A peridynamic theory for linear elastic shells

A state-based peridynamic formulation for linear elastic shells is presented. The emphasis is on introducing, possibly for the first time, a general surface based peridynamic model to represent the deformation characteristics of structures that have one physical dimension much smaller than the other two. A new notion of curved bonds is exploited to cater for force transfer between the peridynamic particles describing the shell. Starting with the three dimensional force and deformation states, appropriate surface based force, moment and several deformation states are arrived at. Upon application on the curved bonds, such states beget the necessary force and deformation vectors governing the motion of the shell. Correctness of our proposal on the peridynamic shell theory is numerically assessed against static deformation of spherical and cylindrical shells and flat plates

A conformal gauge theory of solids: insights into a class of electromechanical and magnetomechanical phenomena

A gauge theory of solids with conformal symmetry is formulated to model various electromechanical and magnetomechanical coupling phenomena. If the pulled back metric of the current configuration (the right Cauchy-Green tensor) is scaled with a constant, the volumetric part of the Lagrange density changes while the isochoric part remains invariant. However, upon a position dependent scaling, the isochoric part also loses invariance. In order to restore the invariance of the isochoric part, a 1-form compensating field is introduced and the notion of a gauge covariant derivative is utilized to minimally replace the Lagrangian. In view of obvious similarities with the Weyl geometry, the Weyl condition is imposed through the Lagrangian and a minimal coupling is employed so the 1-form could evolve. On deriving the Euler-Lagrange equations based on the action functional, we observe a close similarity with the governing equations for flexoelectricity under isochoric deformation if the exact part of 1-form is interpreted as the electric field and the anti-exact part as the polarization vector. Next, we model piezoelectricity and electrostriction phenomena by contracting the Weyl condition in various ways. Applying the Hodge decomposition theorem on the 1-form which leads to the curl of a pseudo-vector field and a vector field, we also model magnetomechanical phenomena. Identifying the pseudo-vector field with magnetic potential and the vector part with magnetization, flexomagnetism, piezomagnetism and magnetostriction phenomena under isochoric deformation are also modeled. Finally, we consider an analytical solution of the equations for piezoelectricity to provide an illustration on the insightful information that the present approach potentially provides.Comment: 46 pages, 1 figur

Prognostic model to predict postoperative acute kidney injury in patients undergoing major gastrointestinal surgery based on a national prospective observational cohort study.

Background: Acute illness, existing co-morbidities and surgical stress response can all contribute to postoperative acute kidney injury (AKI) in patients undergoing major gastrointestinal surgery. The aim of this study was prospectively to develop a pragmatic prognostic model to stratify patients according to risk of developing AKI after major gastrointestinal surgery. Methods: This prospective multicentre cohort study included consecutive adults undergoing elective or emergency gastrointestinal resection, liver resection or stoma reversal in 2-week blocks over a continuous 3-month period. The primary outcome was the rate of AKI within 7 days of surgery. Bootstrap stability was used to select clinically plausible risk factors into the model. Internal model validation was carried out by bootstrap validation. Results: A total of 4544 patients were included across 173 centres in the UK and Ireland. The overall rate of AKI was 14·2 per cent (646 of 4544) and the 30-day mortality rate was 1·8 per cent (84 of 4544). Stage 1 AKI was significantly associated with 30-day mortality (unadjusted odds ratio 7·61, 95 per cent c.i. 4·49 to 12·90; P < 0·001), with increasing odds of death with each AKI stage. Six variables were selected for inclusion in the prognostic model: age, sex, ASA grade, preoperative estimated glomerular filtration rate, planned open surgery and preoperative use of either an angiotensin-converting enzyme inhibitor or an angiotensin receptor blocker. Internal validation demonstrated good model discrimination (c-statistic 0·65). Discussion: Following major gastrointestinal surgery, AKI occurred in one in seven patients. This preoperative prognostic model identified patients at high risk of postoperative AKI. Validation in an independent data set is required to ensure generalizability

Feasibility of preoperative chemotherapy for locally advanced, operable colon cancer: The pilot phase of a randomised controlled trial

