Pure Shear Tests Research Articles

In Situ Pure Shear Tests on Textured Magnesium AZ31B Sheets

Pure shear tests of textured magnesium AZ31B sheet samples were carried out using a 5 kN Kammrath & Weiss in situ tension-compression stage in a scanning electron microscope in combination with real-time electron backscatter diffraction lattice orientation mapping. The sample design was optimized to produce a pure shear stress in the central gauge zone. Distributions of the deformation twins were correlated with finite element simulations using a linear-elastic constitutive law considering large deformations to show that twins form in areas where the principal compressive stress σ3* is a maximum and that they form normal to the trajectories of that minor principal stress. Mappings of the same area at different load values revealed the formation and growth of individual twins and their relationship to the internal elastic strain of individual grains as indicated by the internal grain disorientation. All twins observed were of the extension type, with an 86.3° disorientation with respect to the parent grains. A more detailed study was conducted using transmission electron microscopy to correlate with the EBSD observations and to further elucidate the twin structures within samples.

Discussion: A Comment on “The Trousers Fracture Test for Viscoelastic Elastomers” (Shrimali, B., and Lopez-Pamies, O., 2023, ASME J. Appl. Mech., 90(7), p. 071010)

Abstract The Rivlin–Thomas classical energy balance model for tearing tests suggests that the fracture energy Γ is proportional to the work of the external load in the legs (potential energy), for not too large stretches in the legs, so the increase of Γ with loading rate is observed or measured, but not really explained by the model. Shrimali and Lopez-Pamies (SLP) have recently built a theory on viscoelastic fracture from recent experimental evidence of a critical (stretch rate-independent) stretch on nucleation of cracks in the pure shear tests. The theory in other words incorporates this evidence in an otherwise energy-based criterion. In the paper “The trousers fracture test for viscoelastic elastomers” (ASME J. Appl. Mech., 2023, 90(7), p. 071010), they seem to obtain the critical (stretch rate-independent) stretch condition for the case of trouser tests (applying their theory from a long enough crack) both in nucleation and steady-state propagation. This outcome seems reasonable since for a linear material, looking at the elastic limit cases of very slow and very fast rates, it would produce an increase of the load, and hence of the fracture energy, proportional to the increase of the modulus, which is in line with what has been found experimentally, although possibly in contrast with classical rate-independent cohesive models, at least for crack nucleation.

Experimental and numerical study on weld strengths of built-up steel box columns

This study investigates the demands generated in the panel zone of welded steel built-up box columns with fillet and complete joint penetration (CJP) groove welds, which are mainly used as columns in steel moment-resisting frames. The motivation for this study stems from the a 360–16 specification for structural steel building, which requires the joining of flange and web plates of box columns with CJP groove welds within a zone extending 12 in. above the upper beam flange and 12 in. below the lower beam flange in special and intermediate steel moment frames. Laboratory experiments have been conducted to examine the strength of these welds under pure shear forces. For this purpose, two laboratory specimens, one with fillet welds and the other with CJP groove welds, have been designed, and the strength of these welds were equal to each other in pure shear force conditions. The fillet weld specimen has resisted up to 1670 kN in the pure shear test, and the CJP groove weld has resisted up to 1520 kN. The entire loading process of each specimen was characterized by employing the digital image correlation (DIC) technique, which enabled the extraction of strain values throughout. Numerical modeling is validated in Abaqus software using experimental results, with comprehensive analyses on force-displacement diagrams and rupture. The outcomes of the tests conducted have shown that the demands generated in the panel zone of the built-up steel box welded sections are satisfactorily tolerated by both fillet and CJP groove welds. Research significanceThe significance of this study can be elaborated in multiple aspects. Firstly, it introduces an innovative test setup meticulously designed to replicate the behavior of welded built-up box columns with corner joints to steel plates. This advanced experimental arrangement not only facilitates the current study, but also serves as a versatile tool for conducting forthcoming experiments, allowing for meaningful comparisons and further exploration of diverse phenomena within the field. Secondly, the deliberate imposition of uniform demands on both types of welds during the study enables a comprehensive examination of their behavioral characteristics. This comprehensive analysis contributes to a more profound comprehension of welds performance under identical conditions, thereby enhancing our knowledge within the field. Finally, the research outcome, which reveals that fillet welds exhibit almost identical load-bearing capacity in comparison to CJP groove welds, bears substantial practical significance for the construction industry. This finding has the potential to instigate more cost-effective and efficient welding practices, which are paramount for maintaining the structural integrity of steel structures.In summary, this study makes a noteworthy contribution to the scientific community by presenting an innovative test setup, deepening the knowledge of weld performance, and suggesting practical enhancements in welding methodologies. These collective contributions serve to elevate the field of structural engineering, promoting advancements in construction practices.

