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# New Book: Computational Mesomechanics of Composites, by Leon Mishnaevsky Jr.

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Computational Mesomechanics of Composites, by Leon Mishnaevsky Jr. (Risoe National Laboratory, Technical University of Denmark)

ISBN: 978-0-470-02764-6, Hardcover, 280 pages, Wiley-Interscience, July 2007

Mechanical properties of composite materials can be improved by tailoring their microstructures. Mesomechanics of materials considers the effect of microstructures on the materials properties, seeking to bridge the gap between micro- and macroscale models of materials. Mesomechanics represents an approach to assessing existing and improving new materials, based on the analysis of interrelations between macroscale properties of materials, microscale physical mechanisms of deformation and damage, and the interaction effects between many microstructural elements.

The book presents the concept and methods for the computational analysis of interrelationships between mechanical properties (e.g., strength, damage resistance, and stiffness) and microstructures of composite materials. The methods of mesomechanics of composites are reviewed, and applied to the modelling of the mechanical behaviour of different groups of composites. Individual chapters are devoted to the computational analysis of the microstructure- mechanical properties relationships of particle reinforced composites, functionally graded and particle clusters reinforced composites, interpenetrating phase and unidirectional fiber reinforced composites, and machining tools materials.

**Contents:**

Preface.

**1 Composites.**

1.1. Classification and types of composites.

1.2. Deformation, damage and fracture of composites: micromechanisms and roles of phases.

**2. Mesoscale level in the mechanics of materials.**

2.1. On the definitions of scale levels: Micro- and mesomechanics.

2.2. Size effects.

2.3. Biocomposites.

2.4. On some concepts of the improvement of material properties.

2.5. Physical mesomechanics of materials.

2.6 Topological and statistical description of microstructures of composites.

**3. Damage and failure of materials: Concepts and methods of modeling.**

3.1. Fracture mechanics: Basic concepts.

3.2. Statistical theories of strength.

3.3. Damage mechanics.

3.4 Numerical modeling of damage and fracture.

**4. Microstructure-strength relationships of composites: Concepts and methods of analysis.**

4.1. Interaction between elements of microstructures: physical and mechanical models.

4.2. Multi-scale modeling of materials and homogenization.

4.3. Analytical estimations and bounds of overall elastic properties of composites.

4.4. Computational models of microstructures and strength of composites.

**5. Computational experiments in the mechanics of materials: concepts and tools. **

5.1. Concept of computational experiments in the mechanics of materials.

5.2. Input data for the simulations: Determination of material properties.

5.3. Program codes for the automatic generation of 3D microstructural models of materials.

**6. Numerical mesomechanical experiments: Analysis of the effect of microstructure of materials on the deformation and damage resistance by virtual testing.**

6.1 Finite element models of composite microstructures.

6.2 Material properties used in the simulations.

6.3 Damage modeling in composites with the User Defined Fields.

6.4 Stability and reproducibility of the simulations.

6.5 Effect of the amount and the volume content of particles on the deformation and damage in the composite.

6.6 Effect of particle clustering and the gradient distribution of particles.

6.7 Effect of the variations of particle sizes on the damage evolution.

6.8 Ranking of microstructures and the effect of gradient orientation.

**7. Graded particle-reinforced composites: Effect of the parameters of graded microstructures on the deformation and damage.**

7.1 Damage evolution in graded composites and the effect of the degree of gradient.

7.2 Bilayer model of a graded composite.

7.3 Effect of the shape and orientation of whiskers and elongated particles on the strength and damage evolution: non-graded composites.

7.4 Effect of the shape and orientation of elongated particles on the strength and damage evolution: the case of graded composite materials.

7.5 Effect of statistical variations of local strengths of reinforcing particles and the distribution of the particle sizes.

7.6 Combined Reuss/Voigt model and its application to the estimation of stiffness of graded materials.

**8. Particle clustering in composites: Effect of clustering on the mechanical behavior and damage evolution.**

8.1. Finite element modeling of the effect of clustering of particles on the damage evolution.

8.2. Analytical modeling of the effect of particle clustering on the damage resistance.

**9. Interpenetrating phase composites: Numerical simulations of deformation and damage**.

9.1. Geometry-based and voxel array based 3D FE model generation: comparison.

9.2. Gradient interpenetrating phase composites.

9.3. Isotropic interpenetrating phase composites.

**10. Fiber reinforced composites: Numerical analysis of damage initiation and growth.**

10.1 Modeling of strength and damage of fiber reinforced composites: a brief overview.

10.2 Mesomechanical simulations of damage initiation and evolution in fiber reinforced composites.

**11. Contact damage and wear of composite tool materials: Micro-macro relationships. **

11.1 Micromechanical modeling of the contact wear of composites: a brief overview.

11.2 Mesomechanical simulations of wear of grinding wheels.

11.3 Micro-macro dynamical transitions for the contact wear of composites: black box modeling approach.

11.4 Microscale scattering of the tool material properties and the macroscopic efficiency of the tool.

**12. Future fields: Computational mesomechanics and nanomaterials.**

Conclusions.

References.

http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0470027649.html

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## Comments

## A good book

I have introduced this book to our library

It's really a goog book for material simulation

## Toughnening mechanisms of nano-composotes ceramics

Dear Leon,

I am trying to get your new book; it will be helpful to my current researches on solid propellants and high explosives, where high energy particles are embedded in the polymeric binder.

I am happy that some of my previous works were cited in several of your papers:

L. Mishnaevsky Jr and S. Schmauder (2001) Continuum mesomechanical finite element modeling in materials development: a state-of-the-art review. Applied Mechanics Reviews 54, 49-69http://www.risoe.dk/afm/personal/lemi/applmech.pdf

Tan and Yang (1998) considered nanocomposite alumina ceramics with dispersed Si nano particles analytically. It was shown that higher toughness of nano-composite ceramics is achieved by particles distributed within the matrix grains along grain boundaries. Three toughening mechanisms were identified:1. switching from the intergranular cracking to the transgranular one“ (by nano-particles distributed along the grain boundaries),

2. fracture surface roughening by zigzag crack path“ (by the fluctuated residual stresses

from the nano-particles within the grains), and

3. shielding by clinched rough surfaces near the crack tip

Computational design of multiphase materials at the mesolevel

By varying the mutual arrangement of phases in a multiphase material, the materials properties may be improved.Optimization of Materials Microstructures: Information Theory Approach

The effect of heterogeneity and microstructure of materials on their fracture resistance is analyzed with the use of the information theory approach. Among the main ways of increasing the fracture resistance of multiphase materials the following approaches may be mentioned: adding second phase particles or network, which cause accompanying, energy-consuming processes during crack growth in the first phase (matrix) (like friction, additional microcracking, etc.); varying degrees of phase networking and clustering; creating such an arrangement of inclusions that a growing crack deflects most frequently from the path which it would follow in a homogeneous material (like the pure matrix) (this is achieved by ductile inclusions, like metal fiber premixing in the ceramic-rich region , or weak interfaces , or special arrangements of brittle inclusions).## Dear Leon I'm looking

Dear Leon

I'm looking forward to your book. i studied the composite and teach the mesomechanics of materials.

I have introduced this book to my students and our library.

## Congratulations

Dear Leon,

Congratulations on your new book. I will be buying a copy of this book soon.

~Shailendra