A Multifeatured Data-Driven Homogenization for Heterogeneous Elastic Solids

A computational homogenization of heterogeneous solids is presented based on the data-driven approach for both linear and nonlinear elastic responses. Within the Double-Scale Finite Element Method (FE2) framework, a data-driven model is proposed to substitute the micro-level Finite Element (FE) simulations to reduce computational costs in multiscale simulations. The heterogeneity of porous solids at the micro-level is considered in various material properties and geometrical attributes. For material properties, elastic constants, which are Lame’s coefficients, are subjected to be heterogeneous in the linear elastic responses. For geometrical features, different numbers, sizes, and locations of voids are considered to reflect the heterogeneity of porous solids. A database for homogenized microstructural responses is constructed from a series of micro-level FE simulations, and machine learning is used to train and test our proposed model. In particular, four geometrical descriptors are designed, based on N-probability and lineal-path functions, to clearly reflect the geometrical heterogeneity of various microstructures. This study indicates that a simple deep neural networks model can capture diverse microstructural heterogeneous responses well when given proper input sources, including the geometrical descriptors, are considered to establish a computational data-driven homogenization scheme.

Another perspective on elastic and plastic anisotropy of textured metals

In textured metals, the elastic directionality reflects the crystallographic organization, while the plastic flow follows the preferential pathways of deformation beyond the elastic limit. In here, the elastic and plastic anisotropies are characterized by two observers. One of them is immersed into the material and, while there, is unaware of the texture-induced reorganizations, still, is in a position to detect elastic distortions. Another observer is located outside the material, monitors the elastic strain too and realizes that texture makes the elastic responses directional. The externally measured elastic strain will be called the texture strain. The key idea is to determine the transformation rules that correlate the elastic strains seen by the two observers. In what follows, the rules are derived by projecting the texture-distorted basis onto the basis of the external observations. It turns out that the rules reproduce directionality of elastic properties and include constraints that result from the limits imposed by the yield stress. The elastic anisotropy is linked to the strain that is free of the plasticity-induced constraints. By contrast, the constraints enable complete characterization of the plastic flow directionality. The concept is derived in the framework of tensor representations discussed in the electronic supplementary material.

Elastic Responses of a Composite Shell Structure Subjected to Impact Loading

Received 17 December 2019; accepted 17 June 2020 This work investigated the elastic responses of a composite laminate shell subjected to a transverse low-velocity impact. The governing equation based on the equations of motion of both the impactor and target was developed to detetrmine the impact force. The displacement of the shell subjected to unit impulse loading was solved using the finite element method. A non-linear differential equation in terms of the indentation depth was derived by incorporating the Hertzian contact law and theory of convolution. Runge-Kutta method was employed to solve the non-linear integro-differential equation, leading to the determination of the impact force at the point of contact between the impactor and the composite shell. The elastic responses including the displacement and stress of the composite laminate shell were evaluated using the finite element method by exerting the impact force on the apex of the composite shell. Present approach was verified with the analytical, experimental and numerical results reported in the existing literatures. The influences of stacking sequence of the composite laminate shell on the impact responses were examined through a series of parametric studies. In addition, impact responses of the spherical shells with different materials such as steel, aluminum and glass were studied.

Elastostatics of Bernoulli–Euler Beams Resting on Displacement-Driven Nonlocal Foundation