Shear rate effect on clay-structure interface strength properties in various interface boundary conditions

Based on the modified simple direct shear device which can directly measure the interface pore pressure and interface shear displacement, a series of interface shear tests and corresponding pure clay shear tests were conducted at an undrained state in constant normal load (CNL) boundary conditions or equivalent undrained state in constant volume (CV) boundary conditions. The clay-structure interfaces, consisting of seabed clay and Speswhite kaolin clay with overconsolidation ratios (OCR) of 1 and 3, were tested at three shear rates, respectively V1 = 0.0002 mm/s, V2 = 0.001 mm/s, and V3 = 0.01 mm/s. The results demonstrated that the shear strength of the clay-structure interface is lower than that of pure clay, and this difference is more pronounced under CV boundary conditions. In CNL condition, though the pure clay strength decreases with increasing shear rate at OCR = 1 and increases with increasing shear rate at OCR = 3, the shear rate effect on clay-structure interface strength is not obvious. In CV condition, the strength of the interface with the normally consolidated (NC) and over consolidated (OC) clay increases approximately linearly with the shear rate on the semi-logarithmic scale. the shear rate parameter ρ is used to describe the growth rate of pure clay or clay-structure interface shear strength with a tenfold increase in shear rate. As for normally consolidated clay, in CV condition, the corresponding shear rate parameter satisfies that ρ (with R1 roughness)> ρ (pure clay)> ρ (with R2 roughness). The rate parameter corresponding to NC seabed clay is significantly higher than the rate parameter corresponding to NC Speswhite kaolin clay. For OC clay, the shear rate parameter for interface strength is higher than that for pure clay, meeting with the relationship that ρ (with R1 roughness)> ρ (with R2 roughness)> ρ (pure clay).

Machine learning-based multiscale framework for mechanical behavior of nano-crystalline structures

In this paper, a computational atomistic-continuum multiscale framework is developed based on the machine learning (ML) architecture to capture the nonlinear behavior of nano-crystalline structures. The dataset of the ML process is derived from analyzing the atomistic representative volume element (RVE) through the molecular dynamics method under various deformation paths. A comprehensive investigation is performed on the influential parameters of the atomistic RVE that leads to the determination of an appropriate atomistic RVE for reproducing the mechanical characteristics from fine-scale to coarse-scale level. The multilayer perceptron neural network approach (MLP–ANN) is employed in the optimization algorithm of the ML process to train the atomistic dataset. The performance of the ML model is validated by predicting the response of atomistic RVE under various deformation gradients. Finally, the proposed computational algorithm is employed for the simulation of several mechanical benchmark problems, including the uniaxial tensile test, pure shear test, pure torsion test, and nano-indentation problem. Numerical simulations are validated by comparing the results of machine learning-based multiscale analysis with the fully atomistic model and experimental data. It is shown that the proposed ML-based method enhances the multiscale analysis to capture the nonlinear behavior of nano-crystalline structures without computational complexities associated with conventional multiscale methods. The results highlight that the proposed multiscale framework can be utilized as a constitutive model for the large-scale analysis with a great accuracy and unique efficiency.

Shear performance investigation of recycled concrete load-bearing blocks for sustainable masonry

PurposeRecycled concrete is an economical and environmentally friendly green material. The shear performance of recycled concrete load-bearing masonry is studied, which is great of significance for its promotion and application and also has great significance for the sustainable development of energy materials.Design/methodology/approachIn total, 30 new load-bearing block masonry samples of self-insulating recycled concrete are subjected to pure shear tests, and 42 samples are tested subjected to shear-compression composite shear tests. According to the axial design compression ratio, the test is separated into seven working conditions (0.1–0.8).FindingsAccording to the test results, the recommended formula for the average shear strength along the joint section of recycled concrete block masonry is given, which can be used as a reference for engineering design. The measured shear-compression correlation curves of recycled concrete block masonry are drawn, and the proposed limits of three shear-compression failure characteristics are given. The recommended formula for the average shear strength of masonry under the theory of shear-friction with variable friction coefficient is given, providing a valuable reference for the formulation of relevant specifications and practical engineering design.Originality/valueSimulated elastoplastic analysis and finite element modeling on the specimens are performed to verify the test results.

