Built upon the two original books by Mike Crisfield and their own lecture notes, renowned scientist Rene de Borst and his team offer a thoroughly updated yet condensed edition that retains and builds upon the excellent reputation and appeal amongst students and engineers alike for which Crisfield's first edition is acclaimed. Together with numerous additions and updates, the new authors have retained the core content of the original publication, while bringing an improved focus on new developments and ideas. This edition offers the latest insights in non-linear finite element technology, including non-linear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity. The authors' integrated and consistent style and unrivalled engineering approach assures this book's unique position within the computational mechanics literature.

Non-Linear Finite Element Analysis of Solids and Structures: de Borst/Non-Linear Finite Element Analysis of Solids and Structures

An incremental approach to the solution of snapping and buckling problems

SUMMARY AN ANALYSIS is presented which relates the critical value of tensile stress (a,) for unstable cleavage fracture to the fracture toughness (K,,) for a high-nitrogen mild steel under plane strain conditions. The correlation is based on (i) the model for cleavage cracking developed by E. Smith and (ii) accurate plastic*lastic solutions for the stress distributions ahead of a sharp crack derived by J. R. Rice and co-workers. Unstable fracture is found to be consistent with the attainment of a stress intensification close to the tip such that the maximum principal stress a,, exceeds a, over a characteristic distance, determined as twice the grain size. The model is seen to predict the experimentally determined variation of K,, with temperature over the range -150 to -75°C from a knowledge of the yield stress and hardening properties. It is further shown that the onset of fibrous fracture ahead of the tip can be deduced from the position of the maximum achievable stress intensiiication. The relationship between the model for fracture ahead of a sharp crack, and that ahead of a rounded notch, is discussed in detail.

On the relationship between critical tensile stress and fracture toughness in mild steel

Introduction Metal forming process Analysis and technology in metal forming Plasticity and viscoplasticity Methods of analysis The finite element method (1) The finite element method (2) Plane-strain problems Axisymmetric isothermal forging Steady state processes of extrusion and drawing Sheet metal forming Thermo-viscoplastic analysis Compaction and forging of porous metals Three dimensional problems Preform design in metal forming Solid formulation, comparison of two formulations, and concluding remarks Index.

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Metal Forming and the Finite-Element Method

Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates

WO general methods have been developed for the elasticplastic analysis of continuous solid bodies. The method of "thermal" or "initial strains"1 is based on the idea of modifying the elastic equations of equilibrium to compensate for the fact that the plastic strains do not cause any change in stress. On the other hand, the tangent modulus method2 is based on the linearity of the incremental laws of plasticity. The load is applied in increments, and at each stage, a new set of coefficients are obtained for the equilibrium equations. Both methods have been used in conjunction with finite element theory. The matrix equations for finite element analysis using the method of initial strains were developed in Refs. 3-5, whereas the equations for the tangent modulus method were developed in Refs. 6-8. Since both methods solve the same problem, there should be a close relation between them, and perhaps a comparison could lead to a better understanding of the original problem. This note addresses itself to such a comparison. II. Elastic-Plastic Stress-Strain Relations The linear relation between the increments of stress and strain developed in Marcal and King8 is taken here as the point of departure. With the definition of the elastic components of the strain increments,

A comparative study of numerical methods of elastic - plastic analysis

Closure to “Finite Element Analysis of Nonlinear Structures”


 Based on a recently developed multi-scale fatigue-fracture-NDE reliability model for uncracked and cracked pipes (see Fong-Marcal-Rainsberger-Heckert-Filliben-Doctor-Finney, PVP2021-62169), we apply the same modeling technique to a comparative study of three approaches to fatigue-life prediction and design: Approach (1). Deterministic. Approach (2). Probabilistic using the A- and B-basis design allowables. Approach (3). Reliability Target using the concept of a co-reliability or an upper bound of failure probability as a tool for damage assessment and control. To illustrate the comparison of the three approaches to both uncracked and cracked components, we present numerical examples for generic components of three engineering materials at room temperatures, namely, (a) AISI 4340 steel for piping, (b) 2024-T4 aluminum for aircraft structures, and (c) BK-7 borosilicate crown glass for aircraft windows. In particular, for cracked components inspected by NDE personnel with varying probability of detection (POD) qualifications, we find both Approach (1) and Approach (2) inadequate as a guide for maintenance decision-making and compliance with the ASME Boiler and Pressure Vessel Section XI Division 2 Reliability and Integrity Management (RIM) Code. Significance and limitations of the methodology for Approach (3) based on the concepts of co-reliability and reliability target are presented and discussed. Some concluding remarks and future work are included at the end of this paper.

Fatigue-Life Prediction and Design for Uncracked and Cracked Components: Deterministic, A- and B-Basis Probabilistic, and Reliability Target Approaches

Pedro V. Marcal

Papers

A comparative study of numerical methods of elastic - plastic analysis

Closure to “Finite Element Analysis of Nonlinear Structures”

Fatigue-Life Prediction and Design for Uncracked and Cracked Components: Deterministic, A- and B-Basis Probabilistic, and Reliability Target Approaches

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