Rudra Bhattacharrya, Ruize Hu and Xiang Zhang presented their research at ASME IMECE 2017 in Tampa, FL
The title of the Xiaoyu’s presentation was: “Mesh Objective Multiscale Damage Modeling for Fiber-Composites Subjected to Multi-Axial Loading”.
The damage accumulation and progression in structural components made of fiber-reinforced composites is complicated due to the interactions between complex microstructural damage mechanisms. In particular, the internal stress states within a laminated composite are multidimensional even when subjected to unidirectional loading. In this study, a multiscale continuum damage model is presented for fiber composites to predict failure under different stress triaxiality. The particular focus of this work is on capturing the ductile failure behavior under shear dominated load states along with the brittle behavior observed under axial loading, and relating the observed behavior at the lamina scale to the constitutive constituents, i.e. the fiber and the resin.
A thermodynamically consistent continuum damage mechanics model is developed for the polymeric resin material, and deployed within the eigendeformation-based reduced order homogenization (EHM) framework. EHM is a reduced order multiscale modeling approach that has been demonstrated to capture the behavior of composite structures of various microstructural configurations. The proposed damage model directly addresses the presence of nonlinearity observed under the shear dominated load states. The continuum damage mechanics based model is regularized using a multiscale version of crack band modeling to alleviate the issues of mesh size and microstructure size effects. The proposed framework is verified using numerical simulations, and applied to investigate static tensile and compressive behavior of IM7/977-3, a graphite fiber reinforced epoxy composite.
The title of the Ruize’s presentation was: “SSpatial-Temporal Nonlocal Homogenization Model for Transient Wave Propagation in Viscoelastic Phononic Crystals”.
Heterogeneous materials exhibit complex response patterns when subjected to dynamic loading due to the intrinsic wave interactions induced by reflections and refractions at material constituent interfaces. Controlling these interactions offer tremendous opportunities in many engineering applications. Acoustic metamaterials and phononic crystals have received significant recent attention due to the unique and tailorable properties including negative effective density and bulk modulus, and wave attenuation within band gaps. Homogenization models, targeting predicting the overall response of heterogeneous materials, provide an efficient route towards analysis and design of phononic crystals and acoustic metamaterials in large scale.
We present a spatial-temporal nonlocal homogenization model for transient wave propagation in elastic and viscoelastic composites. The homogenization model is particularly directed to capturing wave dispersion and attenuation induced by material heterogeneity. The proposed model is derived based on asymptotic homogenization with up to eighth order expansions. A momentum balance equation that is nonlocal in both space and time is consistently derived. Contributions from the high order terms in the momentum balance equation account for the heterogeneity induced wave dispersion and stop band formation. The coefficient tensors of the momentum balance equation are computed directly from microstructural material parameters and geometry. A Hybrid Laplace Transform/Isogeometric Analysis (HLT/IGA) is developed to solve the nonlocal momentum balance equation, which provides global C1 continuity as required by the spatial nonlocal term. The high order boundary conditions are also discussed. Response field in time domain is obtained by applying discrete inverse Laplace transform method. The performance of the proposed model is assessed against direct finite element simulations and compared to classical homogenization models. Examples demonstrating the effect of microstructural morphology, constituent material properties and the effect of viscoelasticity will be presented. The proposed model has demonstrated high level of computational efficiency over direct finite element simulation and accuracy over classical homogenization models. The key contributions of our work are: (1) the proposed model captures the wave dispersion in the first and second pass band and attenuation in the first stop band; (2) all the model parameters are computed directly from the microscale initial-boundary problem as an off-line process; (3) the proposed model is applicable to both elastic and viscoelastic composites.
The title of the Xiang’s presentation was: “Sparse and Scalable Eigenstrain-based Reduced Order Homogenization Models for Polycrystal Plasticity”.
In this work, we seek to develop the computational framework needed to perform multiscale simulations, where polycrystal plasticity modeling at the scale of the material microstructure is fully coupled to structural analysis in the context of computational homogenization. To alleviate the prohibitive computational cost of crystal plasticity finite element (CPFE) on a polycrystal representative volume element (RVE), an accelerated, sparse and scalable eigenstrain-based reduced order homogenization modeling approach is developed. The proposed approach is based on the eigenstrain-based reduced order homogenization model (EHM) for polycrystalline materials, which operates in a computational homogenization setting, and employs concepts from the transformation field theory to pre-compute certain microscale information (e.g. localization tensors, concentration tensors) by evaluating linear elastic microscale problems prior to a macroscale simulation to arrive at model order reduction at the microscale. By this approach, a significant reduction in computational cost is achieved, compared with classical computational homogenization approaches that employ CPFE simulation to describe the microscale response.
While EHM provides approximately two orders of magnitude efficiency compared with CPFE for middle-sized microstructures, its efficiency degrades as microstructure size increases. A grain-cluster accelerated, sparse and scalable reduced order homogenization model has been developed to address this issue. The acceleration is achieved by introducing sparsity into the linearized reduced order system through selectively considering the interactions between grains based on the idea of grain clustering. The proposed approach results in a hierarchy of reduced models that recovers eigenstrain-based homogenization, when full range of interactions are considered, and degrades to the Taylor model, when all inter-grain interactions are neglected. The resulting sparse system is solved efficiently using both direct and iterative sparse solvers, both of which show significant efficiency improvements compared to the full EHM. A layer-by-layer neighbor grain clustering scheme is proposed and implemented to define ranges of grain interactions. Performance of the proposed approach is evaluated by comparing the results against the full EHM and crystal plasticity finite element (CPFE) simulations.