Fracture Toughness of Hydrogel Laminates: Experiments, Theory, and Modeling

Abstract Possessing enhanced mechanical durability and multiple novel functions, hydrogel laminates have found wide applications in diverse areas, including stretchable and bio-integrated electronics, soft robotics, tissue engineering, and biomedical devices. In the aforementioned scenarios, hydrogels are often required to sustain large deformation without mechanical failure over a long time. Compared to the fast movement in functions design, the failure mechanism of hydrogel laminates has been much less explored and researched, as well as laminates’ fracture toughness—a key parameter characterizing their fracture behavior. To address this largely unexplored issue, this article further studies the fracture toughness of hydrogel laminates both experimentally and theoretically. A kind of modified pure-shear test suitable for measuring the fracture toughness of hydrogel laminates is proposed, which is then applied to testing a PAAm-PAA laminate’s toughness. Through theoretical analysis and numerical modeling, the experimentally observed enhancement in the fracture toughness of PAAm-PAA laminates is explained—the fracture toughness of the laminates covers the energy required for both the crack and concomitant interfacial delamination to propagate, and the theoretical predictions agree well with the experimental results. The results from this study provide quantitative guidance for understanding the fracture behavior of hydrogel laminates.

Swelling Effect on the Yielding, Elasticity, and Fracture of Double-Network Hydrogels with an Inhomogeneous First Network

Typical double-network (DN) gels are formed by free radical polymerization, and the constituent network strands have a wide molecular weight distribution. It is important to clarify what determines the specific mechanical behaviors of DN gels with a strongly inhomogeneous first network, including the criteria for the occurrence of yielding and strain hardening during tensile deformation, as well as their impact on the fracture toughness. In this work, we first studied the influence of swelling ratio λs of the first network synthesized from radical polymerization on the yielding and strain hardening of DN and triple-network (TN) gels by tensile tests. We observed scaling relations for the yielding stretch ratio λy ∝ λs–1 and engineering yielding stress σy ∝ λs–2, like those found for DN hydrogels with a homogeneous first-network structure. Furthermore, we found a universal relationship λyσy ∝ λs–3 that is independent of the cross-linking structure of the first network. We found that these scaling relations agree well with the theoretical predictions derived from a simple one-dimensional affine model for the fracture of a homogeneous network, suggesting the affine swelling effect on the fracture of network strands. Next, we showed that swelling induces more tension in the inhomogeneous network than in the homogeneous network, suggesting non-affine swelling behavior at the network strand scale for the inhomogeneous network. We discussed the molecular origin of the discrepancy between the affine swelling effect on the fracture of network strands and the non-affine swelling behavior for strand tension. Finally, we investigated the influence of swelling ratio λs on the local yielding behavior ahead of the crack tip and the fracture toughness of the DN and TN hydrogels using pure shear tests. We found that crack-tip yielding zone size hy ∝ λs1 and fracture energy Γ ∝ λs–2. Furthermore, we found that the relationship Γhy∝λs−3 is also independent of cross-linking structure and obeys a universal relationship with the true yielding stress λyσy ∝ λs–3 determined from the tensile tests, which is in excellent agreement with nonlinear elastic fracture mechanics theory. This work provides important insight into the specific mechanical behaviors of the DN gels with an inhomogeneous first network.

Hyperelastic material modelling using symbolic regression

AbstractRecently, data‐driven approaches in the field of material modeling have gained significant attention. A major advantage of these approaches is the direct integration of experimental results into the models. Nevertheless, artificial neural networks (ANNs) are especially challenging to interpret from a physical point of view, since internal processes of ANNs are difficult to understand.In this work a new automatic method for the generation of constitutive models for hyperelastic materials is introduced. The presented method is based on symbolic regression, which is a genetic algorithm. Thereby, a mathematical model in the form of an algebraic expression is found that fits the given data as accurately as possible and has a compact representation. The strain energy density function is determined directly as a function of the strain invariants. The proposed ansatz is embedded into a continuum mechanical framework combining the benefits of known physical relations with the unbiased optimization approach of symbolic regression. Benchmark tests for the generalized Mooney‐Rivlin model for uniaxial, equibiaxial and pure shear tests are presented. Finally, the presented procedure is tested on a temperature‐dependent dataset of a thermoplastic polyester elastomer. A good agreement between obtained material models and experimental data is demonstrated.

