency. This paper addresses the resulting uncertainty in the center-of-mass drift of the float components of a high-precision inertial device. An interval-based non-probabilistic convex model is used to characterize the uncertainty of the bonding defect parameters of the adhesive assembly process, and the uncertainty transferring from those parameters to the center-of-mass drift is constructed by using a surrogate model and numerical simulations. A reliability analysis is carried out to understand the effect of the uncertainties of three types of bonding defects on the center-of-mass drift, and the sensitivities of the center-of-mass drift to the bonding defects are also found. The results show that the reliability index of the center-of-mass drift obtained under the initial parameter intervals is 0.689, indicating the center-of-mass drift at the risk of being out of the accuracy requirement. By adjusting the parameter intervals of the bonding defects to stabilize the center-of-mass of the assembled components, the reliability index is then improved to greater than 1. [ABSTRACT FROM AUTHOR]