Explore constitutive modeling from fundamental theory through cutting-edge AI applications

Constitutive Models of Solid Materials: From Mechanical Principles to Engineering Applications provides researchers and engineers with comprehensive methods to predict material responses under complex loading conditions. Written by internationally recognized experts in materials mechanics and computational methods, this systematic treatment connects rigorous theoretical foundations to practical engineering applications, demonstrating the accurate modeling of material behavior across multiple scales.

The text progresses methodically from tensor analysis and continuum mechanics through elasticity, plasticity, and damage mechanics to micromechanics and numerical implementation strategies. Coverage extends to artificial intelligence integration in constitutive research, featuring Physics-Informed Neural Networks for constitutive parameter prediction. Four detailed case studies examine sintered nano-silver, high-strength steel, solder alloys, rock modeling, and high-temperature concrete performance.

The book offers:

• Comprehensive coverage from mathematical foundations through elastoplastic theory, damage mechanics, and micromechanics to AI-enhanced modeling approaches
• Numerical implementation strategies including time-stepping schemes, Newton-Raphson iteration, and elastic predictor plastic corrector methods for simulations
• Detailed case studies on sintered nano-silver, high-strength steels, solder alloys, rocks, and concrete under extreme conditions
• Integration of machine learning including Artificial Neural Networks, XGBoost, and Physics-Informed Neural Networks with example programs
• Multiscale frameworks combining Eshelby’s theory, Hill’s method, and homogenization techniques linking microstructure to macroscopic behavior

This comprehensive resource serves materials scientists, mechanical engineers, civil engineers, aerospace professionals, and graduate students seeking to master constitutive modeling. By combining rigorous mathematical formulation with computational methods and practical case studies, it provides an essential foundation for advanced materials research and engineering practice.

Yao Yao is a Professor researching mechanical properties of materials and disaster prevention of engineering structures under extreme loads. His research is also focused on engineering material construction, fatigue, and damage under multi-physical fields.

Hu Fang, PhD, develops high-temperature damage constitutive models for solid materials. His research is also focused on material fracture and damage theory, as well as the research on the mechanical properties of composite material interfaces.

Hongcun Guo, PhD, researches the mechanical behavior of green building materials and the high-temperature mechanical properties of ultra-high performance concrete.

Tao Zeng, PhD, is a council member of the Shaanxi Society for Rock Mechanics and Engineering. His research is focused on underground engineering, including rock mechanics and the development of micromechanical models of rock materials.

Xu He, PhD, specializes in multi-scale modeling of mechanical properties, constitute behavior, and failure processes of advanced materials under extreme loads.