Structural Properties of Commercial Australian Plantation Hardwood CLT

Significant volumes of plantation hardwood are available in Australia to produce value-added engineered wood products such as cross-laminated timber (CLT). To validate the possibility of utilising this available resource, the bending structural properties of plantation Eucalyptus nitens solid board and finger-jointed feedstock were measured. The studied CLT panels produced from finger-jointed lamellas were subjected to bending strength, bending stiffness, rolling shear strength in bending, and pure rolling shear tests to obtain characteristic design values. Solid and finger-jointed timber test results suggested that boards used in longitudinal lamellas have a bending strength of 36.0 MPa and a modulus of elasticity (MOE) of 13,000 MPa. Finger-jointed timber in crossed lamellas presented a declared bending strength of 25.0 MPa. CLT panels showed a bending strength of 24.0 MPa and a rolling shear strength of 2.0 MPa. The experimental results for the CLT panels evidenced that the CLT bending stiffness matches up very well with the modelled results when an MOE of 13,000 MPa is used to describe the stiffness of longitudinal boards. The results presented in this study establish a basis for the commercial use of Australian plantation hardwood CLT in structural applications such as floors and roofs in commercial and residential buildings.

Circumferential pure shear test of thin-walled aluminum alloy tubes

In order to obtain the pure shear deformation characteristics along the circumferential direction of tubes, a circumferential shear test for thin-walled tubes is proposed in this paper. The experimental device consists of a tubular sample and two cylindrical mandrels with shear plates. The torque along the circumferential direction was applied to the tubular sample by the two shear plates to make the pre-set shearing zone of the sample under a circumferential pure shear stress state. The two cylindrical mandrels support the inner wall of the tube to avoid buckling so that the pure shear stress state can be maintained during the whole deformation process. A 5052 aluminum alloy tube with an outer diameter of 50 mm and a wall thickness of 1.2 mm was used in the test. It is shown through simulation and experiment that shear deformation is concentrated in the pre-set shearing zone. This test can be used to obtain the circumferential pure shear stress-strain relationship.

A Gradient-Enhanced Plasticity Based Phase-Field Model for Ductile Fracture Simulations

Ductile fracture is modeled by using a novel phase-field method of geometric type to avoid the use of the complicated discretization approaches for crack discontinuities. The plasticity model is defined by an over-nonlocal implicit gradient-enhanced framework, which is equivalent to the integral-type plasticity models and therefore strongly nonlocal. A modified phenomenological barrier function is used as the crack phase-field driving force by mainly considering the effects of the nonlocal plastic deformation under shear-dominated stress states. The ductile damage is assumed to solely affect the plastic energy stored capacity from the micro-mechanical perspective such that the proposed approach can be easily extended to more general loading conditions. The implementation of the proposed phase-field method is shown to be easily integrated into the commercial codes (e.g., ABAQUS) through the coupling use of several user interfaces. We present simulations of the shear band formation under axial compression and the ductile crack propagations in a single-edged notched plate, a slanted fracture specimen and a pure shear test specimen to elucidate the viability of the current nonlocal method. The numerical results adequately demonstrate that mesh dependency can be apparently alleviated if material softening occurs.

Anisotropic damage model for collagenous tissues and its application to model fracture and needle insertion mechanics.

The analysis of tissue mechanics in biomedical applications demands nonlinear constitutive models able to capture the energy dissipation mechanisms, such as damage, that occur during tissue deformation. Furthermore, implementation of sophisticated material models in finite element models is essential to improve medical devices and diagnostic tools. Building on previous work toward microstructure-driven models of collagenous tissue, here we show a constitutive model based on fiber orientation and waviness distributions for skin that captures not only the anisotropic strain-stiffening response of this and other collagen-based tissues, but, additionally, accounts for tissue damage directly as a function of changes in the microstructure, in particular changes in the fiber waviness distribution. The implementation of this nonlinear constitutive model as a user subroutine in the popular finite element package Abaqus enables large-scale finite element simulations for biomedical applications. We showcase the performance of the model in fracture simulations during pure shear tests, as well as simulations of needle insertion into skin relevant to auto-injector design.

Experimental Investigation of the Mechanical Properties of the Sand-Concrete Pile Interface Considering Roughness and Relative Density.

