A Micropolar Peridynamic Theory in Linear Elasticity

A state-based micropolar peridynamic theory for linear elastic solids is proposed. The main motivation is to introduce additional micro-rotational degrees of freedom to each material point and thus naturally bring in the physically relevant material length scale parameters into peridynamics. Non-ordinary type modeling via constitutive correspondence is adopted here to define the micropolar peridynamic material. Along with a general three dimensional model, homogenized one dimensional Timoshenko type beam models for both the proposed micropolar and the standard non-polar peridynamic variants are derived. The efficacy of the proposed models in analyzing continua with length scale effects is established via numerical simulations of a few beam and plane-stress problems

A thermo-visco-plastic damage model and SPH simulations of plugging failure

A thermo-visco-plasticity model, recently developed based on a microinertia driven dynamic flow rule, is exploited to account for damage due to fracture. This is accomplished by adjoining the equations for thermo-visco-plasticity, herein discretized through the smooth particle hydrodynamics (SPH), with a ``pseudospring'' based discrete damage model. In treating ductile fractures, this coupled material model accounts for the inertia associated with moving microstructural defects and time lags for the dissipative fluxes to attain the steady state. In this approach, while the microinertia-driven flow rule provides a vehicle to evolve plastic strain, pseudosprings are exploited to treat material damage and the resulting reduced force transfer. The current scheme does not necessitate the introduction of a yield or damage surface in evolving the plastic-strain/damage parameters, and thus the numerical implementation avoids a computationally intensive return mapping. We demonstrate the performance of the proposed model through SPH-based numerical simulations and also undertake a validation exercise against experimental observations from gas-gun penetration tests on an 8-mm thick Weldox 460 E steel plate

A thermodynamically consistent peridynamics model for visco-plasticity and damage

This article presents a unified visco-plastic-damage model in the peridynamics set-up which may be applied across different regime of strain rates and temperatures. In the model, we introduce two internal variables, one describing plastic flow and other the damage in the material. Exploiting the idea of master balance, in addition to the conventional momentum balances, we postulate micro-force balances for both plastic flow and damage evolution in terms of additional peridynamic force states. The equations of motion are in the form of integro-differential equations and do not require continuity of field variables. Using the idea of energy equivalence and entropy equivalence, constitutive relations for the peridynamic force states are determined. The proposed peridynamic visco-plastic-damage model may be thought as a non-trivial extension of the recently developed peridynamic viscoplasticity model (Rahaman et al.,2017). The current scheme couples the visco-plasticity and damage in a thermo-dynamically consistent manner and provides temperature evolution which reflects contribution from both plasticity and damage. The efficacy of the model is demonstrated through simulations of the adiabatic shear band propagation as observed in Kalthoff-Winkler experiment and the shear plugging failure of Weldox 460 E steel plates along with the determination of the ballistic limit. (C) 2019 Elsevier B.V. All rights reserved

A peridynamic model for plasticity: Micro-inertia based flow rule, entropy equivalence and localization residuals

This article presents a non-ordinary state-based peridynamic (PD) model for thermo-visco-plasticity that incorporates a microinertia driven dynamic flow rule. In addition to the three displacement degrees of freedom, the model assigns, to each particle, an internal degree of freedom, namely, the equivalent plastic strain. The flow rule itself is in the form of an integro-differential micro-force balance, written in terms of appropriate PD states associated with micro-stresses corresponding to the internal degree of freedom. An equation for entropy balance, adapted to the PD setup, is also proposed. Along with the internal energy equivalence, we exploit a notion of equivalence of the local entropy production for the constitutive modelling of the force states. As we also demonstrate, the PD model naturally accounts for the localization residual terms in the local balances for internal energy and entropy, originally conceived of by Edelen and co-workers nearly half a century ago as a source of nonlocal interaction. The model is numerically implemented for the problem of impact between two 4340 steel plates, and the results show that the model provides information on nontrivial effects of micro-inertia on the plastic flow and temperature generation. By incorporating a classical damage model in the PD set-up, we also discuss an extension of the approach for ductile failure, and report on the numerical results against tension test on an A440 steel plate with holes. (C) 2017 Elsevier B.V. All rights reserved

Variational formulation for dissipative continua and an incremental J-integral

Our aim is to rationally formulate a proper variational principle for dissipative (viscoplastic) solids in the presence of inertia forces. As a first step, a consistent linearization of the governing nonlinear partial differential equations (PDEs) is carried out. An additional set of complementary (adjoint) equations is then formed to recover an underlying variational structure for the augmented system of linearized balance laws. This makes it possible to introduce an incremental Lagrangian such that the linearized PDEs, including the complementary equations, become the Euler-Lagrange equations. Continuous groups of symmetries of the linearized PDEs are computed and an analysis is undertaken to identify the variational groups of symmetries of the linearized dissipative system. Application of Noether's theorem leads to the conservation laws (conserved currents) of motion corresponding to the variational symmetries. As a specific outcome, we exploit translational symmetries of the functional in the material space and recover, via Noether's theorem, an incremental J-integral for viscoplastic solids in the presence of inertia forces. Numerical demonstrations are provided through a two-dimensional plane strain numerical simulation of a compact tension specimen of annealed mild steel under dynamic loading

A Phase-Field Damage Model for Orthotropic Materials and Delamination in Composites

A phase-field damage model for orthotropic materials is proposed and used to simulate delamination of orthotropic laminated composites. Using the deviatoric and hydrostatic tensile components of the stress tensor for elastic orthotropic materials, a degraded elastic free energy that can accommodate damage is derived. The governing equations follow from the principle of virtual power and the resulting damage model, by its construction, conforms with the physical relevant condition of no matter interpenetration along the crack faces. The model also dispenses with the traction separation law, an extraneous hypothesis conventionally brought in to model the interlaminar zones. The model is assessed through numerical simulations on delaminations in mode I, mode II, and another such problem with multiple initial notches. The present method is able to reproduce nearly all the features of the experimental load displacement curves, allowing only for small deviations in the softening regime. Numerical results also show forth a superior performance of the proposed method over existing approaches based on a cohesive law