E.B. Marin

A Nonlocal Phenomenological Anisotropic Finite Deformation Plasticity Model Accounting for Dislocation Defects

A phenomenological, polycrystalline version of a nonlocal crystal plasticity model is formulated. The presence of geometrically necessary dislocations (GNDs) at, or near, grain boundaries is modeled as elastic lattice curvature through a curl of the elastic part of the deformation gradient. This spatial gradient of an internal state variable introduces a length scale, turning the local form of the model, an ordinary differential equation (ODE), into a nonlocal form, a partial differential equation (PDE) requiring boundary conditions. Small lattice elastic stretching results from the presence of dislocations and from macroscopic external loading. Finite deformation results from large plastic slip and large rotations. The thermodynamics and constitutive assumptions are written in the intermediate configuration in order to place the plasticity equations in the proper configuration for finite deformation analysis.

Review of Hierarchical Multiscale Modeling to Describe the Mechanical Behavior of Amorphous Polymers

Modern computational methods have proved invaluable for the design and analysis of structural components using lightweight materials. The challenge of optimizing lightweight materials in the design of industrial components relates to incorporating structure-property relationships within the computational strategy to incur robust designs. One effective methodology of incorporating structure-property relationships within a simulation-based design framework is to employ a hierarchical multiscale modeling strategy. This paper reviews techniques of multiscale modeling to predict the mechanical behavior of amorphous polymers. Hierarchical multiscale methods bridge nanoscale mechanisms to the macroscale/continuum by introducing a set of structure-property relationships. This review discusses the current state of the art and challenges for three distinct scales: quantum, atomistic/coarse graining, and continuum mechanics. For each scale, we review the modeling techniques and tools, as well as discuss important recent contributions. To help focus the review, we have mainly considered research devoted to amorphous polymers.

Optimization of structures under material parameter uncertainty using evidence theory

An evidence-based approach is developed for optimization of structural components under material parameter uncertainty. The approach is applied to evidence-based design optimization (EBDO) of externally stiffened circular tubes under axial impact load using an isotropic–elastic–plastic plasticity model to simulate dynamic material behaviour. Uncertainty modelling considers the changes in material parameters that are caused by variability in material properties as well as incertitude and errors in experimental data and procedure to determine the material parameters. Spatial variation of material parameters across the structural component is modelled using a field joint belief structure and propagated for the calculation of evidence-based objective function and design constraints. Surrogate models are used in both uncertainty propagation and solution of the optimization problem. The methodology and the solution to the EBDO example problem are presented and discussed.

Coupled experiment/finite element analysis on the mechanical response of porcine brain under high strain rates

This paper presents a coupled experimental/modeling study of the mechanical response of porcine brain under high strain rate loading conditions. Essentially, the stress wave propagation through the brain tissue is quantified. A Split-Hopkinson Pressure Bar (SPHB) apparatus, using a polycarbonate (viscoelastic) striker bar was employed for inducing compression waves for strain rates ranging from 50 to 750 s(-1). The experimental responses along with high speed video showed that the brain tissues response was nonlinear and inelastic. Also, Finite Element Analysis (FEA) of the SHPB tests revealed that the tissue underwent a non-uniform stress state during testing when glue is used to secure the specimen with the test fixture. This result renders erroneous the assumption of uniaxial loading. In this study, the uniaxial volume averaged stress-strain behavior was extracted from the FEA to help calibrate inelastic constitutive equations.

NANOSCALE VOID GROWTH IN MAGNESIUM: A MOLECULAR DYNAMICS STUDY

Molecular dynamics calculations were carried out in single crystal magnesium specimens to reveal the dependence of strain rate, temperature, and orientation of the crystal on damage evolution as defined by pore growth. Two specific crystallographic orientations [0001] and were examined. During a [0001] tensile test, twin boundaries developed at the void surface leading to a constraint on the crystallographic orientation. On the other hand, during the tensile deformation, emission of shear loops in the prismatic slip planes arose when void growth initiated. Furthermore, analysis of the damage components (nucleation, growth and coalescence) revealed that a large number of small voids nucleated that rapidly grew and fractured the specimens independent of the temperature and the strain rate.

