Micromechanics Plugin for Abaqus

The increasing complexity of material systems and manufacturing techniques used to create engineering structures continually drives the need to consider physical phenomena occurring at a variety of scales to realistically simulate a structure’s response. Composites and metamaterials provide highly tailored, optimized responses and blur the line between structure and material. Their effective response observed at the scale of an engineering component is entirely dependent on the microstructural response of the material system.

Multiscale methods provide means to bridge these scales – from the scale of an engineering component down to the microscale where the material’s microstructure is resolved. One such method is the Finite Element Representative Volume Element (FE-RVE) approach. In this approach, a finite element model of the material’s microstructure is created that is large enough to yield the material’s aggregate behavior. Through the imposition of appropriate boundary conditions, the FE-RVE can be loaded with a far-field (averaged over the RVE) quantity that corresponds to that field quantity observed at the scale of an engineering component. The local solution field in the RVE’s microstructure can then be obtained through finite element analysis.

One special type of RVE is the periodic unit cell. For microstructures that exhibit repeating patterns, the representative/effective response can be obtained from a single repeating cell through the application of periodic boundary conditions.

The value of FE-RVE simulation

The ability to drive an FE-RVE using a far-field quantity (e.g., strain, temperature gradient) to obtain the local solution in the microstructure as well as the far-field response (e.g., stress, heat flux) enables a broad variety of helpful analyses.

Material calibration

By applying appropriate far-field loadings to the RVE and observing the effective response, it is possible to simulate material tests (e.g. uniaxial pull tests, shear tests, stress relaxation tests, etc.) that are used to measure or calibrate effective macroscopic properties for various constitutive models, such as elastic moduli, plastic hardening curves, viscoelastic prony series, and hyperelastic constants, among others.

Virtual testing

The ability to simulate material tests permits quick and inexpensive study of composite/material parameters that can be varied (such as volume fraction or lattice size) and has the potential to reduce the number of material systems that must be physically tested.

Determination of unknown constituent properties

In many cases, it may not be possible to directly measure or test certain properties of a composite’s constituents. For instance, consider the transverse moduli of a carbon fiber, which typically has a diameter on the order of 10 μm, or the in-situ yield stress of an alloy in a lattice fabricated using selective laser sintering (SLS) additive manufacturing. Through the use of optimization methods, it is possible to use FE-RVE models to solve the inverse problem of determining the constituent/in-situ properties that yield an effective material response prediction that matches experiments. Such calibrated properties can be useful for more comprehensive investigations of material behaviors or for predicting the response of new composite or metamaterial systems.

Prediction of microscale failure, damage, and plasticity

Failure or nonlinear response of a composite initiates within its microstructure. Therefore, predicting whether a composite will fail or experience plasticity or damage depends on knowing the solution within the microstructure. FE-RVE modeling enables an analyst to use the far-field solution from an engineering component simulation to predict if it will induce failure or some other nonlinear material behavior (e.g. damage or plasticity) within the material’s microstructure that may not be correctly accounted for in the original engineering component simulation. Furthermore, an a prioi examination of the solution in the microstructure under a broad variety of multiaxial loads allows an analyst to predict the safe envelope of loadings for a material system.

Validation of mean-field homogenization

The primary detractor for the FE-RVE approach is that it’s generally too expensive to be run concurrently as part of an analysis at the scale of an engineering component. In such an analysis, the nonlinear response of every composite material point in the component-scale model would be determined using a separate FE-RVE, which would generally be very costly both in terms of time and computing requirements. However, alternative multiscale methods exist which are fast enough to be run concurrently as part of an analysis of an engineering component. One of these - mean field homogenization (MFH) - is a new feature introduced in Abaqus 2017. MFH relates the mean solution field in each constituent to the far-field quantity observed at the component scale through analytical equations that can generally be solved in a negligible amount of time as compared to the FE-RVE approach. The main disadvantages of MFH are (1) it is based on simplifying assumptions that may not be appropriate in all circumstances and (2) it does not account for spatial variation in the solution field within each constituent. The FE-RVE approach permits analysts to study the response of the composite under the same far-field history without the assumptions inherent to MFH. Direct comparisons can be made between the effective responses and constituent-averaged field quantities obtained using MFH and the FE-RVE approach, allowing analysts to determine whether the assumptions of MFH are appropriate for the composite and loading they are examining, and also helping analysts to calibrate their MFH model so that it gives more realistic response prediction.

Example Workflow

The following figure illustrates a multiscale workflow over several different scales that can be accomplished using FE-RVE analysis.  

A fiber-matrix unit cell is used to obtain tow properties which are used in a laminated textile unit cell model. This textile unit cell is used to obtain the effective section stiffness properties (the ABD matrix) for the laminated textile. These section stiffnesses are assigned to shell elements in an analysis of an engineering structure. The engineering structure is analyzed under some service load, and the shell section curvature and membrane strain are obtained at some point of interest. These are used to drive the textile laminate unit cell model, and transverse stresses in tows are examined to see if they are sufficiently high to cause matrix cracking in the tows. The local strain history at some point in the tow is then used to drive the fiber-matrix unit cell to predict whether it will experience plasticity due to longitudinal shear.

The Micromechanics Plugin for Abaqus

Abaqus has included the technology required to perform FE-RVE analysis for quite some time. However, setting up these analyses can be a tedious and time-consuming exercise. Therefore, a plugin has been developed for Abaqus/CAE that facilitates the setup, analysis, and post-processing of FE-RVE models.

The plugin provides a number of functionalities.

Parameterized FE-RVE generation for certain geometries:

• Unidirectional continuous fiber reinforced composites with hexagonal fiber packing
• Body-centered ellipsoids
• Users can also develop their own FE-RVE geometries

Boundary Conditions:

• Periodic BCs, even if the mesh isn’t periodic
• Taylor BCs (RVE boundary constrained to far-field gradient)
• Neumann BCs (far-field flux applied to RVE boundary)
• Drive RVE with user-defined load history
• Drive RVE with field history from a component-scale FE analysis

Study of various RVE physics:

• Mechanical analysis of both solid-continuum and shell-like microstructures
• Steady state heat transfer
• Steady state coupled temperature-displacement

Homogenization:

• Elastic stiffness
• Thermal expansion
• Shell section stiffness (ABD matrix)
• Thermal conductivity
• Fully coupled conductivity + stiffness (9x9 constitutive matrix)
• Density
• Specific heat

Post Processing:

• Field averaging in the whole RVE and per-phase
• Histogram generation

This post on the Simulia Learning Community describes the plugin and provides instructions for obtaining it.