Summary: Background Preoperative (neoadjuvant) chemotherapy and radiotherapy are more eff ective than similar postoperative treatment for oesophageal, gastric, and rectal cancers, perhaps because of more eff ective micrometastasis eradication and reduced risk of incomplete excision and tumour cell shedding during surgery. The FOxTROT trial aims to investigate the feasibility, safety, and effi cacy of preoperative chemotherapy for colon cancer. Methods In the pilot stage of this randomised controlled trial, 150 patients with radiologically staged locally advanced (T3 with ≥5 mm invasion beyond the muscularis propria or T4) tumours from 35 UK centres were randomly assigned (2:1) to preoperative (three cycles of OxMdG [oxaliplatin 85 mg/m², l-folinic acid 175 mg, fl uorouracil 400 mg/m² bolus, then 2400 mg/m² by 46 h infusion] repeated at 2-weekly intervals followed by surgery and a further nine cycles of OxMdG) or standard postoperative chemotherapy (12 cycles of OxMdG). Patients with KRAS wild-type tumours were randomly assigned (1:1) to receive panitumumab (6 mg/kg; every 2 weeks with the fi rst 6 weeks of chemotherapy) or not. Treatment allocation was through a central randomisation service using a minimised randomisation procedure including age, radiological T and N stage, site of tumour, and presence of defunctioning colostomy as stratifi cation variables. Primary outcome measures of the pilot phase were feasibility, safety, and tolerance of preoperative therapy, and accuracy of radiological staging. Analysis was by intention to treat. This trial is registered, number ISRCTN 87163246. Findings 96% (95 of 99) of patients started and 89% (85 of 95) completed preoperative chemotherapy with grade 3–4 gastrointestinal toxicity in 7% (seven of 94) of patients. All 99 tumours in the preoperative group were resected, with no signifi cant diff erences in postoperative morbidity between the preoperative and control groups: 14% (14 of 99) versus 12% (six of 51) had complications prolonging hospital stay (p=0·81). 98% (50 of 51) of postoperative chemotherapy patients had T3 or more advanced tumours confi rmed at post-resection pathology compared with 91% (90 of 99) of patients following preoperative chemotherapy (p=0·10). Preoperative therapy resulted in signifi cant downstaging of TNM5 compared with the postoperative group (p=0·04), including two pathological complete responses, apical node involvement (1% [one of 98] vs 20% [ten of 50], p<0·0001), resection margin involvement (4% [ four of 99] vs 20% [ten of 50], p=0·002), and blinded centrally scored tumour regression grading: 31% (29 of 94) vs 2% (one of 46) moderate or greater regression (p=0·0001). Interpretation Preoperative chemotherapy for radiologically staged, locally advanced operable primary colon cancer is feasible with acceptable toxicity and perioperative morbidity. Proceeding to the phase 3 trial, to establish whether the encouraging pathological responses seen with preoperative therapy translates into improved long-term oncological outcome, is appropriate

Peridynamics model for flexoelectricity and damage

A flexoelectric peridynamic (PD) theory is proposed. In the PD framework, the formulation introduces a nanoscale flexoelectric coupling that entails non-uniform strain in centrosymmetric dielectrics. This potentially enables PD modeling of a large class of phenomena in solid dielectrics involving cracks, discontinuities etc. wherein large strain gradients are present and the classical electromechanical theory based on partial differential equations do not directly apply. PD electromechanical equations, derived from Hamilton's principle, satisfy the global balance laws. Linear PD constitutive equations reflect the electromechanical coupling effect, with the mechanical force state affected by the polarization state and the electrical force state in turn by the displacement state. An analytical solution to the PD electromechanical equations is presented for the static case when a point mechanical force and a point electric force act in an infinite 3D solid dielectric. A parametric study on how different length scales influence the response is undertaken. In addition, the model is extended to incorporate damage using phase field - an order parameter, supplemented with a PD bond breaking criterion to study flexoelectric effects in damage and fracture problems. To demonstrate the performance of our proposal, we first simulate, considering small flexoelectricity effect and no damage, an externally pressured 2D flexoelectric disk subjected to a potential difference between the inner and outer surfaces and compare the results with existing solutions in the literature. Next, we simulate a plate with a central pre-crack under tension considering damage and flexoelectricity effects, and study the effect of various constitutive parameters on the damage evolution. We also furnish a classical derivation of phase field based flexoelectricity in Appendix 1. (C) 2018 Elsevier Inc. All rights reserved

A modified peridynamics correspondence principle: Removal of zero-energy deformation and other implications

We look for an enhancement of the correspondence model of peridynamics, emphasizing the elimination of zero-energy deformation modes. We propose an approach based on the notion of sub-horizons. The most useful feature of this proposal is the setup which, whilst providing solutions with the necessary stability, deviates only marginally from the original correspondence formulation. A thorough analysis of the sub-horizon based method is furnished based on the well-posedness of integral equations and energy spectrum, which clearly demonstrate a removal of zero energy modes. We also show how other forms of unphysical deformation modes, e.g. material collapse within horizon, jump discontinuities and vanishing energy modes, can be prevented with the present proposal. Finally, a set of numerical simulations are undertaken that attest to the remarkable efficacy of the sub-horizon based approach. (C) 2018 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

Phase field based peridynamics damage model for delamination of composite structures

We extend and exploit a phase field based peridynamics (PD) damage model ( 39]) for studying delamination of composite structures. Utilizing a phase field augmented PD framework, our idea is to model the interfacial cohesive damage through degradation functions and the fracture or fragmentation through the critical energy release rate. Our model eliminates the conventional traction-separation law (TSL) that is known to result in the popular cohesive zone model (CZM). In the process, the approach potentially addresses some limitations of the existing techniques, for example, CZM, virtual crack closure technique (VCCT) and so on, which make use of an empirical interaction among different modes of loading (e.g., mode I, mode II etc.). By regarding delamination under different loading conditions as problems that differ only in their boundary conditions, our approach provides for a more general scheme for tracking delamination growth. Our proposal thus accords no special treatment to the different modes and can handle general spatial locations of weaker interface layers. With no special crack tracking algorithms or additional ad-hoc criteria for crack propagation, considerable computational simplicity also accrues. The approach admits an easy extension to cases where cracks can propagate even in the bulk material body. The new bond breaking criterion that we employ replaces the ad-hoc approach inherent in bond-stretch-based or bond-energy-based conditions. Unlike standard phase field models, physical fragmentation of the body is feasible in the present model. The proposed methodology also eliminates the problem of matter interpenetration by its very construction. Apart from an initial validation exercise for a laminated composite plate with a hole where no or little damage occurs, we also use numerical simulations on mode I, mode II, and mixed mode delamination cases in order to assess the performance of our model by benchmarking it against available experimental evidence. Simulations on modified mixed mode bending and multiple layer delamination are also presented. (C) 2017 Elsevier Ltd. All rights reserved