The aim of this study was to investigate the effect of roughness and relative density on the mechanical properties of sand–concrete pile interface. A series of direct shear tests were carried out on the interface using a large-scale direct shear apparatus with various relative densities of sand (73%, 47%, and 23%) and concrete blocks with four roughness values (I = 0, 10, 20, and 30 mm). Various mechanical properties (such as shear stress, volume change, peak shear strength, secant friction angle, and normalized friction coefficient) from the interface tests were compared with trends obtained from the pure sand direct shear test. For the smooth interface, the shear stress–horizontal displacement curves of the dense sand specimen exhibited a slight softening response, which became more apparent as the roughness increased. The curves of the loose sand specimen demonstrated a hardening response. The volumetric response was influenced by the combination of normal stress, relative density, and roughness. The peak shear strength demonstrated a nonlinear increasing trend as the normal stress increased. With an increase in the normal stress, the secant friction angle and peak friction coefficient decreased as exponential and power functions, respectively. Additionally, a critical roughness value Icr resulted from the tests, which halted the upward trend of the peak friction coefficient and normalized the secant friction angle when I exceeded Icr.

An experimental study of morphological formation in bilayered tubular structures driven by swelling/growth

Circumferential wrinkling in soft tubular tissues is vital in supporting normal physiological functions. Most existing literature was dedicated to theoretical modeling and finite element simulations based on a specific growth model. This paper presents an experimental investigation on pattern formation and evolution in bilayered tubular organs using swelling deformation of polydimethylsiloxane (PDMS) and aims at supplying a thorough comparison with theoretical and finite element results. To create a twin model in modeling and simulation, the shear modulus in the incompressible neo-Hookean material is estimated via uni-axial tensile and pure shear tests. Five bilayered tubes with different material or geometrical parameters are fabricated. Swelling experiments are carried out for these samples in an individual experimental setup where a plane-strain deformation is guaranteed, and several surface patterns and the associated mode transformations are observed, namely, creases, wrinkles, period-doubling profiles, wrinkle-to-crease transition, and wrinkle-to-period-doubling transition. In particular, an interfacial wrinkling pattern is also observed. To make comparisons, a buckling analysis is conducted within the framework of finite elasticity by means of the Stroh formulation and a refined surface impedance matrix method. In addition, a finite element analysis (FEA) is performed to trace the evolution of surface instabilities. It turns out that the experimental findings agree well with the theoretical predictions as well as the finite element results. From our experiments, it is found that creasing mode may appear instead of wrinkling mode when both layers share a similar mechanical property. It is expected that the current work could provide novel experimental insight into pattern formation in tubular structures. In particular, the traditional impedance matrix method has been adapted, which enables us to resolve eigenvalue problems with displacement boundary conditions, and the good agreement among experimental, theoretical, and simulation consequences supplies strong evidence that a phenomenological growth model is satisfactory to reveal mechanisms behind intricate surface morphology in tubular tissues.

Development of a large-scale torsional split Hopkinson tube for dynamic shear test of mortar material

Due to the lack of reliable dynamic shear test technology, there are few studies on dynamic pure shear performance of concrete materials. Based on the one-dimensional stress wave propagation theory, a large-scale torsional split Hopkinson Tube (LTSHT) with an outer diameter of 110 mm was developed. The LTSHT comprises a bearing system, an axial driving system, a four-lug symmetrical impact loading system, an incident tube, and a transmission tube. Numerical simulations showed that the LTSHT produced a well-defined torsional wave, and the bending wave was very small when the lug-error was not more than 0.05 mm. Furthermore, a data measurement and processing of the LTSHT were proposed. Dynamic pure shear tests with shear strain rate ∼14 s−1 on three thin-walled mortar specimens were conducted. The failure process was recorded. The dynamic shear strength was ∼8 MPa and shear stress–strain curves of the three thin-walled mortar specimens showed great repeatability.

Reverse physically motivated frameworks for investigation of strain energy function in rubber-like elasticity

This paper introduces three innovative frameworks to obtain the strain energy function for rubber-like materials through an inverse approach. To this end, we inspire from the statistical background of physically motivated models to represent the strain energy function in terms of variables that correspond to the kinetics of a polymeric chain. We employ the micro-sphere concept to cast different structure-based models with unknown core functions or kernels and reveal them directly from experimental data. Accordingly, we use the basis spline (B-Spline) curve to represent these core functions and derive the macroscopic stress tensor based on the unknown control points associated with the B-Spline curves. Following this, we define a loss function to tie experimental data to these unknown control points, followed by a least-square error minimization technique that ultimately leads to a linear system of equations. In this way, we circumvent the nonlinear optimization in current structure-based models used for material parameter fitting that comes with the solution’s uncertainty. We also minimize simplifying hypotheses and bypass the unnecessary assumptions that have been influenced the accuracy of physical-based methods. Furthermore, one can integrate these functions with a high accuracy scheme over the micro-sphere, resulting in an integration-free model with competitive computational complexity to closed-form models. Finally, we validate the robustness of each framework in a challenging benchmark for three different polymeric materials. Considering the same dataset for the calibration of all models( which is uniaxial, pure shear, and equi-biaxial tests), the proposed frameworks outperform other well-known physical-based models in the literature in this challenging benchmark to the best of our knowledge ( we also show that the same performance is attainable by using only uniaxial and equi-biaxial tests ). Moreover, in the case of a limited dataset, we show that it is possible to apply prior knowledge regarding a material into one of the frameworks (RFN) to enhance the accuracy of predictions.