The simplest elasticity model of the foundation underlying a slender beam under flexure was conceived by Winkler, requiring local proportionality between soil reactions and beam deflection. Such an approach leads to well-posed elastostatic and elastodynamic problems, but as highlighted by Wieghardt, it provides elastic responses that are not technically significant for a wide variety of engineering applications. Thus, Winkler’s model was replaced by Wieghardt himself by assuming that the beam deflection is the convolution integral between soil reaction field and an averaging kernel. Due to conflict between constitutive and kinematic compatibility requirements, the corresponding elastic problem of an inflected beam resting on a Wieghardt foundation is ill-posed. Modifications of the original Wieghardt model were proposed by introducing fictitious boundary concentrated forces of constitutive type, which are physically questionable, being significantly influenced on prescribed kinematic boundary conditions. Inherent difficulties and issues are overcome in the present research using a displacement-driven nonlocal integral strategy obtained by swapping the input and output fields involved in Wieghardt’s original formulation. That is, nonlocal soil reaction fields are the output of integral convolutions of beam deflection fields with an averaging kernel. Equipping the displacement-driven nonlocal integral law with the bi-exponential averaging kernel, an equivalent nonlocal differential problem, supplemented with non-standard constitutive boundary conditions involving nonlocal soil reactions, is established. As a key implication, the integrodifferential equations governing the elastostatic problem of an inflected elastic slender beam resting on a displacement-driven nonlocal integral foundation are replaced with much simpler differential equations supplemented with kinematic, static, and new constitutive boundary conditions. The proposed nonlocal approach is illustrated by examining and analytically solving exemplar problems of structural engineering. Benchmark solutions for numerical analyses are also detected.

Anisotropic hyperelastic constitutive modeling of in-plane finite deformation responses of commercial composite hexagonal honeycombs

This research presents the adaptation of an anisotropic hyperelastic constitutive model for predicting the experimentally observed in-plane, orthotropic, bi-modular and nonlinear-elastic responses of a commercial adhesively bonded HRP-C fiberglass/phenolic hexagonal honeycomb core. The hyperelastic constitutive model is evaluated under simple states of loading using single-element finite element analysis. The predictions of the model, including stress-strain behavior, Poisson effects, and strain energy densities, are compared with test data for the in-plane uniaxial tension/compression responses of the honeycomb core as well as the single-element model with a linear orthotropic constitutive model to highlight the effectiveness of the hyperelastic model at high strain levels. Good agreement is observed between the model predictions and test data. Tension tests in ribbon and transverse directions with the full-scale honeycomb core are also simulated to ensure the suitability of the single element model for simulations of the simple loading cases and preliminary validation process.

Elastostatics of Bernoulli-Euler Beams Resting on Displacement-Driven Nonlocal Foundation

The simplest elasticity model of foundation underlying a slender beam under flexure was conceived by Winkler, requiring local proportionality between soil reactions and beam deflection. Such an approach leads to well-posed elastostatic and elastodynamic problems, but, as highlighted by Wieghardt, it provides elastic responses which are not technically significant for a wide variety of engineering applications. Thus, Winkler's model was replaced by Wieghardt himself by assuming that the beam deflection is the convolution integral between soil reaction field and an averaging kernel. Due to conflict between constitutive and kinematic compatibility requirements, the corresponding elastic problem of an inflected beam resting on Wieghardt foundation results to be ill-posed. Modifications of the original Wieghardt model were proposed by introducing fictitious boundary concentrated forces of constitutive type, which are physically questionable, being significantly influenced on prescribed kinematic boundary conditions. Inherent difficulties and issues are overcome in the present research using a displacement-driven nonlocal integral strategy got by swapping input and output fields involved in Wieghardt's original formulation. That is, nonlocal soil reaction fields are output of integral convolutions of beam deflection fields with an averaging kernel. Equipping the displacement-driven nonlocal integral law with the bi-exponential averaging kernel, an equivalent nonlocal differential problem, supplemented with non-standard constitutive boundary conditions involving nonlocal soil reactions, is established. As a key implication, the integro-differential equations governing the elastostatic problem of an inflected elastic slender beam resting on displacement-driven nonlocal integral foundation are replaced with much simpler differential equations supplemented with kinematic, static and new constitutive boundary conditions. The proposed nonlocal approach is illustrated by examining and analytically solving exemplar problems of structural engineering. Benchmark solutions for numerical analyses are also detected.

Exploring the diversity of elastic responses of crystalline cadmium(ii) coordination polymers: from elastic towards plastic and brittle responses

Noticeable differences in mechanically induced elastic responses were observed for isostructural crystalline coordination polymers, and their mechanical properties were examined through a highly integrated approach, using both theory and experiment.