Peridynamic (PD) models are commonly implemented by exploiting a particle-based method referred to as standard scheme. Compared to numerical methods based on classical theories (e.g., the finite element method), PD models using the meshfree standard scheme are typically computationally more expensive mainly for two reasons. First, the nonlocal nature of PD requires advanced quadrature schemes. Second, non-uniform discretizations of the standard scheme are inaccurate and thus typically avoided. Hence, very fine uniform discretizations are applied in the whole domain even in cases where a fine resolution is per se required only in a small part of it (e.g., close to discontinuities and interfaces). In the present study, a new framework is devised to enhance the computational performance of PD models substantially. It applies the standard scheme only to localized regions where discontinuities and interfaces emerge, and a less demanding quadrature scheme to the rest of the domain. Moreover, it uses a multi-grid approach with a fine grid spacing only in critical regions. Because these regions are identified dynamically over time, our framework is referred to as multi-adaptive. The performance of the proposed approach is examined by means of two real-world problems, the Kalthoff–Winkler experiment and the bio-degradation of a magnesium-based bone implant screw. It is demonstrated that our novel framework can vastly reduce the computational cost (for given accuracy requirements) compared to a simple application of the standard scheme.

Two nanomicas of similar composition, containing muscovite and quartz, but with different particle size distributions, have been used to prepare transparent epoxy nanocomposites. Their homogeneous dispersion, due to the nano-size, was achieved even without being organically modified, and no aggregation of the nanoparticles was observed, thus maximizing the specific interface between matrix and nanofiller. No exfoliation or intercalation has been observed by XRD, despite the significant dispersion of the filler in the matrix which produced nanocomposites with a loss in transparency in the visible domain of less than 10% in the presence of 1% wt and 3% wt of mica fillers. The presence of micas does not affect the thermal behavior of the nanocomposites, which remains similar to that of the neat epoxy resin. The mechanical characterization of the epoxy resin composites revealed an increased Young’s modulus, whereas tensile strength was reduced. A peridynamics-based representative volume element approach has been implemented to estimate the effective Young’s modulus of the nanomodified materials. The results obtained through this homogenization procedure have been used as input for the analysis of the nanocomposite fracture toughness, which has been carried out by a classical continuum mechanics–peridynamics coupling approach. Comparison with the experimental data confirms the capability of the peridynamics-based strategies to properly model the effective Young’s modulus and fracture toughness of epoxy-resin nanocomposites. Finally, the new mica-based composites exhibit high values of volume resistivity, thus being excellent candidates as insulating materials.