Identifying Material Parameters for a Micro-Polar Plasticity Model via X-Ray Micro-Computed Tomographic (Ct) Images: Lessons Learned From the Curve-Fitting Exercises

Abstract

Unlike a conventional first-order continuum model, the material parameters of which can be identified via an inverse problem conducted at material point that exhibits homogeneous deformation, a higher-order continuum model requires information from the derivative of the deformation gradient. This study concerns an integrated experimental-numerical procedure designed to identify material parameters for higher-order continuum models. Using a combination of micro-CT images and macroscopic stress-strain curves as the database, we construct a new finite element inverse problem which identifies the optimal value of material parameters that matches both the macroscopic constitutive responses and the meso-scale micropolar kinematics. Our results indicate that the optimal characteristic length predicted by the constrained optimization procedure is highly sensitive to the types and weights of constraints used to define the objective function of the inverse problems. This sensitivity may in return affect the resultant failure modes (localized vs. diffuse), and the coupled stress responses. This result signals that using the mean grain diameter alone to calibrate the characteristic length may not be sufficient to yield reliable forward predictions.

A configurational force for adaptive re-meshing of gradient-enhanced poromechanics problems with history-dependent variables

“…The path-dependent responses of geological materials, such as clay, sedimentary rock, limestone and crystalline rock are inherently anisotropic and size-dependent. These material characteristics can be captured, for example, via nonlocal models by incorporating the internal microstructure (e.g., [1][2][3][4][5]) or gradient plasticity models (e.g., [6][7][8][9][10][11]). Due to the introduction of a material length scale, the resultant computational models are able to circumvent the spurious mesh bias even in the post-bifurcation regimes where strain localization occurs.…”

“…While there are theoretical frameworks that capture the size effect of metals with isochoric plastic flow (e.g., [7,[11][12][13][14][15][16]), the applications of these frameworks often present additional challenges on the computational resources due to high demand of degree of freedom required to resolve the gradients and fluxes in a discretized spatial domain. Presumably, this can be solved by using a very fine spatial discretization related to the length scale of the material models.…”

“…where the regularization is established through the characteristic (plastic) length scale l p . Note that l p not only constitutes as the characteristic length of the materials, but also prevents mesh sensitivity upon strain localization [11,[36][37][38]. In this work, we introduce gradient dependence to the local preconsolidation pressure p ′ c such that p ′ c =ᾱ.…”

Mixed Arlequin method for multiscale poromechanics problems

“…For instance, Fleck and Hutchinson [8] incorporate a strain gradient term into constitutive models such that multiple material length parameters can be defined for the field equations corresponding to different dominant mechanisms. Also, for capturing deformation bands much thinner than feasible mesh sizes, one can insert enhanced basis functions or localization elements to embed strong or weak discontinuous displacement fields [9][10][11][12].The second category of multiscale methods is a class of hierarchical methods that incorporate micro-structural information from unit cells to compute effective (homogenized) properties of coarse (macroscopic) domains [13][14][15][16][17][18]. Kouznetsova et al [19] present a gradient-enhanced homogenization scheme which obtains macroscopic stress, strain measure, and their gradients from solutions of boundary-value problems applied on representative volume elements.…”

“…The second category of multiscale methods is a class of hierarchical methods that incorporate micro-structural information from unit cells to compute effective (homogenized) properties of coarse (macroscopic) domains [13][14][15][16][17][18]. Kouznetsova et al [19] present a gradient-enhanced homogenization scheme which obtains macroscopic stress, strain measure, and their gradients from solutions of boundary-value problems applied on representative volume elements.…”