On the formulation, parameter identification and numerical integration of the EMMI model :plasticity and isotropic damage.

In this report we present the formulation of the physically-based Evolving Microstructural Model of Inelasticity (EMMI) . The specific version of the model treated here describes the plasticity and isotropic damage of metals as being currently applied to model the ductile failure process in structural components of the W80 program . The formulation of the EMMI constitutive equations is framed in the context of the large deformation kinematics of solids and the thermodynamics of internal state variables . This formulation is focused first on developing the plasticity equations in both the relaxed (unloaded) and current configurations. The equations in the current configuration, expressed in non-dimensional form, are used to devise the identification procedure for the plasticity parameters. The model is then extended to include a porosity-based isotropic damage state variable to describe the progressive deterioration of the strength and mechanical properties of metals induced by deformation . The numerical treatment of these coupled plasticity-damage constitutive equations is explained in detail. A number of examples are solved to validate the numerical implementation of the model.

Concurrent Design of Product-Material Systems using Multilevel Optimization

†‡ § ** In traditional structural optimization, the geometric properties of the product are optimized for a specific set of material properties. This paper seeks to extend the domain of product optimization to also include the material modeling parameters by treating the product and material as a hierarchical multilevel system that can be decomposed and solved using the analytical target cascading (ATC) method. Two material models are considered here. The low-fidelity model is based on a simple elastic-plastic constitutive law with linear hardening whereas the high-fidelity model is based on an internal-state-variable representation that is influenced by the microstructural features of the material. The ATC method is applied to product-material design optimization of a multi-cell, thin-walled tube for impact energy absorption and durability. The integrated product-material optimization problem is solved using both single and multilevel approaches with results compared.

FINITE DEFORMATION ELASTOPLASTICITY FOR RATE AND TEMPERATURE DEPENDENT POLYCRYSTALLINE METALS

An elastoplasticity model is formulated and demonstrated in one-dimension (1D) for modeling finite deformations in po lycrystalline metals. Quasi-static to high strain rate effec ts as well as temperature sensitivity are included. A multiplicativedecomposition of the deformation gradient into elastic, plastic , and thermal parts, that includes a volumetric/isochoric splitof the elastic stretching tensor is assumed. The kinematics and th ermodynamic formulation lead to constitutive equations, str esses, and constraints on the evolution of the internal state varia bles. The model accounts for (i) dislocation drag effects on flow st ress, and (ii) generation (hardening) and annihilation (recover y) of statistically-stored dislocations (SSDs). The resultingmodel is normalized to dimensionless form to allow dimensionless ma terial parameters fit for one metal to approximate the behaviorof another metal of similar lattice structure, if data are limi ted. One dimensional material parameter fitting is demonstrated fortwo refractory metals, body centered cubic (bcc) Tantalum and T ungsten.

Traumatic Injury: Mechanical Response of Porcine Liver Tissue Under High Strain Rate Compression Testing

The injury metrics for dummies in car crash scenarios are typically force and acceleration; however, real injuries in humans are characterized by damage and fracture (rupture) processes of internal tissues and organs. An accurate prediction of the risk of these injuries using modeling and simulation requires knowledge of the mechanical properties of different human tissues/organs under various loading conditions. Especially in high-impact situations, quasi-static biomechanics may not be sufficient in characterizing the actual mechanical response of a tissue; therefore, high-strain rate testing becomes an area of interest [1].Copyright

Development of an internal state variable model to describe the mechanical behavior of amorphous polymer and its application to impact testing

The use of lighter and impact resistant materials, such as polymers, in vehicular systems is an important motivation for the automotive industry as these materials would make vehicles more fuel-efficient without compromising safety standards. In general, polymers exhibit a rich variety of material behavior originating from their particular microstructural (long molecular chains) behavior that is strongly temperature, pressure, and time dependent. To capture such intricate behavior, a number of polymer constitutive models have been proposed and implemented into finite element codes in an effort to solve complex engineering problems (see [1] for a review of these models). However, developing improved constitutive models for polymers that are physically-based is always a challenging area that has important implications for the design of polymeric structural components.