Efficient and Robust Method for Identifying Material Constant of Hyperelastic Material Model via Complex-step Derivative Approximation

An efficient and robust method for deriving the stress-strain relationship of hyperelastic material model (HM-model) was proposed via complex-step derivative approximation. This method has a capability to calculate the stress-strain relationship with the same accuracy as the analytical solution by coding only the strain energy density function, being applied for the implementation of an identification program of material constants for HM-model using a Microsoft/Excel. The performance evaluation of HM-models (Yeoh and Ogden models) using this method revealed that all models could reproduce the results of the three types of material tests (uniaxial tensile (UT), pure shear (PS) and equibiaxial tensile (BT) tests) of carbon-black-filled SBR. Moreover, only the hyperelastic model composed of the first invariant of the right Cauchy-Green tensor could predict the PS and BT test results from the UT data. As a future prospect, we would like to proceed with studies on other rubber materials and HM models.

Prediction of strength and fatigue life for 2D plain-woven high-alumina fiber reinforced alumina matrix composites under a complex in-plane stress state

This paper presents a strength criterion and fatigue life prediction method for 2D braided alumina matrix composites under a complex in-plane stress state. The static strength of the material was obtained by in-plane tensile, compression, and pure shear tests. Considering the difference between tensile and compressive properties of materials and the influence mechanism of in-plane tensile and shear coupling on material strength, a revised Hoffman strength theory was proposed. The predicted off-axis tensile strength is consistent with the test results, and the deviation is not more than 10%. Tensile fatigue tests were carried out with the off-axis angle θ=0°, 15°, 30°, 45°, the stress ratio R=0.1, and frequency f=10 Hz. The test results show that the fatigue life decreases with the increase of off-axis angle. Due to the in-plane shear stress component, the fatigue failure is gradually changed from fiber-dominated to fiber-matrix dominated mode. Based on a combination of the uniaxial tensile fatigue life curve, the Broutman-Sahu residual strength model, which is used to characterize the variation of the residual strength with the fatigue cycles, and the modified Hoffman strength theory, the paper proposes a fatigue life prediction model under complex in-plane loading conditions. The fatigue shear damage factor is defined to characterize the effect of the normal and shear stress interaction on fatigue life. The fatigue life prediction model is used to predict the fatigue life of specimens in the off-axis tensile fatigue tests. The predicted result agrees with the test result, and the deviation is within the 1-time life span. The results indicate that the proposed fatigue life prediction model can be used to predict the fatigue life of 2D braided alumina matrix composites under the complex in-plane stress condition with the given stress ratio, temperature, and fatigue load frequency.

A Thermodynamically Consistent Model of Quasibrittle Elastic Damaged Materials Based on a Novel Helmholtz Potential and Dissipation Function.

In the paper, a thermodynamically consistent model of elastic damaged material in the framework of small strain theory is formulated, describing the process of deterioration in quasibrittle materials, concrete in particular. The main goal is to appropriately depict the distinction between material responses in tension and compression. A novel Helmholtz energy and a dissipation potential including three damage parameters are introduced. The Helmholtz function has a continuous first derivative with respect to strain tensor. Based on the assumed functions, the strain–stress relationship, the damage condition, the evolution laws, and the tangent stiffness tensor are derived. The model’s predictions for uniaxial tension, uniaxial compression, uniaxial cyclic compression–tension, and pure shear tests are calculated using Wolfram Mathematica in order to identify the main features of the model and to grasp the physical meaning of an isotropic damage parameter, a tensile damage parameter, and a compressive damage parameter. Their values can be directly bound to changes of secant stiffness and generalized Poisson’s ratio. An interpretation of damage parameters in association with three mechanisms of damage is given. The considered dissipation potential allows a flexible choice of a damage condition. The influence of material parameters included in dissipation function on damage mode interaction is discussed.